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PostPosted: Mon Jul 14, 2008 4:13 am 
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Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Old SSv3.2.1:
Killer rating table      
Rounded Score from SSv3.2.1
! = 0.10+ change from previous Score
pg# on this thread - PART B
(E) = Easy (H) = Hard
======================================================================
|A ## Rate Score|A ## Rate Score|A ## Rate Score|
|----------------------+----------------------+----------------------|
|A.73v1.5 H1.50 !1.60|A.74BWall 2.00 !2.25| |
|Mav.01 H1.50 1.75|A.75 1.25 1.30| |
|A.74 1.00 0.90| | |
|A.74v2 1.25 1.15| | |
|====================================================================|
page #7
Old scores SSv3.3.0:
Rounded Score from SSv3.3.0 
! = 0.10 change from previous Score
pg# on this thread - PART B
(E) = Easy (H) = Hard
======================================================================
|A ## Rate Score|A ## Rate Score|A ## Rate Score|
|----------------------+----------------------+----------------------|
|A.73v1.5 H1.50 !1.75|A.74BWall 2.00 !3.30| |
|Mav.01 H1.50 !1.90|A.75 1.25 !1.20| |
|A.74 1.00 !1.00| | |
|A.74v2 1.25 !1.05| | |
|====================================================================|
page #7
Killer rating table
SudokuSolver Target range v3.6.3
Rating.....Score
0.50 = 0.85
0.75 = 0.90-0.95
1.00 = 1.00-1.20
1.25 = 1.25-1.45
1.50 = 1.50-1.70 (E) = Easy (H) = Hard
===========================================================================================
|A ## by Rate Score|A ## by Rate Score|A ## by Rate Score|
|-----------------------------+-----------------------------+-----------------------------|
|A73v1.5 mhp H1.50 1.50|A74BrickRuud 2.00 2.75| |
|Mav.01 mhp H1.50 1.65|A.75 Ruud 1.25 1.35| |
|A.74 Ruud 1.00 1.00| | |
|A.74v2 Ruud 1.25 1.20| | |
|=========================================================================================|
page #7



Assassin 73 v1.5 by mhparker (Jan 08)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:5632:5632:3330:3330:3076:3589:3589:3335:3335:5632:3850:3850:3330:3076:3589:4623:4623:3335:2066:3850:5396:5396:3076:3095:3095:4623:3866:2066:2066:5396:4894:5919:5919:3095:3866:3866:3108:3108:4894:4894:4894:5919:5919:2091:2091:4909:4909:3119:3888:3888:3888:5427:4660:4660:4909:2359:3119:3119:3888:5427:5427:1597:4660:3647:2359:2359:4930:2883:4420:1597:1597:4935:3647:3647:4930:4930:2883:4420:4420:4935:4935:
Solution:
+-------+-------+-------+
| 5 8 3 | 2 4 6 | 7 1 9 |
| 9 2 7 | 8 5 1 | 6 4 3 |
| 1 6 4 | 9 3 7 | 2 8 5 |
+-------+-------+-------+
| 2 5 8 | 1 7 9 | 3 6 4 |
| 3 9 6 | 4 8 2 | 5 7 1 |
| 4 7 1 | 5 6 3 | 8 9 2 |
+-------+-------+-------+
| 8 3 5 | 6 1 4 | 9 2 7 |
| 6 4 2 | 7 9 5 | 1 3 8 |
| 7 1 9 | 3 2 8 | 4 5 6 |
+-------+-------+-------+
Quote:
mhparker, lead-in: this attractive cage pattern is very suitable for creation of V2s...It contains some interesting opportunities (Est. rating: 1.5)
Afmob, WT1: What a demanding killer! I haven't been able to find a short-cut for this version..Rating: Easy 1.75. Although the moves weren't that difficult (Rating 1.5) there were lots of them with no short-cuts in sight
Afmob, WT2: Rating: Hard 1.5. I rated it down since I was able to omit one chain so that I only use one short chain to crack this assassin [edit:... this wt uses no chains at all]
Andrew: It starts fairly easily, which draws one into the puzzle, then gets really difficult. At one stage I was thinking of giving up but ... State diagrams... can be helpful in providing hints..I'll go along with Afmob's rating of a hard 1.5
2022 forum Revisit to this puzzle here
Walkthrough 1 by Afmob:
What a demanding killer! I haven't been able to find a short-cut for this version so there a lot of little moves with no real breakthrough move. As you can see my walkthrough is very long, which shows what I mean with little steps.

A73 V1.5 Walkthrough (old version):

1. R89
a) Innies = 10(4) = {1234} locked for R8, 4 locked in 9(3) for N7; R7C2 <> 4
b) 4 locked in 9(3) = {234} locked for N7
c) Outies = 5(2) = {23} locked for R7
d) 14(3) = 1{58/67} -> 1 locked for R9+N7
e) 6(3) = {123} locked for N9
f) 11(2): R9C5 <> 7,8,9
g) 19(3) @ R8C4: R9C4 <> 7,9 because R8C4+R9C3 <> 2,3,4

2. C6789
a) Outies C89 = 7(2) = [43/52/61]
b) 18(3) @ N3 <> 1,2 because R2C7 = (456)
c) Innies C89 = 17(4): R23C8 <> 3 because Innies would be <= 15
d) 13(3) <> 6 because 6{25/34} blocked by Killer pairs (46,56) of 18(3) @ N3
e) Innies+Outies: 4 = R4C5 - R6C6 -> R4C5 = (56789), R6C6 = (12345)

3. C1234
a) Outies C12 = 9(2) = [54/63/72]
b) 22(3) = 9{58/67} -> 9 locked for N1
c) Innies N1 = 8(3) = 1{25/34} locked for N1
d) 21(3) = 9{48/57} because R3C3 = (45) -> R3C4+R4C3 <> 4,5,6
e) 21(3) = 9{48/57} -> 9 locked between C4+R4 -> R4C4 <> 9
f) 12(3) @ N7: R6C3+R7C4 <> 7,8,9 because R7C3 >= 5
g) Innies N1 = 8(3) must have 4 xor 5 and R3C3 = (45) -> R1C3+R3C1 <> 4,5
h) 4 locked in R456C1 for N4
i) 12(2): R5C1 <> 8
j) 8(3): R4C1 <> 3 because 4 only possible there
k) Innies+Outies: 3 = R5C5 - R6C4 -> R5C5 <> 1,2,3; R6C4 <> 7,8,9

4. C123 !
a) 15(3) = 2{58/67} because 5{37/46} blocked by Killer pairs (56,57) of 22(3) and R2C3 = (567)
-> 2 locked for C2+N1
b) 9(3) = {234} -> R8C3 = 2, R7C2 = 3, R8C2 = 4
c) R7C8 = 2
d) Hidden Single: R3C3 = 4 @ N1
e) Outies C12 = 9(2) = [72] -> R2C3 = 7
f) 15(3) = {267} -> 6 locked for C2+N1
g) 8(3) must have 2 xor 4 and it's only possible @ R4C1 -> R4C1 = (24)
h) 19(3) @ N4: R6C1 <> 7,9 because R6C2+R7C1 <> 2,3,4
i) 21(3) = {489} -> R4C4 <> 8 (step 3e)
j) 12(2): R5C1 <> 9
k) 12(3) = {138/156/345} <> 9

5. C89
a) Outies = 7(2) = [43/61]
b) 8(2): R5C9 <> 6

6. C123
a) Innies N7 = 22(3): R7C1 <> 6 because 7 only possible there
b) Innies N7 = 22(3): R7C1 <> 5 because 5{89} blocked by R4C3 = (89)
c) 19(3) @ N4: R6C1 <> 5,8 because R6C2+R7C1 <> 2,4,6
d) Innies N7 = 22(3): R9C3 <> 6 because R7C3 <> 7,9
e) Coloring 9 in N7: R1C456 <> 9
- i) R9C3 = 9 -> R3C4 @ 21(3) = 9 -> R1C456 <> 9
- ii) R7C1 = 9 -> R1C2 = 9 (HS @ N1) -> R1C456 <> 9
f) 13(3): R2C4 <> 1,3 because R1C4 <> 9

7. R123
a) Outies R12 = 17(3) <> 1,5 because R3C2 = (26)
-> 17(3) = {269/278/368}
b) Killer pair (89) locked in Outies R12 + R3C4 for R3
c) 12(3) @ R3C6 <> 8 because {13}8 blocked by R3C1 = (13)
d) 12(3) @ R3C6 <> 9 because R3C167 = {123} blocked by Killer pair (23) of Outies R12

8. C123 !
a) ! 5,6 locked in R5679C3 for C3 but R79C3 can't have both of (56) because of Innies N7 = 22(3)
-> R56C3 must have 1 of (56)
b) 19(3) @ N4 <> 5 since R6C12 would be [65] -> impossible (step 8a)
c) 19(3) <> 6 because R6C2+R7C1 <> 4
d) 6 locked in 14(3) @ C1 -> 14(3) = {167} locked for N7
e) 22(3): R1C2 <> 5 because R12C1 = {89} blocked by R7C1 = (89)
f) 22(3) = {589} -> 5 locked for C1
g) 12(2): R5C2 <> 7
h) Naked triple (589) locked in R479C3 for C3
i) 12(3) must have 5 xor 8 and R7C3 = (58) -> R7C4 <> 5

9. R123
a) Innies N3 = 14(3) <> 4{19/28} because R3C79 <> 4,8,9
b) Innies N3 <> 9 because 9{23} blocked by Killer pair (23) of Outies R12
c) 18(3) <> 7 because {567} blocked by Killer triple of Innies N3
d) 18(3) = 4{59/68} -> 4 locked for R2+N3
e) Innies N3 <> 8 because {158} blocked by Killer pair (58) of 18(3)
f) 18(3): R2C8 <> 9 because R3C8 <> 4,5
g) 13(3) @ N2: R1C4 <> 6 because R1C3 <> 2,5 and 4 only possible @ R1C4
h) 12(3) @ R1: R1C5 <> 6 because 4 only possible there and R3C5 <> 1,5
i) 6 locked in 14(3) = 6{17/35} @ R1 -> R2C6 <> 6
j) 8,9 in N3 only possible @ 18(3) and 13(3) neither of them can have both
-> 13(3) must have 8 xor 9
k) 13(3) @ N3 = 3{19/28} -> 3 locked for N3
l) 14(3): R1C67 <> 1 because (67) only possible there
m) 12(3) @ R1 <> 8 because {138} blocked by Killer pair (13) of 14(3)
n) 8 locked in R123C4 for C4

10. R789
a) 19(3) @ R8C4: R9C3 <> 5 because R89C4 <> 8
b) Hidden Single: R7C3 = 5 @ N7
c) Innies N9 = 20(3): R9C7 <> 6,8 because R7C79 <> 5
d) 21(3): R6C7 <> 4 because 4{89} blocked by R7C1 = (89)
e) 17(3): R9C6 <> 9 since R8C6+R9C7 <> 2,3

11. R123
a) Innies+Outies N2: -6 = R1C37 - R3C46 -> R3C6 <> 1,2 because R1C37 >= 6
b) 13(3) @ N3: R2C9 <> 9 because {13}9 blocked by R1C3 = (13)
c) 12(3) @ N3: R4C7 <> 7 because R3C6 <> 1,4 and {23}7 blocked by Killer pair (23) of Outies R12
d) Innies+Outies N2: -6 = R1C37 - R3C46 -> R3C6 <> 3 since it forces 14(3) = {356} with 3 in N2
e) 12(3) @ N3: R3C7 <> 7 because R3C6 >= 5
f) 12(3) @ N3: R4C7 <> 2 because R3C67 <> 4 and R3C7 <> 3,7
g) 12(3) @ N3 <> {246} because it's blocked by Killer pair (26) of Outies R12

12. N56
a) Killer pair (13) locked in 12(3) + R8C7 for C7
b) Outies N5 = 12(2+1): R7C5 <> 8 because R5C7 <> 1,3
c) Outies N5 = 12(2+1): R5C7 <> 6,9 since R5C3+R7C5 <> 2,5 and R7C5 <> 3

13. N2 !
a) 13(3) <> 5,7 because 1{57} blocked by Killer triple (567) of 14(3) + R3C6
b) ! 12(3): R1C5 <> 7 since 7{23} blocked by Killer pair (37) of 14(3)
c) 14(3) = {167} -> R2C6 = 1, {67} locked for R1
d) 12(3) = {237/246/345}
e) Killer triple (567) locked in 12(3) + R13C6
f) 9 locked in R123C4 for C4
g) 12(3): R1C5 <> 5 because 4 only possible there

14. R123
a) Hidden Single: R1C1 = 5 @ R1
b) Outies R12 = 17(3) must have 8 xor 9 and it's only possible @ R3C8 -> R3C8 = (89)
c) 18(3) must have 8 xor 9 and R3C8 = (89) -> R2C8 <> 8

15. C456
a) Killer pair (47) of 12(3) @ C5 blocks {47} of 11(2)
b) 19(3) <> 2 because R89C4 <> 8,9

16. R123 !
a) ! Innies+Outies R1: 16 = R2C149 - R1C5 -> R1C5 <> 2 because R2C149 <> 1,5,6,7
b) Killer pair (34) locked in 13(3) @ N2 + R1C5 for R1
c) Hidden Single: R2C9 = 3 @ N3
d) 13(3) @ N3: R1C9 <> 8
e) 8 locked in R13C8 for C8
f) Killer pair (89) locked in 13(3) @ N3 + R1C2 for R1
g) 13(3) @ N2 must have 8 xor 9 and it's only possible @ R2C4 -> R2C4 = (89)
h) Innies+Outies R1: 13 = R2C14 - R1C5 -> R1C5 = 4 because R2C14 = {89}
i) 12(3) = 4[26/53/62]
j) 7 locked in R13C6 for C6

17. C789
a) 8(2): R5C8 <> 5
b) 21(3): R7C6 <> 8 because {678} blocked by R1C7 = (67)

18. N789 !
a) ! Innies+Outies N8: 2 = R9C37 - R7C456
-> R9C7 <> 9 because R7C456 can't be 15(3)
b) 9 locked in 21(3) @ C7 -> 21(3) = 9{48/57}; R7C6 <> 9
c) 21(3) = {489} -> R7C6 = 4, {89} locked for C7
d) Killer pair (89) locked in 19(3) @ N9 + R7C7 for N9
e) Killer pair (67) locked in 19(3) @ N9 + R7C9 for N9
f) 17(3) = 5{39/48} because R9C7 = (45) -> R9C45 <> 5
g) Hidden Single: R9C5 = 2 @ R9 -> R8C5 = 9
h) 17(3) = {458} -> R9C7 = 4, {58} locked for C6+N2
i) 19(3) @ N8 = {379} -> R8C4 = 7, R9C4 = 3, R9C3 = 9
j) 19(3) @ N9 = {568} locked for N9, 8 locked for C9
k) 18(3) = 7{29/56}; R6C9 <> 9
l) 19(3) @ N7 = 8{29/47} -> R7C1 = 8

19. Rest is singles.

Rating: Easy 1.75. Although the moves weren't that difficult (Rating 1.5) there were lots of them with no short-cuts in sight
Quicker route using AIC(Grouped X-Cycle) and Grouped Swordfish by mhparker:
Epic walkthrough, Afmob. Well persevered! :D
Andrew wrote:
I wouldn't expect any puzzle with an estimated rating of 1.5 to become an Unsolvable.
Me, neither! However, it's the only consolidated list we currently have for puzzles that do not yet have a WT posted for them. I wasn't seriously expecting this puzzle to become one of them. With the next Assassin being imminent, and unaware that Afmob had in fact already finished the puzzle, I really just wanted to stimulate you all into action... :wink:
Afmob wrote:
What a demanding killer! I haven't been able to find a short-cut for this version so there a lot of little moves with no real breakthrough move. As you can see my walkthrough is very long, which shows what I mean with little steps.
Andrew wrote:
I ... got half a dozen placements very quickly. Then I had to start thinking and am currently only able to find little moves, as Afmob said above.
There was no obvious single shortcut intended for this puzzle. However, there is a quicker route available starting from immediately after Afmob's step 9, as follows:

Grid state after Afmob's step 9:

Code:
.-----------------------.-----------------------.-----------.-----------------------.-----------------------.
| 589         89        | 13          1234578   | 123457    | 3567        567       | 1389        12389     |
|           .-----------'-----------.           |           |           .-----------'-----------.           |
| 589       | 26          7         | 25689     | 123569    | 135       | 46          4568      | 12389     |
:-----------:           .-----------'-----------:           :-----------'-----------.           :-----------:
| 13        | 26        | 4           89        | 23679     | 123567      12567     | 689       | 12567     |
|           '-----------:           .-----------+-----------'-----------.           :-----------'           |
| 24          15        | 89        | 1234567   | 56789       123456789 | 1234567   | 13456789    123456789 |
:-----------------------+-----------'           '-----------.           '-----------+-----------------------:
| 347         589       | 136         12345679    456789    | 123456789   123456789 | 13567       12357     |
:-----------------------+-----------.-----------------------'-----------.-----------+-----------------------:
| 234         789       | 136       | 123456      123456789   12345     | 456789    | 13456789    123456789 |
|           .-----------:           '-----------.           .-----------'           :-----------.           |
| 89        | 3         | 58          146       | 1456789   | 456789      456789    | 2         | 456789    |
:-----------:           '-----------.-----------+-----------+-----------.-----------'           :-----------:
| 67        | 4           2         | 5679      | 56789     | 56789     | 13          13        | 56789     |
|           '-----------.-----------'           |           |           '-----------.-----------'           |
| 167         17        | 589         23456     | 23456     | 23456789    456789    | 456789      456789    |
'-----------------------'-----------------------'-----------'-----------------------'-----------------------'


From this position, the following moves can be made (disguised in Afmob-like WT style... :-)):

Quote:
10. R123
a) R2C9 <> 9 because {13}9 for 13(3) blocked by R1C3
b) AIC (Grouped X-Cycle): (9)R3C4=R4C3-R9C3=R7C1-R2C1=R2C45 -> R3C5 <> 9
c) Hidden pair {89} in R3C48 -> R3C8 <> 6
d) 18(3) can only have 1 of {89} and it must be in R3C8 -> R2C8 <> 8
e) Innies+Outies R12: 9 = R2C278 - R3C5 -> R3C5 <> 7, because max. R2C278 = 15
f) Hidden killer pair {57} in R3C67 + R3C9 -> R3C9 = {57}, R4C7 <> 5,7
g) Hidden killer pair {12} in R3C7 + 13(3) -> R3C7 = {12}
h) -> R3C6 = {57} (step 10f)
i) 12(3): R34C7 cannot have both of {12} because R3C6 <> 9 -> R4C7 <> 1,2
j) 12(3): R4C7 <> 4 because R34C7 = [14] blocked by C89 outies (R28C7, step 5a)
k) Killer pair {36} locked in R4C7 + R28C7 for C7
l) Naked pair {57} locked in R1C7 + R3C9 -> R3C7 = 2 (Innies N3)
...
(Rest of puzzle is trivial now)

[Note: Alternative explanation of step 10b for those unfamiliar with Eureka notation:
(a) R3C4 <> 9 => R4C3 = 9 (strong link, 21(3))
(b) -> R9C3 <> 9 (weak link, C3)
(c) -> R7C1 = 9 (strong link, N7)
(d) -> R2C1 <> 9 (weak link, C1)
(e) -> R2C45 = {9..} (strong link, R2)
=> either R3C4 and/or R2C45 must contain a 9
-> R3C5 <> 9 (common peer)]


Note that one of the reasons for choosing to publish this puzzle was the fact that JSudoku found quite an exotic creature, namely a Grouped Swordfish, which can be applied here immediately after step 10a above. After the removal of the candidate 9 from R2C9, the 9 in R2, N7 and 21(3)n124 is constrained to C1, C3 and N2 -> no 9 elsewhere in C13 and N2. This avoids the explicit use of a chain in step 10b above, and would also have eliminated 9 from R1C456 if they hadn't already been removed by the chain used by Afmob in his earlier step 6e. However, although more elegant, the grouped Swordfish is probably considerably harder to find than the two chains of Afmob's and mine (respectively) that it replaces.

I intend to elaborate on grouped Swordfishes soon, in a separate post. Stay tuned!
Double Optimized Walk-through by Afmob but still his 7th longest:
After getting some helpful advice from Mike I decided to rewrite my walkthrough to make it shorter. I could remove one chain (old wt: step 6) and I saw that steps 10-12 were unncessary since the cracker (old wt: step 13b, new wt: step 10f) could be applied earlier. Additionaly I optimized the end game to make the walkthrough even shorter.

Nevertheless, this walkthrough is the 7th longest (old wt: 3rd longest :shock:) I've written so far.

Edit: Andrew indirectly showed my a way to simplify step 10f, so that this wt uses no chains at all and is shortened a bit.

A73 V1.5 Walkthrough (improved):

1. R89
a) Innies = 10(4) = {1234} locked for R8, 4 locked in 9(3) for N7; R7C2 <> 4
b) 4 locked in 9(3) = {234} locked for N7
c) Outies = 5(2) = {23} locked for R7
d) 14(3) = 1{58/67} -> 1 locked for R9+N7
e) 6(3) = {123} locked for N9
f) 11(2): R9C5 <> 7,8,9

2. C6789
a) Outies C89 = 7(2) = [43/52/61]
b) 18(3) @ N3 <> 1,2 because R2C7 = (456)
c) Innies C89 = 17(4): R23C8 <> 3 because Innies would be <= 15
d) 13(3) <> 6 because 6{25/34} blocked by Killer pairs (46,56) of 18(3) @ N3

3. C1234
a) Outies C12 = 9(2) = [54/63/72]
b) 22(3) = 9{58/67} -> 9 locked for N1
c) Innies N1 = 8(3) = 1{25/34} locked for N1
d) 21(3) = 9{48/57} because R3C3 = (45) -> R3C4+R4C3 <> 4,5,6
e) 12(3) @ N7: R6C3+R7C4 <> 7,8,9 because R7C3 >= 5
f) Innies N1 = 8(3) must have 4 xor 5 and R3C3 = (45) -> R1C3+R3C1 <> 4,5
g) 4 locked in R456C1 for N4
h) 12(2): R5C1 <> 8
i) 8(3): R4C1 <> 3 because 4 only possible there

4. C123
a) 15(3) = 2{58/67} because 5{37/46} blocked by Killer pairs (56,57) of 22(3) and R2C3 = (567)
-> 2 locked for C2+N1
b) 9(3) = {234} -> R8C3 = 2, R7C2 = 3, R8C2 = 4
c) R7C8 = 2
d) Hidden Single: R3C3 = 4 @ N1
e) Outies C12 = 9(2) = [72] -> R2C3 = 7
f) 15(3) = {267} -> 6 locked for C2+N1
g) 8(3) must have 2 xor 4 and it's only possible @ R4C1 -> R4C1 = (24)
h) 19(3) @ N4: R6C1 <> 7,9 because R6C2+R7C1 <> 2,3,4
i) 21(3) = {489}
j) 12(2): R5C1 <> 9
k) 12(3) = {138/156/345} <> 9

5. C89
a) Outies = 7(2) = [43/61]
b) 8(2): R5C9 <> 6

6. C123
a) Innies N7 = 22(3): R7C1 <> 6 because 7 only possible there
b) Innies N7 = 22(3): R7C1 <> 5 because 5{89} blocked by R4C3 = (89)
c) 19(3) @ N4: R6C1 <> 5,8 because R6C2+R7C1 <> 2,4,6
d) Innies N7 = 22(3): R9C3 <> 6 because R7C3 <> 7,9

7. R123
a) Outies R12 = 17(3) <> 1,5 because R3C2 = (26)
-> 17(3) = {269/278/368}
b) Killer pair (89) locked in Outies R12 + R3C4 for R3
c) 12(3) @ R3C6 <> 8 because {13}8 blocked by R3C1 = (13)
d) 12(3) @ R3C6 <> 9 because R3C167 = {123} blocked by Killer pair (23) of Outies R12

8. C123 !
a) ! 5,6 locked in R5679C3 for C3 but R79C3 can't have both of (56) because of Innies N7 = 22(3)
-> R56C3 must have 1 of (56)
b) 19(3) @ N4 <> 5 since R6C12 would be [65] -> impossible (step 8a)
c) 19(3) <> 6 because R6C2+R7C1 <> 4
d) 6 locked in 14(3) @ C1 -> 14(3) = {167} locked for N7
e) 22(3): R1C2 <> 5 because R12C1 = {89} blocked by R7C1 = (89)
f) 22(3) = {589} -> 5 locked for C1
g) 12(2): R5C2 <> 7
h) Naked triple (589) locked in R479C3 for C3
i) 12(3) must have 5 xor 8 and R7C3 = (58) -> R7C4 <> 5

9. R123
a) Innies N3 = 14(3) <> 4{19/28} because R3C79 <> 4,8,9
b) Innies N3 <> 9 because 9{23} blocked by Killer pair (23) of Outies R12
c) 18(3) <> 7 because {567} blocked by Killer triple of Innies N3
d) 18(3) = 4{59/68} -> 4 locked for R2+N3
e) Innies N3 <> 8 since {158} blocked by Killer pair (58) of 18(3)
f) 18(3): R2C8 <> 9 because R3C8 <> 4,5
g) 13(3) @ N2: R1C4 <> 6 because R1C3 <> 2,5 and 4 only possible @ R1C4
h) 12(3) @ R1: R1C5 <> 6 because 4 only possible there and R3C5 <> 1,5
i) 6 locked in 14(3) = 6{17/35} @ R1 -> R2C6 <> 6
j) Hidden Killer pair (89) @ 13(3) + 18(3) for N3
-> 13(3) = 3{19/28} -> 3 locked for N3

10. R123 !
a) 14(3): R1C67 <> 1 because (67) only possible there
b) 12(3) @ R1 <> 8 because {138} blocked by Killer pair (13) of 14(3)
c) 8 locked in R123C4 for C4
d) Innies+Outies N12: -10 = R1C7 - R3C146; R1C7 = (567)
-> R3C6 <> 1,2,3 because R3C14 <= 12 ([39])
e) 13(3) <> 5,7 because R1C3 = (13) and 1{57} blocked by Killer triple (567) of 14(3) + R3C6
f) ! 12(3): R1C5 <> 7 since 7{23} blocked by Killer pair (37) of 14(3)
g) 7 locked in 14(3) = {167} -> R2C6 = 1
h) 12(3) = {237/246/345}
i) 9 locked in R123C4 for C4

11. R123
a) Hidden Killer pair (89) locked in 13(3) + R3C4 for N2 -> 13(3) <> 6
b) Hidden pair (89) locked in R3C4 + R3C8 for R3 -> R3C8 <> 6
c) 18(3) must have 8 xor 9 and R3C8 = (89) -> R2C8 <> 8
d) Innies+Outies R12: -9 = R3C5 - R2C278
-> R3C5 <> 7 because R2C278 <= 15
e) Outies R12 = 17(3) = 6{29/38} -> 6 locked for R3
f) 12(3) @ R1C5 = 4{26/35} -> R1C5 = 4; R2C5 <> 3
g) 7 locked in R13C6 for C6
h) 12(3) @ R3C6 = {147/156/237/345} because R3C6 = (57); R34C7 <> 5,7
i) 12(3) @ R3C6 = {147/157/237} because R3C7 = (12) -> R4C7 <> 1,2
j) Hidden pair (57) locked in R3C69 for R3 -> R3C9 <> 1,2

12. C789
a) 12(3) <> 4 because 7[14] blocked by Killer pair (14) of Outies R89
b) Killer pair (36) locked in Outies R89 + R4C7 for C7
c) R1C7 = 7, R1C6 = 6, R3C9 = 5
d) 12(3) = {237} -> R3C6 = 7, R3C7 = 2, R4C7 = 3
e) 21(3) = {489}
f) 8(2): R5C8 <> 5

13. C456
a) 12(3) = {345} -> R2C5 = 5, R3C5 = 3
b) 11(2) = {29} -> R9C5 = 2, R8C5 = 9
c) 21(3) = {489} -> 9 locked for C7
d) 17(3) = {458} -> 4 locked for R9

14. C89
a) 19(3) @ N9 = {568} -> R9C8 = 5, {68} locked for C9+N9
b) 8 locked in R13C8 for C8
c) 18(3) @ N6 = {279} -> R6C9 = 2

15. Rest is singles.

Rating: Hard 1.5. I rated it down since I was able to omit both chains but the walkthrough is still quite long
Walkthrough by Andrew with some combination analysis and non-heavy contradictions:
Thanks Mike for a very challenging killer! :D It starts fairly easily, which draws one into the puzzle, then gets really difficult.

At one stage I was thinking of giving up but then compared how far I'd got against Mike's state diagram which made me think what I'd been missing and I found steps 20e and 28, which was enough to get me going again. State diagrams like that can be helpful in providing hints while making one think how to reach the position. Thanks Mike!

The way I solved it, the later stages needed a bit more combination analysis and some contradictions but nothing particularly heavy. That includes step 39 which I don't think I used later but have left it in since I'd done it.

I'll go along with Afmob's rating of a hard 1.5.

Here is my walkthrough for A73 V1.5.

Prelims

a) R5C12 = {39/48/57}, no 1,2,6
b) R5C89 = {17/26/35}, no 4,8,9
c) R89C5 = {29/38/47/56}, no 1
d) 22(3) cage in N1 = 9{58/67}, 9 locked for N1
e) 8(3) cage at R3C1 = 1{25/34}, CPE no 1 in R6C1
f) 21(3) cage at R3C3 = {489/579/678}, no 1,2,3
g) 19(3) cage at R6C1 = {289/379/469/478/568}, no 1
h) 21(3) cage at R6C7 = {489/579/678}, no 1,2,3
i) 9(3) cage in N7 = {126/135/234}, no 7,8,9
j) 19(3) cage at R8C4 = {289/379/469/478/568}, no 1
k) 19(3) cage in N9 = {289/379/469/478/568}, no 1
l) 6(3) cage in N9 = {123}, locked for N9

1. 45 rule on N1 3 innies R1C3 + R3C13 = 8 = 1{25/34}, 1 locked for N1
1a. R3C3 = {45} -> no 4,5 in R1C3 + R3C1
1b. 15(3) cage in N1 = {258/267/348} (cannot be {357/456} which clash with 22(3) cage)

2. 45 rule on N7 3 innies R7C13 + R9C3 = 22 = 9{58/67}, 9 locked for N7
2a. 14(3) cage in N7 = {158/167/248/347} (cannot be {257/356} which clash with R7C13 + R9C3)

3. 45 rule on C12 2 outies R28C3 = 9 = {36/45}/[72/81], no 2 in R2C3

4. 45 rule on C89 2 outies R28C7 = 7 = [43/52/61], R2C7 = {456}
4a. Max R2C7 = 6 -> min R23C8 = 12, no 1,2

5. 21(3) cage at R3C3 = {489/579} (cannot be {678} because R3C3 only contains 4,5), no 6
5a. R3C3 = {45} -> no 4,5 in R3C4 + R4C3
5b. R3C4 + R4C3 must contain 9, CPE no 9 in R4C4

6. 12(3) cage at R6C3, min R7C3 = 5 -> max R6C3 + R7C4 = 7, no 7,8,9

7. 45 rule on R89 2 outies R7C28 = 5 = {23}/[41], no 1,5,6 in R7C2
7a. 45 rule on R89 4 innies R8C2378 = 10 = {1234}, locked for R8, clean-up: no 3,4 in R2C3 (step 3), no 7,8,9 in R9C5
7b. 9(3) cage in N7 = {234} (only remaining combination), locked for N7, clean-up: no 8 in R2C3 (step 3)
7c. 1 in R8 locked in R8C78, locked for N9, clean-up: no 4 in R7C2 (step 7)
7d. Naked pair {23} in R7C28, locked for R7
7e. 1 in N7 locked in R9C12, locked for R9
7f. Min R8C6 + R9C7 = 9 -> max R9C6 = 8

8. 15(3) cage in N1 (step 1b) = {258/267} (cannot be {348} because R2C3 only contains 5,6,7), no 3,4, 2 locked in R23C2 for C2 and N1 -> R78C2 = [34], R8C3 = 2, R7C8 = 2, R2C3 = 7 (step 3), R23C2 = 8 = {26}, clean-up: no 5 in R2C7 (step 4), no 8,9 in R5C1, no 6 in R5C9
[I was going to do killer triple 2,3,4 in R23C2 and R78C2, locked for C2 until I realised that step 8 takes away the use of this nice move.]
8a. Naked pair {26} in R23C2, locked for C2 and N1
8b. R3C3 = 4 (step 1 or as hidden single in N1), R3C4 + R4C3 (step 5) = {89}, CPE no 8 in R4C4

9. 12(3) cage at R6C3 = {138/156/345}, no 9

10. R7C13 + R9C3 (step 2) = 9{58/67}
10a. 6 of {679} must be in R7C3 -> no 6 in R7C1 + R9C3

11. 19(3) cage at R6C1 = {289/379/478/568} (cannot be {469} because 4,6 only in R6C1)
11a. 2,3,4,6 only in R6C1 -> R6C1 = {2346}

12. 8(3) cage at R3C1 = 1{25/34}
12a. 2,4 only in R4C1 -> R4C1 = {24}

13. 13(3) cage at R1C3 = {139/148/157/238/346} (cannot be {247/256} because R1C3 only contains 1,3)
13a. 7 of {157} must be in R1C4 -> no 5 in R1C4

14. 45 rule on C89 4 innies R2378C8 = 17 = {1259/1268/2348/2357} (cannot be {2456} because R8C8 only contains 1,3)
14a. 3 of {2348/2357} must be in R8C8 -> no 3 in R23C8
14b. 18(3) cage in N3 = 4{59}/4{68}/[648]/[657]
14c. 13(3) cage in N3 = {139/148/157/238/256} (cannot be {247/346} which clash with 18(3) cage)
14d. R1C89 = {13} clashes with R1C3 -> no 9 in R2C9
14e. Hidden killer pair 1,2 in N3 for 13(3) cage and R1C7 + R3C79 -> R1C7 + R3C79 must contain 1 or 2
14f. 45 rule on N3 3 innies R1C7 + R3C79 = 14 = {149/167/239/248/257} (cannot be {158} which clashes with 13(3) cage and with 18(3) cage)

15. 45 rule on C1234 1 outie R5C5 = 1 innie R6C4 + 3, no 1,2,3 in R5C5, no 7,8,9 in R6C4

16. 45 rule on C6789 1 outie R4C5 = 1 innie R6C6 + 4, no 1,2,3,4 in R4C5, no 6,7,8,9 in R6C6

17. 1 in R7 locked in R7C45, CPE no 1 in R6C4, clean-up: no 4 in R5C5 (step 15)

18. 45 rule on R12 3 outies R3C258 = 17 = {269/278/368} (cannot be {179/359} because R3C2 only contains 2,6), no 1,5, clean-up: no 9 in R2C8 (step 14b)
18a. Killer pair 8,9 in R3C4 and R3C58, locked for R3

19. Hidden killer triple 1,2,3 in R3C1, R3C25 and R3C679 for R3 -> R3C679 must contain one of 1,2,3
19a. Min R3C67 = {15} = 6 -> max R4C7 = 6
19b. Hidden killer pair 6,7 in R3C258 and R3C679 for R3 -> R3C679 must contain one of 6,7
19c. R3C679 must contain 5, one of 1,2,3 and one of 6,7

20. R1C7 + R3C79 (step 14f) = {167/257} (cannot be {149/248} because 4,8,9 only in R1C7, cannot be {239} because R3C79 = {23} clashes with R3C258), no 3,4,8,9, 7 locked for N3
20a. R3C79 cannot be {67} (step 19c) -> no 1 in R1C7
20b. 18(3) cage in N3 (step 14b) = 4{59}/4{68}/[648], 4 locked in R2C78, locked for R2 and N3
20c. 3 in N3 locked in 13(3) cage = {139/238}, no 5,6
[Alternatively killer pair 5,6 in R1C7 + R3C79 and 18(3) cage]
20d. 13(3) cage at R1C3 (step 13) = {139/148/157/238/346}
20e. 4 of {346} must be in R1C4 -> no 6 in R1C4

21. Hidden killer pair 1,3 in R1C3 and R56C3 for C3 -> R56C3 must contain one of 1,3
21a. 45 rule on N4 3 innies R456C3 = 2 outies R37C1 + 6
21b. Min R37C1 = 6 -> min R456C3 = 12 = {138} clashes with R1C3
21c. Min R37C1 = 8 -> min R456C3 = 14 = {158} clashes with R4C2
21d. Min R37C1 = 9, no 5 in R7C1

22. R7C13 + R9C3 (step 2) = 9{58/67}
22a. R79C3 must contain 5 or 6, hidden killer pair 5,6 in R56C3 and R79C3 -> R56C3 must contain one of 5,6
22b. Combining steps 21 and 22a, R56C3 = {1356}, no 8,9

23. Hidden killer triple 7,8,9 in R4C3, R5C12 and R6C2 -> R6C2 = {789}
23a. 19(3) cage at R6C1 (step 11) = {289/379/478}, no 6

24. 6 in N4 locked in R56C3, locked for C3, clean-up: no 7 in R7C1 (step 2)
24a. R7C13 + R9C3 (step 2) = {589} (only remaining combination), locked for N7, 5 locked in R79C3 for C3
[Alternatively 6 locked in R56C3 (step 24) -> no 5 in R56C3 (step 22a).]
24b. R7C67 = {89} clashes with R7C1 -> no 4 in R6C7

25. Naked triple {589} in R127C1, locked for C1, clean-up: no 7 in R5C2
25a. 5 in C1 locked in R12C1, locked for N1

26. 12(3) cage at R6C3 (step 9) = {138/156/345}
26a. 5 of {156/345} must be in R7C3 -> no 5 in R7C4

27. 19(3) cage at R8C4 = {289/379/469/478/568}
27a. 2,3,4 of {289/379/469/478} must be in R9C4 -> no 7,9 in R9C4

28. R123C5 = {129/138/147/156/237/246/345}
28a. 6 of {156} must be in R3C5, 4 of {246} must be in R1C5 -> no 6 in R1C5

29. 6 in R1 locked in R1C67, locked for 14(3) cage -> no 6 in R2C6
29a. 14(3) cage = {167/356}, no 2,4,8,9
29b. 1 of {167} must be in R2C6 -> no 1 in R1C6

30. R123C5 = {129/147/156/237/246/345} (cannot be {138} which clashes with R12C6), no 8
30a. 8 in N3 locked in R123C4, locked for C4

31. 19(3) cage at R8C4 = {289/379/469/478/568}
31a. 8 of {568} must be in R9C3 -> no 5 in R9C3

32. R7C3 = 5 (hidden single in C3)

33. R1C7 + R3C79 (step 20) = {167/257}
33a. R1C7 = {567} -> R3C79 must contain 1 or 2
33b. R3C679 must contain one of 1,2,3 (step 19) -> no 1,2,3 in R3C6
33c. 12(3) cage at R3C6 = {147/156/237/246} (cannot be {345} because 3,4 only in R4C7)
33d. 7 of {147/237} must be in R3C6 -> no 7 in R3C7
33e. 3,4 of {237/246} must be in R4C7 -> no 2 in R4C7

34. 13(3) cage at R1C3 (step 13) = {139/148/157/238/346}
Hidden killer pair 2,4 in N2 for R12C4 and R123C5 -> R123C5 must contain at least one of 2,4 -> R123C5 = {129/147/237/246/345} (cannot be {156} which doesn’t contain 2,4)
34a. 4 of {345} must be in R1C5 -> no 5 in R1C5

35. 45 rule on N9 3 innies R7C79 + R9C7 = 20 = {479/569/578}
35a. 5 of {569/578} must be in R9C7 -> no 6,8 in R9C7

36. 45 rule on N5 3 outies R5C37 + R7C5 = 12 = [38/65]1/[17/35/62]4/[15]6/[14/32]7/{13}8/[12]9, no 6,9 in R5C7

37. 45 rule on R5 3 outies R4C456 = 17 = {179/269/278/359/368/458/467}
Some permutations are eliminated by R4C5 = R6C6 + 4 (step 16)
37a. {269} must have 9 in R4C5 = [296/692]
37b. {359} must have 5 in R4C5 = [359]
37c. {458} must have 5 in R4C5 = [458]
37d. -> no 5 in R4C46

38. R7C79 + R9C7 (step 35) = {479/569/578}
38a. Hidden killer pair 4,6 in R7C456 and R7C79 for R7 -> R7C456 must have at least one of 4,6
38a. 45 rule on N8 2 outies R9C37 = 3 innies R7C456 + 2
38b. Max R9C37 = 17 -> max R7C456 = 15
38c. Only remaining permutation with 9 in R7C456 = {149} => R7C1 = 8 => R7C79 = {67} clashes with R7C79 + R9C7
38d. -> no 9 in R7C56
38e. 9 in N8 locked in R8C456, locked for R8

39. 15(4) cage at R6C4 = {1239/1248/1257/1347/1356/2346}
39a. R6C456 + R7C5 = {234}6 clashes with R6C1
39b. R6C456 + R7C5 = {236}4 => R6C3 = 1 => R7C4 = 6 -> no 1 in R7
39c. -> cannot be {2346}
39d. -> 15(4) cage = {1239/1248/1257/1347/1356}

40. 13(3) cage at R1C3 (step 13) = {139/148/157/238/346}
40a. Cannot be {157} because R3C4 = 8 => 9 must be in R123C5 and cannot then place 4 for N2
40b. -> 13(3) cage = {139/148/238/346}, no 5,7
40c. {139} can be 1{39} or 3{19}
If 1{39} => R3C4 = 8 => R123C5 = 4{26} (step 34) => R123C6 = {157} = [715] (step 29a), R1C7 = 6 clashes with R34C7 = {16}
If 3{19} => R3C4 = 8 => R123C5 = 4{26} (step 34) => R123C6 = {357} = [537] (step 29a), R1C7 = 6 -> cannot place 7 in N3
40d. -> no {139}, no 1,3,9 in R12C4

41. 13(3) cage at R1C3 = 1[48]/3{28}/3[46]
41a. If 1[48] => R3C4 = 9 => R123C5 = {237} (step 34) -> no 3 in R1C6
41b. If 3{28}/3[46], R1C3 = 3 -> no 3 in R1C6
41c. -> no 3 in R1C6
41d. R123C5 (step 34) = {129/147/237/345} (cannot be {246} which clashes with R12C4), no 6

42. 14(3) cage at R1C6 (step 29a) = {167/356}
42a. 3 of {356} must be in R2C6 -> no 5 in R2C6

43. 13(3) cage at R1C3 = 1[48]/3{28}/3[46]
43a. If 1[48] => R3C4 = 9 -> R123C5 cannot be {129}
43b. If 3{28} -> R123C5 cannot be {129}
43c. If 3[46] => R3C4 = 8 => R123C5 = {129} (only place for 9) => R123C6 = {357} = [537] (step 29a), R1C7 = 6 -> cannot place 7 in N3
43d. -> R123C5 cannot be {129}
43e. -> R123C5 (step 34) = {147/237/345}, no 9

44. R3C4 = 9 (hidden single in N2), R4C3 = 8, R9C3 = 9, R7C1 = 8
44a. R1C2 = 8 (hidden single in N1), R2C4 = 8 (hidden single in N2)
44b. R3C8 = 8 (hidden single in R3), R2C78 = 10 = {46}, locked for R2 and N3 -> R23C2 = [26]
44c. R1C6 = 6 (hidden single in R1)

45. 13(3) cage in N3 = {139} (only remaining combination), locked for N3
45a. 9 locked in R1C89, locked for R1 -> R12C1 = [59], R1C7 = 7, R2C6 = 1 (step 29a), R2C9 = 3, R2C5 = 5, R13C5 = [43] (step 43e), R3C1 = 1, R1C34 = [32], R4C2 = 5, R4C1 = 2, R5C2 = 9, R5C1 = 3, R6C12 = [47], R9C2 = 1, R3C6 = 7, clean-up: no 5 in R5C89, no 7 in R5C5, no 6 in R6C4 (both step 15), no 4 in R7C4 (step 9)

46. R3C6 = 7 -> R34C7 = 5 = [23], R3C9 = 5, R8C78 = [13]

47. R9C3 = 9 -> R89C4 = 10 = [64/73], no 5, no 6 in R9C4

48. Naked pair {67} in R8C14, locked for R8 -> R8C9 = 8, R8C5 = 9, R8C6 = 5, R9C5 = 2

49. Killer pair 1,6 in R5C3 and R5C89, locked for R5 -> R5C5 = 8, R6C4 = 5 (step 15)

50. Naked pair {16} in R6C35, locked for R6 -> R6C8 = 9, R6C9 = 2, R1C89 = [19], R6C6 = 3, R4C5 = 7 (step 16), clean-up: no 6 in R5C8

and the rest is naked singles

Near the end I also noticed 45 rule on R12 4 innies R2C2378 = 1 outie R3C5 + 16, but never got to find out if it was useful.

Mike's analysis and alternative path after step 9 of Afmob's original walkthrough was interesting. I look forward to reading Mike's further posts about Grouped Swordfish. I did one use an ordinary Swordfish, a 3 row and 3 column X-Wing, in a walkthrough almost a year ago. Therefore I could understand what Mike said about the Grouped Swordfish in this puzzle and also agree with his comment that it would be difficult to spot; something that's probably easier for a software solver to spot
Continuous loop: grouped Swordfish formations: explanation by mhparker:
Andrew wrote:
I look forward to reading...about Grouped Swordfish. I did one use an ordinary Swordfish... Therefore I... agree... that it would be difficult to spot; something that's probably easier for a software solver to spot.
Probably true. At least being able to filter all candidates for a given digit on the grid via software would be very helpful in such cases.

Actually, I realise now that I overlooked something with my AIC in my previous post:

I wrote:
10. R123
a) R2C9 <> 9 because {13}9 for 13(3) blocked by R1C3
b) AIC (Grouped X-Cycle): (9)R3C4=R4C3-R9C3=R7C1-R2C1=R2C45 -> R3C5 <> 9
...
[Note: Alternative explanation of step 10b for those unfamiliar with Eureka notation:
(a) R3C4 <> 9 => R4C3 = 9 (strong link, 21(3))
...
(e) -> R2C45 = {9..} (strong link, R2)
...


What I failed to realize when originally writing that is that the two ends of the chain can be joined up to form a continuous loop, because R2C45 = {9..} implies R3C4 <> 9, taking us back to our starting premise again. So the full loop would now be:

Code:
(9)R3C4=R4C3-R9C3=R7C1-R2C1=R2C45...

[Note: Alternative explanation of step 10b for those unfamiliar with Eureka notation:
(a) R3C4 <> 9 => R4C3 = 9 (strong link, 21(3))
(b) -> R9C3 <> 9 (weak link, C3)
(c) -> R7C1 = 9 (strong link, N7)
(d) -> R2C1 <> 9 (weak link, C1)
(e) -> R2C45 = {9..} (strong link, R2) (grouped node)
(f) -> R3C4 <> 9 (weak link, N2)
...]


Now, because AICs begin and end with a strong link, and because the above AIC is a continuous loop, we can "cut" the loop at any weak link and end up with a bona-fide AIC chain, where one of the two ends must be "true". In other words, one of the ends of each weak link in steps b), d) and f) above must be true, thus eliminating the digit 9 elsewhere in C3, C1 and N2, respectively. (Not just in N2, as I mentioned in my post above... :oops: )

Note also that what we have above is a continuous grouped X-Cycle on the digit 9 with 3 strong (and 3 weak) links. But this is exactly what a grouped Swordfish is! To be more specific: it's exactly what a grouped Swordfish with the so-called "222" formation is, where each group of the primary set (where the strong links are, namely 21(3), N7 and R2) intersects with 2 groups of the secondary set (where the weak links are, namely C3, C1 and N2), and vice versa. Unfortunately, other Swordfish formations (such as 322, 333, etc.) can only be represented by a net, and not by a simple loop. That explains why JSudoku can only detect generalized/grouped Swordfish and Jellyfish with the 222 formation - namely, because it's using chains (continuous X-Cycles, as above) to find them.

So, generalized/grouped fish (X-Wing, Swordfish, ...) can sometimes be found indirectly by detecting continuous X-Cycles (length 4 = X-Wing, length 6 = Swordfish, ...), from which it's a small step to re-express it in "Fish" terms. As mentioned above, this is exactly what JSudoku is doing internally. Instead of reporting a continuous grouped X-Cycle (aka. "Fishy" cycle), it displays the move using standard Fish terminiology instead. In this case:
JSudoku wrote:
R2, N7, Cage 21/3 in R3C34+R4C3 and C13, N2 forms a Grouped Swordfish (222) on 9 -> not elsewhere in C13, N2


Last edited by Ed on Sun Dec 28, 2008 9:14 am, edited 1 time in total.

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PostPosted: Mon Jul 14, 2008 4:22 am 
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Location: Sydney, Australia
Maverick 1 (aka M1) by mhparker (Oct 07)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:3840:3840:3586:3586:4356:3333:3333:1543:1543:3840:3338:3338:4356:4356:4356:3087:3087:1543:2066:3091:3091:3093:6422:2839:3352:3352:3866:2066:5148:3091:3093:6422:2839:3352:5154:3866:5148:5148:2342:2342:6422:3625:3625:5154:5154:3885:5148:4399:2352:6422:2354:2099:5154:2101:3885:4399:4399:2352:6422:2354:2099:2099:2101:1599:3392:3392:5186:5186:5186:3141:3141:4423:1599:1599:2634:2634:5186:3149:3149:4423:4423:
Solution:
+-------+-------+-------+
| 4 2 5 | 9 8 6 | 7 3 1 |
| 9 7 6 | 5 1 3 | 4 8 2 |
| 3 8 1 | 4 7 2 | 6 5 9 |
+-------+-------+-------+
| 5 1 3 | 8 4 9 | 2 7 6 |
| 6 4 2 | 7 3 5 | 9 1 8 |
| 8 9 7 | 6 2 1 | 5 4 3 |
+-------+-------+-------+
| 7 6 4 | 3 9 8 | 1 2 5 |
| 1 5 8 | 2 6 7 | 3 9 4 |
| 2 3 9 | 1 5 4 | 8 6 7 |
+-------+-------+-------+
Quote:
mhparker, lead-in: (Est. rating: 1.5) This puzzle .... should provide plenty of opportunity for creativity and individualism, as its name implies
gary w: I'm finding this one tough going!!... Finally cracked it
Afmob: Definitely a fun assassin with lots of cool moves..Thanks for posting this.. Sudoku mhparker
Para: all this talk about x-wing and x-cycles going on... It is also solvable by just sticking to the basic killer techniques as 45-test cage combos and Killer Subsets
Andrew: It took me a week, on and off .. If I hadn't received encouragement .. I might well have given up on this one.
Andrew: felt.. at least as hard as any of the other 1.75s that I've done. I spent longer on it than on any of those others. It's definitely my longest walkthrough yet. Therefore I've no hesitation in rating Maverick 1 as 1.75.
Para: This puzzle felt more like a 1.5 rating to me. But that is mostly because it fell fairly quickly compared to say A60RP-Lite which i rated a 1.75. For me it wasn't in the same league as that puzzle.
Afmob, Nov 07: M2 was more difficult than M1 so... now I would rate M1 with a 1.5
A 2022 Revisit to this puzzle here
Indicative Solution by gary w:
Mike,

Finally cracked it.

Hopefully get a chance to put a reasonably detailed wt together but in the meantime ..here's just an indication..


Innies n6/9 =25.Innies N369 -> R159C7=24={789}.This together with some combo work on cages at r159c67 -> r1c7={79} r5c7={89} r9c7={78} r8c7<>9

r4c7=1/2/3 only possibilities to complete 13(3) cage N3
Therefore in N6/9 6 is in C89.The X wing on 6 -> r3c7=6

O-I r1 -> r1c5<>1/2/3 -> r1 a 1,2 or 3 must be at c12

I next considered the placement of 4s in c1 and c9.
In c1 if 4 is at r1 -> 7 at r1c7 if 4 at r2c1 -> 29 or 38 in r1c12 -> r1c7=7
If 4 is at r5c1 (only other place) in c9 4 must be at r89 -> 12(2) cage N9=39

Now combos conflict in (c7r159,innies on N6/9) if 9 at r1c7

Thus in all cases r1c7<>9 so r3c9=9

Mop up now.



A great work out Mike..many thanks

Regards

Gary
Walkthrough by Afmob:
Definitely a fun assassin with lots of cool moves. My original/unpolished walkthrough had 3 XY-Wings so sometimes I felt I was solving a normal Sudoku. So it was no surprise that the "finishing move" (step 11a) was another Sudoku technique though it took me quite a while to find it.

M1 Walkthrough:

1. C1234
a) 6(3) = {123} locked for N7
b) 10(2): R9C4 <> 7,8,9
c) 1,2,3 locked in 8(2) + R89C1 for C1
d) Innies C1234 = 7(2) = {16/25/34}

2. C6789
a) 6(3) = {123} locked for N3
b) 12(2) @ N3 = {48/57}
c) 13(3) must have 1,2 or 3 -> only possible @ R4C7 -> R4C7 = (123)
d) 13(3) <> 9 because R3C78 <> 1,3
e) 1,2,3 locked in 8(2) + R12C9 for C9
f) Innies C789 = 24(3) = {789} locked for C7
g) Both 12(2) @ N9 = [39/48/57]
h) Hidden Single: R3C7 = 6 @ C7
i) Innies C6789 = 10(2) -> no 5

3. C67
a) 13(2) = [49/58/67]
b) 14(2) = [59/68]
c) Outies C789 = 15(3) = {456} -> locked for C6
d) 11(2) = {29/38}
e) 9(2) = {18/27}
f) Killer pair (28) locked in 11(2) + 9(2) for C6
g) 12(2) = [48/57]

4. R12
a) Killer pair (58) of 14(2) @ R1 blocks {58} of 13(2)
b) Killer pair (69) locked in 14(2) + 13(2) for R1
c) Killer pair (58) of 12(2) blocks {58} of 13(2) @ R2
d) Killer pair (47) locked in 13(2) + 12(2) for R2
e) Killer pair (46) of 13(2) @ N1 blocks {456} of 15(3)
f) 15(3) must have 1,2 or 3 -> only possible @ R1C2 -> R1C2 = (123)
g) Naked triple (123) locked in R1C289 for R1
h) 12(2) = [48/57]

5. N36
a) 13(3) = 6[43/52] -> R3C8 = (45), R4C7 = (23)
b) 15(2) = [78/87/96]

6. N9
a) 7,8,9 locked in R8C8 + R9C7 + 17(3) -> R7C9 <> 7
b) 8(2): R6C9 <> 1
c) 17(3) must have 7,8 xor 9 -> 17(3) = {269/359/368/458/467} -> no 1
d) 17(3): R9C8 <> 9 since R89C9 >= 9

7. R789
a) 1 locked in R7C789 for R7
b) Both 9(2): R6C46 <> 8
c) Innies+Outies R9: R8C19 = R9C5
-> R9C5 <> 1,2,3,4 since R8C19 >= 5
-> R8C9 <> 9 because R9C5 <= 9

8. C12
a) Innies+Outies C1: -1 = R19C2 - R5C1
-> R5C1 = (456) because R19C2 = 3/4/5
b) 8(2): R4C1 <> 2
c) 1,2,3 locked in R19C2 + 20(4) @ R456C2 for C2

9. N1
a) Hidden triple (123) in R1C2 + R3C13 -> no other candidates
b) 8(2) = [17/26/35]

10. N369
a) Consider both candidates of R1C7 = (79)
-> R1C7 = 7 -> R2C8 = 8 -> R3C9 = 9 -> 15(2) = [96]
-> R1C7 = 9 -> R5C7 = 8 -> 15(2) = [87]
-> 15(2) = [87/96]

11. C1 !
a) ! Coloring 4 in C1:
- i) If R1C1 = 4 -> R2C7 = 4 (Hidden Single @ R2) -> R78C7 <> 4
- ii) If R5C1 = 4 -> 4 locked in R89C9 for C9 -> R78C7 <> 4
-> R78C7 <> 4

12. C789 !
a) 12(2) @ R8 = [39/57]
b) ! XY-Wing: R2C8 = (78) and R3C9 = (89), R8C8 = (79) -> R9C9 <> 9
c) Hidden Single: R8C8 = 9 @ N9 -> R8C7 = 3
d) 13(3) = {256} -> R3C8 = 5, R4C7 = 2
e) R2C7 = 4 -> 12(2) = [48] -> R2C8 = 8
f) R3C9 = 9, R1C7 = 7, R9C7 = 8, R5C7 = 9

13. Rest is clean-up (might involve simple cage combo analysis) and singles.

Thanks for posting this Killer Sudoku mhparker!
Elaboration of Afmob's walkthrough by mhparker:
Hi folks,

It was interesting to see that both Gary and Afmob had similar breakthrough moves for solving this puzzle, namely......using the 4's in C19. However, Afmob made more eliminations than mentioned in Gary's solving outline, and (in particular) had already removed the 4 from r2c1, allowing a "purer" breakthrough combination to be used.

In particular, I would like to present the excellent combination used by Afmob to crack this puzzle to a wider audience, by elaborating on it below. It would be a shame to leave it buried at the end of a walkthrough that may only be read by a few. Also, I would like to express the first part of the combination in a somewhat different form to the way Afmob expressed it in hs WT.

To begin with, let's look at the grid state after Afmob's step 10:

Code:
.-----------------------.-----------------------.-----------.-----------------------.-----------------------.
| 4578        123       | 5689        5689      | 4578      | 46          79        | 123         123       |
|           .-----------'-----------.-----------'           '-----------.-----------'-----------.           |
| 5689      | 4679        4679      | 12356       1235689     139       | 45          78        | 123       |
:-----------+-----------------------+-----------.-----------.-----------+-----------------------+-----------:
| 123       | 45789       123       | 345789    | 12345789  | 2389      | 6           45        | 89        |
|           :-----------.           |           |           |           |           .-----------:           |
| 567       | 123456789 | 123456789 | 345789    | 123456789 | 2389      | 23        | 123456789 | 67        |
:-----------'           :-----------'-----------:           :-----------'-----------:           '-----------:
| 456         123456789 | 12345678    12345678  | 123456789 | 56          89        | 123456789   456789    |
:-----------.           :-----------.-----------:           :-----------.-----------:           .-----------:
| 6789      | 123456789 | 123456789 | 1234567   | 123456789 | 127       | 12345     | 123456789 | 23567     |
|           :-----------'           |           |           |           |           '-----------:           |
| 6789      | 456789      456789    | 2345678   | 23456789  | 278       | 12345       12345     | 12356     |
:-----------+-----------------------+-----------'-----------'-----------+-----------------------+-----------:
| 123       | 456789      456789    | 123456      123456789   1379      | 345         789       | 45678     |
|           '-----------.-----------'-----------.           .-----------'-----------.-----------'           |
| 123         123       | 46789       12346     | 56789     | 45          78        | 2345678     456789    |
'-----------------------'-----------------------'-----------'-----------------------'-----------------------'


From this position, Afmob essentially applied the following breakthrough combination:
11. Grouped X-Cycle with 5 links on 4 as follows:

(4)r89c9=r5c9-r5c1=r1c1-r2c23=r2c7 => r78c7<>4

This can be explained in verbose form as follows:
(i) Either r89c9 contains a 4 or
(ii) r89c9 does not contain a 4
(iii) => r5c9=4 (strong link, c9)
(iv) -> r5c1<>4 (weak link, r5)
(v) => r1c1=4 (strong link, c1)
(vi) -> r2c23<>4 (weak link, n1)
(vii) => r2c7=4 (strong link, r2)
Conclusion: r89c9 contains a 4 and/or r2c7 contains a 4
=> 4 can be eliminated from all common peers of r89c9 and r2c7
=> no 4 in r78c7; cleanup: no 8 in r8c8

12. r8c8 now {79}
=> XY-Wing on 9 with pivot at r2c8 and pincers at r3c9 and r8c8
=> no 9 in r9c9

This can be explained in verbose form as follows:
(i) Either r2c8 contains a 7, implying r8c8=9, OR...
(ii) ...r2c8 contains an 8, implying r3c9=9
=> At least one of r3c9 and r8c8 must contain a 9
=> no 9 in r9c9 (common peer of r3c9 and r8c8)

This left a hidden single in n9 at r8c8=9, cracking the puzzle.

Now that's what I call Sudoku! :D
Elaboration of Andrew's walk-through by mhparker:
sudokuEd wrote:
Andrew wrote:
here is how far I've got
In friendlier format.
Code:
.-------------------------------.-------------------------------.-------------------------------.
| 458       123       5689      | 5689      4578      46        | 79        123       123       |
| 589       4679      4679      | 1356      123569    139       | 45        78        123       |
| 123       45789     123       | 345789    12345789  2389      | 6         45        89        |
:-------------------------------+-------------------------------+-------------------------------:
| 567       123456789 1234567   | 345789    123456789 2389      | 23        123456789 67        |
| 456       123456789 12347     | 25678     123456789 56        | 89        123456789 456789    |
| 789       123456789 12345678  | 123567    123456789 127       | 12345     123456789 23567     |
:-------------------------------+-------------------------------+-------------------------------:
| 678       456789    456789    | 234678    2346789   278       | 12345     245       12356     |
| 123       456789    456789    | 1246      12346789  179       | 345       789       4567      |
| 123       123       46789     | 12346     56789     45        | 78        234678    46789     |
'-------------------------------.-------------------------------.-------------------------------'


Hi folks,

I note that, from Andrew's current position (Ed's marks pic), there's an interesting variation of Afmob's breakthrough move that can be applied (after a preliminary cleanup-like step that Andrew appears to have overlooked :wink:), which also cracks the puzzle. It's not often that something like this crops up in Killers, so I wouldn't want to let it go without a mention:

1. 8(3)n69 = {125/134}
1a. {13} only in r67c7
1b. -> no 4 in r67c7

Note: the 4 in n6 is now locked within the 20(4) cage, making the following move possible:

2. Grouped X-Cycle with 7 links on 4 as follows:

(4)r2c7=r3c8-r456c8=r5c9-r5c1=r1c1-r2c23=r2c7 => r2c7=4

This can be explained in verbose form as follows:
(i) Either r2c7 contains a 4 or...
(ii) ...r2c7 does not contain a 4
(iii) => r3c8=4 (strong link, n3)
(iv) -> r456c8<>4 (weak link, c8)
(v) => r5c9=4 (strong link, n6)
(vi) -> r5c1<>4 (weak link, r5)
(vii) => r1c1=4 (strong link, c1)
(viii) -> r2c23<>4 (weak link, n1)
(ix) => r2c7=4 (strong link, r2)
Conclusion: r2c7=4

This placement breaks the deadlock.

I thought this was worth mentioning because, although grouped X-Cycles with three links (aka. "grouped Turbot fishes") are relatively common in Killers, grouped X-Cycles with 5 links are much less common, and ones with 7 links (as in the above example) are rarer still.

P.S. Now off to "meet up" with Afmob at the Brick Wall...
Full Walkthrough by Para:
Hi all

I see all this talk about x-wing and x-cycles going on. When i solved this i used our basic killer techniques. There's no need really to go looking for these techniques in this puzzle really, but they are a nice shortcut. It is also solvable by just sticking to the basic killer techniques as 45-test cage combos and Killer Subsets.
I'll give my walk-through from Andrew's position, just to show how I solved the final bit of the puzzle. Some steps can be left out, but i just solved it again and didn't try to keep it short. Maybe later on I'll add the beginning steps if Andrew doesn't post his.

Complete Walk-Through Maverick 1:

1. R1C34 and R5C67 = {59/68} = {58..}: no 1,2,3,4,7

2. R1C67 = {49/67}: {58} blocked by R1C34: no 1,2,3,5,8

3. 6(3) at R1C8 = {123} -> locked for N3

4. R2C78 = {48/57} = {58..}: no 6,9

5. R2C23 = {49/67}: {58} blocked by R2C78: no 1,2,3,5,8

6. R34C1 and R67C9 = {17/26/35}: no 4,8,9

7. R34C4, R8C78 and R9C67 = {39/48/57}: no 1,2,6

8. R34C6 = {29/38/47/56}: no 1

9. R34C9 and R67C1 = {69/78}: no 1,2,3,4,5

10. R5C34, R67C4 and R67C6 = {18/27/36/45}: no 9

11. 8(3) at R6C7 = {125/134}: no 6,7,8,9

12. R8C23 = {49/58/67}: no 1,2,3

13. R9C34 = {19/28/37/46}: no 5

14. 6(3) at R8C1 = {123} -> locked for N7
14a. Clean up: R9C4: no 7,8,9

15. Killer Pair {69} in R1C34 + R1C67 -> locked for R1

16. Killer Pair {47} in R2C23 + R2C78 -> locked for R2

17. Killer Triple {123} in R34C1 + R89C1 -> locked for C1

18. Killer Triple {123} in R12C9 + R67C9 -> locked for C9

19. 15(3) at R1C1 = {159/168/249/258/267/348/357}: {456} blocked by R2C23: Needs one of {123} only place is R1C2 -> R1C2 = {123}
19a. Naked Triple {123} in R1C2 + R1C89 -> locked for R1

20. 45 on C789: 3 innies: R159C7 = {789} -> locked for C7
20a. Clean up: R1C6: no 7,9; R2C8: no 4,5; R5C6: no 8,9; R8C8: no 3,4,5; R9C6: no 7,8,9

21. 6 in N3 locked for R3

22. 45 on C789: 3 outies R159C6 = 15 = {456} -> locked for C6
22a. Clean up: R9C7: no 9; R34C6: no 7; R67C6: no 3

23. Killer Pair {28} in R34C6 + R67C6 -> locked for C6

24. 13(3) at R3C7 = [481/571/472]/{56}[2]/{46}[3] -> R3C8: no 9; R4C7 = {123}
24a. R3C7 = 6(hidden)
24b. Clean up: R3C8: no 7,8; R4C7: no 1; R4C9: no 9

25. 1 in C7 locked within 8(3) cage at R6C7 -> R7C8: no 1

26. 17(3) at R8C9 = {269/359/368/458/467} = {789..}: {179/278} blocked by R8C8 + R9C7: no 1
26a. Killer Triple {789} in R8C8 + R9C7 + 17(3) at R8C9 -> locked for N9
26b. Clean up: R6C9: no 1

27. 1 in N9 locked for R7
27a. Clean up: R6C46: no 8

28. 45 on N69: 4 innies: R4C79 + R59C7 = 25 = [2698/3787]: [2797/3697] blocked by R1C7: R4C9: no 8
28a. Clean up: R3C9: no 7

29. 8(3) at R6C7 = {12}[5]/{13}[4]/{15}[2]: {14}[3] blocked by R28C7: R67C7: no 4; R7C8: no 3

30. 4 in C7 locked within 12(2) cage in R2C78 + R8C78 -> 8 in C8 locked within R28C8: locked for C8

31. 8 in N6 locked in R5C79 for R5
31a. Clean up: R5C34: no 1

32. Clearly R3C9 = R5C7(check combos for {789} in C7 and N3) -> 8 in locked in R5C79; 8 locked in R35C9: locked for C9

33. 4 in N6 locked in 20(4) at R4C8 = {1469/147[8]/2459/246[8]/345[8]}(only place for 8 in R5C9): {3467} blocked by R4C9
33a. 20(4) can't have 2 of {245} in R456C8 because of R37C8: {2459/246[8]/345[8]} blocked
33b. 20(4) = {1469/147[8]} = {67..}: no 2,3,5; R5C9: no 7; 1 locked for N6 and C8(only place for 1 in R456C8);

34. R7C7 = 1(hidden single)
34a. Clean up: R6C9: no 7

35. 5 in N6 locked for R6
35a. Clean up: R7C4: no 4

36. 2 in C7 locked for N6
36a. Clean up: R7C9: no 6

37. Killer Pair {67} in R4C9 + 20(4) in R4C8 -> locked for N6
37a. Clean up: R7C9: no 2

38. Naked Pair {35} in R67C9 -> locked for C9
38a. R1C8 = 3(hidden single)

39. 3 in N1 loked for R3
39a. Clean up: R4C4: no 9; R4c6: no 8

40. 45 on C1234: 2 innies: R28C4 = {16/25}/[34]: no 7,8,9; R8C4: no 3

41. 9 in C4 locked for N2
41a. Clean up: R4C6: no 2

42. 45 on C6789: 2 innies: R28C6 = 10 = [19/37]: R8C6 = {79}

43. Killer Triple {789} in R8C23 + R8C6 + R8C8 -> locked for R8

44. 45 on R9: 2 outies + 1 innie: R8C19 = R9C5: Min R8C19 = 5 -> Min R9C5 = 5: no 1,2,3,4

45. 17(3) at R8C9 = [629]/[4]{67}: [6]{47} blocked by R9C67

46. 45 on R9: 3 innies and 1 outie: R8C1 + 17 = R9C589 = [1]-[5]{67}/[1]-[7][29]/[2]-[8][29]: R8C1: no 3; R9C5: no 6,9
46a. R9C589 = [5]{67}/[729]/[829] = {78..}

47. Killer Pair {78} in R9C589 + R9C7 -> locked for R9
47a. Clean up: R9C4: no 2,3

48. 9 in R2 locked for N1
48a. Clean up: R1C4: no 5

49. 45 on C1: 2 outies and 1 innie: R19C2 + 1 = R5C1: R19C2 = 3/4/5 -> R5C1 = {456}

50. R5C34 = {27/36}: {45} blocked by R5C16

51. 45 on C123: 3 innies: R159C3 = 16 = [529/826/574]: R1C3: no 6; R5C3: no 3,6
51a. Clean up: R1C4: no 8; R5C4: no 3,6

52. Naked Pair {27} in R5C34 -> locked for R5

53. 15(3) at R1C1 = [519/429]: [518] blocked by R1C3; [618/627] blocked by R67C1: R1C1 = {45}; R2C1 = 9
53a. Clean up: R2C23: no 4; R67C1: no 6

54. Naked Pair {67} in R2C23 -> locked for R2 and N1

And now it breaks down to naked and hidden singles.

greetings

Para
Walkthrough by Andrew:
Sorry for the delay in posting my walkthrough. I've now worked through Afmob's and Para's walkthroughs and Mike's analysis messages.

Thanks to Para and Mike for their encouragement which helped me finish this puzzle. :D If Para hadn't posted his partial walkthrough from my diagram, since expanded to a full walkthrough, and Mike hadn't given me off-forum encouragement, then I might have given up at the diagram stage. The fact that Mike pointed out that I'd missed a clean-up move in my diagram was also useful because, when I'd worked that out, it led directly to the next few steps.
Andrew wrote:
Maverick 1 felt to me at least as hard as any of the other 1.75s that I've done. I spent longer on it than on any of those others. It's definitely my longest walkthrough yet. Therefore I've no hesitation in rating Maverick 1 as 1.75.
Andrew wrote:
It's easy to forget that each of these ratings represent a range. Obviously, from what people say about A60RP-Lite, it must be at the very top of the 1.75 rating range.
I think the only important move that I missed was part of Para's step 33a. If I'd spotted that then I'd have been down to two combinations for the 20(4) cage in N6, instead of still having three, and would have been able to lock a second number in that cage. It took me a further 20 steps, from my step 46, to eliminate that combination for a completely different reason. Even if I'd spotted that extra move, I think I'd still have rated this puzzle 1.75 because of the time and thought I'd put in up to that stage.

Para's step 46 was impressive to spot that those innies/outie can be so useful. I also missed his step 50 which would have speeded up my later steps.

Afmob's breakthrough shortcut, his step 11a, was a nice use of simple chains. It depended, of course, on spotting that as well as two options for 4 in C1, he also spotted that there were two options for 4 in C9.

Mike's analysis showing a similar breakthrough, from the diagram that I posted earlier, was interesting. However I must admit it does look to me like a formalised way to express what is essentially a T&E step, starting from either R2C7 or R3C8 must be 4, using a long chain.

BTW That diagram was after step 42, but excluding sub-steps 24c and 36e to 36h which were added later.

I’ve tried as much as possible to avoid using hypotheticals and T&E to solve this problem. Some moves, for example step 42, are really combination analysis but are easier to present as if they were hypotheticals.

I must admit that at one stage, when I was stuck, I did look at hypotheticals based on the two permutations for the innies of N69 but the resulting long chains looked too much like T&E to me.

Here is my walkthrough for Maverick 1. I hope it's of interest. I did find a few things not in the other walkthroughs, for example the relationships between pairs of cages in C7, although only the one for R45C7 (step 40) proved useful. Many thanks to Ed for the comments and corrections.

Prelims

a) R1C34 = {59/68}
b) R1C67 = {49/67} (cannot be {58} which clashes with R1C34)
c) R2C23 = {49/58/67}, no 1,2,3
d) R2C78 = {39/48/57}, no 1,2,6
e) R34C1 = {17/26/35}, no 4,8,9
f) R34C4 = {39/48/57}, no 1,2,6
g) R34C6 = {29/38/47/56}, no 1
h) R34C9 = {69/78}
i) R5C34 = {18/27/36/45}, no 9
j) R5C67 = {59/68}
k) R67C1 = {69/78}
l) R67C4 = {18/27/36/45}, no 9
m) R67C6 = {18/27/36/45}, no 9
n) R67C9 = {17/26/35}, no 4,8,9
o) R8C23 = {49/58/67}, no 1,2,3
p) R8C78 = {39/48/57}, no 1,2,6
q) R9C34 = {19/28/37/46}, no 5
r) R9C67 = {39/48/57}, no 1,2,6
s) 6(3) cage in N3 = {123}, locked for N3, clean-up: no 9 in R2C78
t) 8(3) cage at R6C7 = 1{25/34}
u) 6(3) cage in N7 = {123}, locked for N7, clean-up: no 7,8,9 in R9C4

Must be getting close to a record number of prelims!!

1. Killer pair 6,9 in R1C34 and R1C67, locked for R1

2. R2C23 = {49/67} (cannot be {58} which clashes with R2C78), no 5,8

3. Killer pair 4,7 in R2C23 and R2C78, locked for R2

4. Killer triple 1,2,3 in R34C1 and R89C1, locked for C1

5. Killer triple 1,2,3 in R12C9 and R67C9, locked for C9

6. 45 rule on C1234 2 innies R28C4 = 7 = {16/25}/[34], no 7,8,9, no 3 in R8C4

7. 45 rule on C6789 2 innies R28C6 = 10 = {19/28}/[37/64], no 5, no 3,6 in R8C6

8. 45 rule on C12 4 innies R2378C2 = 26 = {2789/3689/4589/4679/5678}, no 1

9. 45 rule on C789 3 innies R159C7 = 24 = {789}, locked for C7, clean-up: no 7,9 in R1C6, no 4,5 in R2C8, no 8,9 in R5C6, no 3,4,5 in R8C8, no 7,8,9 in R9C6
9a. R34C6 = {29/38/47} (cannot be {56} which clashes with R5C6), no 5,6

10. 45 rule on C89 4 innies R2378C8 = 24 = {1689/2589/2679/3489/3579/3678/4578} (cannot be {4569} because R2C8 only contains 7,8)
10a. All combinations require two of 7,8,9 which must be in R28C8 -> no 7,8,9 in R3C8

11. Hidden triple 7,8,9 in N3 -> R3C9 = {789}, clean-up: no 9 in R4C9
[Alternatively, as Para pointed out, there is naked triple {456} in R2C7 + R3C78.]

12. 6 in N3 locked in R3C78, locked for R3 and 13(3) cage at R3C7, clean-up: no 2 in R4C1
12a. 13(3) cage at R3C7 = 6{25/34}, no 1
12b. 2,3 only in R4C7 -> R4C7 = {23}

13. R3C7 = 6 (hidden single in C7)

14. 1 in C7 locked in R67C7 -> no 1 in R7C8

15. 45 rule on C789 3 outies R159C6 = 15 = {456} (only remaining combination), no 3, clean-up: no 9 in R9C7
15a. Naked triple {456} in R159C6, locked for C6, clean-up: no 7 in R34C6, no 3 in R67C6
15b. R28C6 (step 7) = {19}/[37] (cannot be {28} which clashes with R34C6), no 2,8

16. 45 rule on C123 3 outies R159C4 = 17 = {179/269/278/359/368/458/467}
16a. 1 of {179} must be in R9C4 -> no 1 in R5C4, clean-up: no 8 in R5C3
16b. 4 of {458} must be in R9C4
16c. 6 of {467} must be in R1C4 and therefore the 4 must be in R9C4
16d. -> no 4 in R5C4, clean-up: no 5 in R5C3

17. 45 rule on C123 3 innies R159C3 = 16 = {169/178/259/268/349/358/367/457}
17a. 1,2,3 of {169/268/367} must be in R5C3 -> no 6 in R5C3, clean-up: no 3 in R5C4

18. 45 rule on C1 1 innie R5C1 – 1 = 2 outies R19C2, max R19C2 = 8, no 8 in R1C2

19. 45 rule on C9 2 outies R19C8 – 1 = 1 innie R5C9, min R5C9 = 4 -> min R19C8 = 5, no 1 in R9C8

20. 1 in N9 locked in R7C79, locked for R7, clean-up: no 8 in R6C46

21. 45 rule on R9 2 outies R8C19 = 1 innie R9C5, max R8C19 = 9, no 9 in R8C9
[Not sure why I didn’t also do Min R8C19 = 5 -> min R9C5 = 5. It would have avoided the complications of steps 36a to 36d.]

22. 45 rule on N1 2 innies R1C3 + R3C1 – 5 = 1 outie R4C3
22a. IOU no 5 in R3C1, clean-up: no 3 in R4C1
22b. R1C3 + R3C1 cannot total 14 -> no 9 in R4C3

23. 15(3) cage in N1 = {159/249/258/348/357/456} (cannot be {168/267} because R12C1 = [76/86] clashes with R67C1)
23a. 3 of {357} must be in R1C2 -> no 7 in R1C2

24. 45 rule on N7 2 innies R7C1 + R9C3 – 9 = 1 outie R6C3
24a. IOU no 9 in R7C1, clean-up: no 6 in R6C1
24b. Max R7C1 + R9C3 = 17 -> no 9 in R6C3
24c. Deleted.
[Alternatively step 24b comes from min R7C23 = 9 -> max R6C3 = 8.]

25. 45 rule on N9 3 innies R7C789 – 4 = 1 outie R9C6
25a. R9C6 = {45} -> R7C789 = 8,9 and must contain 1 (step 20) = 1{25/26/34/35}, no 7, clean-up: no 1 in R6C9

26. Hidden killer triple 7,8,9 in N9 -> 17(3) cage must contain one of 7,8,9 = {269/359/458/467} (cannot be {278} which contains both of 7,8 (it also clashes with R9C7), cannot be {368} because that leaves no valid cell for 9 in N9)
[Alternatively cannot be {368} because R89C9 = {68} clashes with R34C9. That’s more direct but I saw the other reason first.]
26a. 2 of {269} and 3 of {359} must be in R9C8 -> no 9 in R9C8
26b. If {359} => R8C78 = {48} => R9C67 = [57]
26c. If {458} => R9C67 = [57]
26d. -> 5 of {359/458} must be in R8C9 -> no 8 in R8C9, no 5 in R9C89
26e. R89C9 cannot be {67} which clashes with R34C9

27. 5 in R9 locked in R9C56, locked for N8, clean-up: no 2 in R2C4 (step 6), no 4 in R6C4

28. 1,2,3 in N1 only in R1C2 and R3C123
28a. 45 rule on N1 3 innies R3C123 – 3 = 1 outie R1C4
28b. Min R1C4 = 5 -> min R3C123 = 8 so cannot be {123} -> R1C2 = {123}

29. Naked triple {123} in R1C2 and R1C89, locked for R1

30. 15(3) cage in N1 (step 23) = {159/249/258/348/357} (cannot be {456} which is blocked by R1C2), no 6
30a. Cannot be {357} because R12C1 = [75] => R67C1 = [96] -> no valid combinations for R34C1
30b. 15(3) cage = {159/249/258/348}, no 7
30c. Killer pair 8,9 in R12C1 and R67C1, locked for C1

31. Max R19C2 = 5 -> max R5C1 = 6 (step 18)
[This would also have worked for step 30c but I saw the killer pair first.]
[Ed pointed out R5C34 cannot be [45] because of R5C16. Nice ALS block! I didn’t get this elimination until step 68a but I don’t think that affected the solving path.]

32. R19C2 = {123} -> 20(4) cage in N4 cannot contain more than one of 1,2,3
32a. 20(4) cage = {1469/1478/1568/2459/2468/2567/3458/3467} (cannot be {1289/1379/2369/2378} which contain two of 1,2,3)
32b. Killer triple 1,2,3 in R19C2 and R456C2, locked for C2

33. Hidden triple {123} in N1 -> R3C13 = {123}, clean-up: no 1 in R4C1

34. 12(3) cage at R3C2, min R3C23 = 5 -> max R4C3 = 7

35. 8 in C7 locked in R59C7
35a. 45 rule on N69 4 innies R4C9 + R459C7 = 25 = [6298/7387] (listed in the order R4C9 + R459C7, to make it easier to work out R459C7, rather than normal cage order, cannot be [6397/7297] which clash with R1C7, cannot be [8287] which would repeat 8 in N6) -> no 8 in R4C9, clean-up: no 7 in R3C9

36. 17(3) cage in N9 (step 26) = {269/359/458/467}
36a. {269/359/458} and {467} with 4 in R9C89 all have one of 2,3,4 in R9C89
36b. If 4 of {467} in R8C9 => R9C89 = {67} => R9C67 = [48]
36c. -> one of 2,3,4 in R9C689
36d. Killer quad 1,2,3,4 in R9C12, R9C34 and R9C689, locked for R9
[Alternatively there’s the simpler Min R8C19 = 5 -> min R9C5 = 5 (step 21) but I only saw that afterward. Strange how it’s sometimes easier to see more difficult steps!]
36e-h. Deleted. These sub-steps have been moved to step 44.

37. 45 rule on R2 5 innies R2C14569 = 20 = {12359/12368}
37a. 8 of {12368} must be in R2C1 -> no 8 in R2C5

38. 17(4) cage in N2 = {1259/1268/1349/1358/1367/2357} (cannot be {1457/2348} because 4,7,8 only in R1C5, cannot be {2456} which clashes with R1C6)
[Ed pointed out that 17(4) cage in N2 must have two of 1,2,3 in R2 which would have simplified the combination eliminations for this step.]

39. R3C7 = 6 -> R3C8 + R4C7 = 7
39a. R2C7 + R3C8 = {45} = 9
39b. -> R2C7 – 2 = R4C7, R24C7 = [42/53]

40. R4C9 + R459C7 (step 35a) = [6298/7387] -> R45C7 = [29/38] = 11
40a. 45 rule on N6 3 remaining innies R4C9 + R6C79 = 14 = {167/257/347/356}

41. If R6C7 = 1 -> R7C9 = 1 (step 20) -> R6C9 = 7
41a. If R6C7 <> 1 -> R7C7 = 1 -> R7C9 <> 1 -> R6C9 <> 7
41b. -> R6C79 = [17] or R6C7 <> 1 and R6C9 <> 7

42. R7C8 cannot be 3, here’s how
42a. R7C8 = 3 -> R67C7 = {14} => R2C7 = 5 clash with R8C7
42b. -> no 3 in R7C8

43. 8(3) cage at R6C7 = 1{25/34}
43a. 4 of {134} must be in R7C8 -> no 4 in R67C7

44. 4 in C7 locked in R28C7
44a. Either R2C78 or R8C78 must be [48] -> 8 locked in R28C8, locked for C8
[Ed commented that each of the 8s locked in R28C8 forces 9 into C9 for the same nonet -> no 9 in R5C9]
44b. 17(3) cage in N9 (step 26) = {269/359/458/467}
44c. 4 of {458} must be in R9C8
44d. 4 of {467} must be in R8C9, here’s how
44da. 4 of {467} in R9C8 => R89C9 = {67} clashes with R4C9
44db. 4 of {467} in R9C9 => R9C67 = [57] clashes with {467}
44e. -> no 4 in R9C9
44f. -> no 7 in R8C9 (step 44d)


45. 8 in N6 locked in R5C79, locked for R5, clean-up: no 1 in R5C3

46. 4 in N6 locked in 20(4) cage = {1469/1478/2459} (cannot be {2468} which clashes with R45C7, cannot be {3458} because R456C8 = {345} clashes with R3C8, cannot be {3467} which clashes with R4C9), no 3
46a. 8 of {1478} must be in R5C9 -> no 7 in R5C9
46b. If {1469} => R5C67 = [68] -> no 6 in R5C89
[Para also eliminated {2459} because cannot have two of {245} in R456C8 which would clash with R37C8.]

47. R4C9 + R6C79 (step 40a) = {167/257/356}
47a. 1 of {167} must be in R6C7 => 7 must be in R6C9 (step 41b)
47b. 6 of {356} must be in R4C9
47c. -> no 6 in R6C9, clean-up: no 2 in R7C9

48. 45 rule on N9 3 outies R6C79 + R9C6 = 12
48a. R4C9 + R6C79 = 14 (step 40a)
48b. -> R4C9 – 2 = R9C6
48c. -> R3C9 – 1 = R9C7

49. From steps 48b and 48c R3C9 = 8 or R9C7 = 8 -> no 8 in R9C9
49a. 17(3) cage in N9 (step 36) = {269/359/467}
49b. 4 of {467} must be in R8C9 (step 44d) -> no 4 in R9C8

50. R159C4 (step 16) = {179/269/278/359/368/458/467}
50a. 8,9 of {359/458} must be in R1C4 -> no 5 in R1C4, clean-up: no 9 in R1C3
50b. If R159C4 = {368} => 9 in C4 locked in R34C4 = {39} clashes with R159C4
50c. -> no {368} in R159C4 = {179/269/278/359/458/467}

51. No 5 in R1C5, here’s how
51a. R1C34 = [59]/{68}
51b. If [59] -> no 5 in R1C5
51c. If {68} => R1C67 = [49] => R1C1 = 5
51d. -> no 5 in R1C5

52. 5 in R1 locked in R1C13, locked for N1

53. 15(3) cage in N1 (step 30b) = {159/249/258/348}
53a. R2C1 = {89} -> no 8 in R1C1

54. Killer triple 4,5,6 in R1C1, R1C34 and R1C6, locked for R1
54a. Killer triple 7,8,9 in R2C1, R2C23 and R2C8, locked for R2
54b. 9 in R2 locked in R2C123, locked for N1

55. 15(3) cage in N1 (step 30b) = {159/249/258/348}
55a. Cannot be {348}, here’s how
55b. R1C2 = 3, R12C1 = [48] => R2C23 = {67} -> R12C1 and R2C23 clash with R3C2
55c. -> no {348} in 15(3) cage = {159/249/258}, no 3
55d. 3 in N1 locked in R3C13, locked for R3, clean-up: no 9 in R4C4, no 8 in R4C6
55e. 3 in R1 locked in R1C89, locked for N3

56. 9 in C4 locked in R13C4, locked for N2, clean-up: no 2 in R4C6, no 1 in R8C6 (step 7)
[The second clean-up step should have been in step 54a but I forgot about it until here.
At this stage I also overlooked that R8C23, R8C6 and R8C8 form killer triple 7,8,9 for R8 which would have been much simpler than step 57 which only achieves this result.]


57. 45 rule on C5 4 innies R1289C5 = 20 = {1289/1379/1478/1568/2378/2567/3458/3467} (cannot be {1469/2369/2459} because R1C5 only contains 7,8, cannot be {2468} because R12C5 = [82] clashes with R3C6)
57a. 1,2,3,4 of {1289/1379/1478/2378/2468/3458/3467} must be in R28C5
57b. 8 of {1568} must be in R1C5
57c. 7 of {2567} must be in R1C5
57d. -> no 7,8,9 in R8C5

58. 3 in N2 locked in 17(4) cage
58a. 45 rule on N2 5 innies R1C46 + R3C456 = 28 with 9 locked in R13C4 = {14689/24589/24679} (cannot be {15679} because R3C6 only contains 2,8)
58b. {14689} must be [64918/96418] because R1C7 = 9 when R1C6 = 4
58c. {24589} must be [84952] because R1C7 = 9
58d. {24679} must be [64972/96472/96742] because R1C7 = 9 when R1C6 = 4
58e. -> no 5,8 in R3C4, no 2,8 in R3C5, clean-up: no 4,7 in R4C4
[Ed commented about step 58b
Actually, the first is blocked: [918] clashes with {89} in R3C9. But this doesn't make any additional elims I don't think. Actually, a nice little chain eliminates both. Innies = {14689} -> R2C6 = 3 => R4C6 = 9 => R3C6 = 2: but no 2 in innies {14689}. This would be nice because it locks 2 in innies and from the end of step 58 this must be R3C6!]


59. 17(4) cage in N2 (step 38) must contain 3 = {1358/1367/2357}
59a. 1 in C6 locked in R26C6
59b. If R2C6 <> 1 => R6C6 = 1 => R7C6 = 8 => R3C6 = 2 => R23C6 = [32]
59c. -> 17(4) cage cannot be {2357}

60. 17(4) cage in N2 (steps 59 and 59c) = {1358/1367}, no 2, 1 locked for N2

61. R3C6 = 2 (hidden single in N2), R4C6 = 9, R8C6 = 7, R67C6 = [18], R2C6 = 3, clean-up: no 6 in R4C1, no 7 in R6C1, no 2 in R6C4, no 7 in R6C9 (step 41b), no 1 in R7C9, no 6 in R8C23, no 5 in R8C7

62. R1C2 = 2 (hidden single in N1)

63. R2C9 = 2 (hidden single in R2), clean-up: no 6 in R7C9
[This should have been naked single in step 60 but I overlooked that 1 was also locked for R2.]

64. R7C7 = 1 (hidden single in C7)

65. Naked pair {35} in R67C9, locked for C9 -> R1C89 = [31]

66. Naked triple {235} in R4C7 + R6C79, locked for N6
[That’s now made the combination elimination from the 20(4) cage that I missed at step 46!]

67. 5 in N9 locked in R7C89, locked for R7

68. 5 in N7 locked in R8C23 = {58}
68a. Naked pair {58} in R8C23, locked for R8 and N7 -> R8C8 = 9, R8C7 = 3, R46C7 = [25], R67C9 = [35], R2C78 = [48], R3C89 = [59], R1C67 = [67], R1C5 = 8, R1C34 = [59], R12C1 = [49], R8C23 = [58], R9C7 = 8, R5C67 = [59], R9C6 = 4, R5C1 = 6, R67C1 = [87], clean-up: no 1 in R3C1, no 7 in R3C4, no 3 in R4C4, no 3,4 in R5C3, no 6 in R7C4, no 6 in R9C3, no 2,3,6 in R9C4

69. R34C1 = [35] (naked pair), R3C3 = 1, R34C4 = [48] (naked pair), R3C5 = 7, R3C2 = 8, R9C34 = [91] (naked pair), R9C12 = [23], R8C1 = 1, R2C45 = [51]
69a. R5C3 = 2 (step 17), R5C4 = 7, clean-up: no 2 in R7C4
69b. R67C4 = [63] (naked pair) -> R8C45 = [26], R8C9 = 4, R9C5 = 5, R5C9 = 8, R7C5 = 9

70. R4C9 = 6, R9C89 = [67]

71. R4C3 = 3 (hidden single in C3), R456C5 = [432]

72. R7C23 = {46} -> R6C3 = 7 (cage sum)

and the rest is naked singles


Last edited by Ed on Tue Dec 09, 2008 9:24 am, edited 2 times in total.

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PostPosted: Mon Jul 14, 2008 4:25 am 
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Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Assassin 74 by Ruud (Oct 07)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:1536:1536:5122:5122:2820:2821:2821:5383:5383:1536:4618:5122:3340:2820:4878:2821:4112:5383:4618:4618:3340:3340:2820:4878:4878:4112:4112:4123:4380:4380:3102:4127:4127:5665:1826:1826:4123:4123:4380:3102:3102:4127:5665:5665:1826:3373:3374:3374:3888:3889:3889:3635:5172:5172:3373:3373:3374:3888:3888:3889:3635:3635:5172:6207:1856:1856:5186:3139:3139:3141:3910:3910:6207:6207:1856:5186:5186:3139:3141:3141:3910:
Solution:
+-------+-------+-------+
| 1 2 8 | 3 5 6 | 4 9 7 |
| 3 6 9 | 8 4 7 | 1 2 5 |
| 5 7 4 | 1 2 9 | 3 6 8 |
+-------+-------+-------+
| 2 8 6 | 7 3 5 | 9 4 1 |
| 9 5 3 | 4 1 8 | 6 7 2 |
| 4 1 7 | 6 9 2 | 5 8 3 |
+-------+-------+-------+
| 6 3 5 | 2 7 4 | 8 1 9 |
| 7 4 1 | 9 8 3 | 2 5 6 |
| 8 9 2 | 5 6 1 | 7 3 4 |
+-------+-------+-------+
Quote:
Andrew: This one flowed easily for quite a time, then got a bit stubborn so I'll rate it at 1.0..
CathyW: 13 placements during lunch break
Afmob: This assassin was pretty straightforward but it took me quite a while to finish it since I found no obvious shortcuts..Rating: 1.0
gary w: perhaps this was about a 1.0? Took me about 2.5 hours..I notice Ruud likes to use 3 cages but he excelled himself here.. and all but one was L shaped.
Walkthrough by sublue including Venn Diagram logic and algebra:
Hi guys! I'm a newbie, so please be merciful. Please forgive any notation errors (turns out it's harder to explain one's thinking than to just solve these).

Editted thrice for corrections and clarifications (thanks to Mike and Andrew).

Thank you for your patience with the "New Kid." My apologies to everyone for using the wrong brackets throughout. I was a math major in a former life, and my brain has yet to adjust. I also apologize for mixed case in labeling nonets, rows and columns. I typed everything lower case, but my computer insists on capitalizing the first letter of every sentence.


Prelims:
1) 6(3) n1 = [1,2,3] locked for n1.
2) 20(3) n12: r1c4 => no 1,2
3) 24(3) n7 = [7,8,9] locked for n7
4) 7(3) n7 = [1,2,4] locked for n7
a) R7c123 = [3,5,6] locked for n7, r7.
5) Both 11(3) n2 no 9
6) 19(3) n23 no 1
7) 20(3) n8 no 1,2
8) 21(3) n3 no 1,2,3
9) 22(3) n6 no 1,2,3,4. 9 is locked into 22(3) cage for n6.
10) 7(3) n6 = [1,2,4] locked for n6
11) 20(3) n69 no 1,2

Solving:
Draw in Hidden cages with 45 and Outies
12) R123c3 is 21(3)

13) R123c4 is 12(3)

14) R123c7 is 8(3)
a) R123c7 no 6,7,8,9 and 1 is locked to 8(3) cage and r12c7 for n3, c7.

15) R123c6 is 22(3)
a) R1c6 no 1
b) R123c6 no 2,3,4
c) 9 is locked r23c6 for n2, 19(3) and c6.
i) 19(3) n23 no 5.

16) R6c123 is 12(3)

17) R7c123 is 14(3)

18) R6c456 is 17(3)

19) R7c456 is 13(3)

20) R6c789 is 16(3)

21) R7c789 is 18(3)

Using Venn Diagram logic and algebra, eliminate some choices with “paired” up hidden cages:

(Note: Venn Diagrams are the math major in me leaking out again. Think of the MasterCard symbol. One circle contains all left-handed persons. The other circle contains all blue-eyed people. The overlap area is left-handed blue-eyed people. The area on the card outside the circles is everybody else. I'm told that normal people call this a variant of innies and outies. Para can attest that my brain is having a hard time with that concept.)
22) R7c3 – 1 = r6c1 = (2,4,5)
a) If r6c1 is 5, conflict with n47 13(3), so r6c1 <> 5 and r7c3 <> 6.
b) R6c23 = (1,2,4,6,7,8,9)

23) R7c6 +2 = r6c4 = (3,4,6,9); r7c6 has no 8.

24) R6c7 + 4 = r7c9 = (7,9); r 6c7 is (3,5)

25) R3c7 + 3 = r1c6 = (5,6,7)

Innies & Outies:
26) Innies c89: r579c8 hidden 11(3)
a) No 9 in r579c8
b) See step 9), 9 is now locked to r45c7 for 22(3), n6 and c7.

27) Outies c6789: r468c5 hidden 20(3)
a) R468c5 no 1,2

28) Outies c1234: r579c5 hidden 14(3)

29) Innies c12: r468c2 hidden 13(3)

Picking off choices:
30) N6 hidden 16(3) r6c789 has locked 3, since n/e in r6.
a) No 3 in r6c456 => r7c6 no 1

31) N9 12(3) r89c7 min 5 => r9c8 max 7, so no 8.

32) Step 14a) locks 1 to n23 11(3) => no 2,5 in 11(3)

33) Hidden 8(3) from step 14a) => can’t have 2; r123c7 = (1,3,4) => Naked Triple (1,3,4) for hidden 8(3), n3 and c7.
a) Naked Single 5 at r6c7
i) Cleanup 5s from r7, c7 and n6.
ii) N69 14(3) r7c8 no 4,8.

34) N6 hidden 16(3): since r6c7 = 5, r6c89 = {3,8} locked to N6 hidden 16(3), n69 20(3) and r6.
a) Cleanup: n69 20(3): r7c9 = 9.
i) Cleanup 9s from r7, n9,c9.

35) Step 15c) has 9 locked in n2 19(3). Since r3c7 = (3,4), r23c6 <> 8.
a) N2 hidden 22(3) r123c6 is now a locked triple (6,7,9).
i) Cleanup 6s and 7s at n2, c6:
ii) R6c4 <> 9.

36) N58 15(3) at r6c56 + r7c6 must be r6c5 = 9 and r67c6 = {2,4} NP locked for N4.
a) NP {2,4} at r6c1 and r6c6 locked for R6.

b) Cleanup 9s r6, c5, n5:
c) Cleanup 2s and 4s r6, c6: NS r6c4 = 6.
d) Cleanup 6s r6, c4, n5.
e) N47 13(3) has r6c23 = {1,7} NP locked for N4, thus r7c3 = 5.
f) Cleanup 1s,7s n4, 5s r7, c3: r6c1 = 4 => r6c6 =2 => r7c6 = 4.

37) N58 15(3) at r67c4 + r7c5 has locked 2s in r7c45 => r7c45 = (2,7).
a) Cleanup of 2s and 7s => r7c7 = 8 and r7c8 = 1.

38) N9 12(3) r89c7 = (2,6,7) => r9c8 = (3,4)

39) N58 split hidden 20(3) r6c5 = 9 => r4c5 = (3,5,8) and r8c5 = (3,6,8)

40) N8 12(3) has locked 1 in r89c6 since n/e.
a) Cleanup c5: no 1 in r45c6 => NT at n5 16(3) = (3,5,8)
b) Cleanup 3s,5s,8s from N5: NT at n5 12(3) = (1,4,7)

41) N2 r3c45 locked 1 since n/e in r3.

42) N3 16(3) has locked 2 => no 7 in 16(3)

43) N1 hidden 21(3) must have an 8, so 8 locked in n1 r123c3 and c3.

44) Cannot be a 3 in r4c2.

45) R1c4 + 1 = r3c3 = (4,6,9) and r1c4 = (3,5,8)

46) N1 hidden 21(3) now has 8 locked in r12c3 => must be an 8 in n12 20(3)=> no 8 in r1c4 and no 4 or 6 in r12c3.

47) Repeat of step 45 => now no 9 in r3c3.

48) Check combinations in n12 13(3) => no 8 in r3c4.

49) N2 11(3) r12c5 min 5 => max 6 for r3c5 => no 8.

50) 8 now locked in n3 16(3) in r3c89 since n/e in row.

51) N3 check combos in 21(3) => no 6.=> r1c8 = 9 and r12c9 = (5,7) locked.

52) N1 6(3) has 1 locked in r12c1 since n/e in col.

53) N9 HS r8c8 = 5.

54) N2 HS r1c6 = 6.
a) Thus n23 11(3) r12c7 = (1,4) and r3c7 = 3.

55) N4 17(3) has 3 locked in r45c3 since n/e in col. => no 2 in 17(3).

56) N7 7(3) has 2 locked in r89c3 since n/e in col.

57) Check combos on n47 split hidden 13(3) r468c2 => no 6 or 9 in r4c2.

58) Naked Triple r4c256 = (3,5,8).

59) Cleanup results in HS at r5c3 = 3.

60) N9 12(3) has 7 locked in r89c7 since n/e in n9.
a) R89c7 = (2,7) and r9c8 = 3
b) Cleanup n6 22(3) r45c6 = (6,9) and r5c8 = 7.

61) Cleaning up now getting wild:

62) R4c4 = 7 Hidden Single.

63) NP (6,9) at r4c37 => r4c1 = 2

The rest just seems to fall out as hidden singles and naked singles with iterative cleanups.
Susan
Walkthrough by Andrew including grouped X-wing:
Hi Susan

Welcome to the forum! As a retired engineer it's good to welcome another engineer. It's even better that a newbie posts the first walkthrough for a new Assassin. :D Keep up the good work and we look forward to more of your walkthroughs.

This one flowed easily for quite a time, then got a bit stubborn so I'll rate it at 1.0.
Ruud wrote:
Computer programs would tell you there's no symmetry in this Assassin. We humans know better.
There was certainly plenty of pattern repetition giving repeating themes for the solving path. That made it fairly easy with the given cage totals but I suspect it could have been extremely difficult with different totals. Oops, have I invited a variant for the weekend? :wink: I suspect that there was going to be either a variant or a new puzzle this weekend anyway.

Here is my walkthrough. I'll have another look at it tomorrow (well later today since it's already after midnight) to see if I can move step 31 earlier and if that simplifies the later steps.

OK, done that. It didn't make much difference but I said I'd do it.
Previous steps 31 and 32 are now 25 and 26 with resulting renumbering and a few minor corrections.


Prelims

a) 6(3) cage in N1 = {123}, locked for N1
b) 20(3) cage at R1C3 = {389/479/569/578}, no 1,2
c) R123C5 = {128/137/146/236/245}, no 9
d) 11(3) cage at R1C6 = {128/137/146/236/245}, no 9
e) 19(3) cage at R2C6 = {289/379/469/478/568}, no 1
f) 21(3) cage in N3 = {489/579/678}, no 1,2,3
g) 22(3) cage in N6 = 9{58/67}, 9 locked for N6
h) 7(3) cage in N6 = {124}, locked for N6
i) 20(3) cage at R6C8 = {389/479/569/578}, no 1,2
j) 24(3) cage in N7 = {789}, locked for N7
k) 7(3) cage in N7 = {124}, locked for N7
l) 20(3) cage in N8 = {389/479/569/578}, no 1,2

1. Naked triple {356} in R7C123, locked for R7

2. 3 in N6 locked in R6C789, locked for R6
2a. R6C789 = 3{58/67}

3. 45 rule on N9 3 innies R7C789 = 18 = {189/279} = 9{18/27}, no 4, 9 locked for R7 and N9
3a. 45 rule on N8 3 innies R7C456 = 13 = {148/247} = 4{18/27}, 4 locked for N8

4. 20(3) cage in N8 = {389/569/578} -> 12(3) cage in N8 must have 3/5 = {138/156/237}, no 9
[Alternatively 12(3) cage must have 1/2 from step 3a.]
4a. 9 in N8 locked in 20(3) cage = {389/569}, no 7

5. 45 rule on N7 1 innie R7C3 – 1 = 1 outie R6C1 -> R6C1 = {245}
5a. 13(3) cage at R6C1 = {256/346} (only remaining combinations) = 6{25/34}, 6 locked in R7C12, locked for R7, clean-up: no 5 in R6C1 (step 5)
[Alternatively 2,4 only in R6C1 -> R6C1 = {24}, R7C3 = {35} (step 5).]

6. 13(3) cage at R6C2 = {139/157/256/346} (cannot be {148/247} because R7C3 only contains 3,5, cannot be {238} which clashes with R6C1 = 2 because 3 of {238} is in R7C3), no 8
6a. 5 of {157/256} must be in R7C3 -> no 5 in R6C23

7. 45 rule on N8 1 outie R6C4 – 2 = 1 innie R7C6 -> R6C4 = {469}, R7C6 = {247}

8. 15(3) cage at R6C4 = {168/249/267}
8a. 9 of {249} must be in R6C4 -> no 4 in R6C4, clean-up: no 2 in R7C6 (step 7)

9. 15(3) cage at R6C5 = {249/267} (cannot be {159/168/258} because R7C6 only contains 4,7, cannot be {456} which clashes with R6C4 = 6 because 4 of {456} is in R7C6) = 2{49/67}, no 1,5,8, 2 locked for R6 and N5 -> R6C1 = 4, R7C3 = 5 (step 5)
9a. 7 of {267} must be in R7C6 -> no 7 in R6C56

10. Grouped X-wing 3 in 6(3) cage at R1C1 and split-cage R7C12, locked for C12
10a. 3 in C3 locked in 17(3) cage at R4C2 = 3{59/68}, no 1,2,7
10b. 5 of {359} must be in R4C2 -> no 9 in R4C2

11. Naked triple {269} in R6C456, locked for R6 and N4, clean-up: no 7 in R6C789 (step 2a)

12. Naked pair R6C23 = {17}, locked for N4

13. Naked triple {358} in R6C789, locked for N6

14. 45 rule on N3 3 innies R123C7 = 8 = 1{25/34}, 1 locked for C7 and N3
14a. 1 locked in R12C7 for 11(3) cage -> no 1 in R1C6
14b. 11(3) cage = 1{28/37/46}, no 5
14c. 6,7,8 only in R1C6 -> R1C6 = {678}

15. 45 rule on N3 1 outie R1C6 – 3 = 1 innie R3C7 -> no 2 in R3C7

16. 45 rule on N9 1 innie R7C9 – 4 = 1 outie R6C7 -> R6C7 = {35}, R7C9 = {79}
16a. R7C789 (step 3) = {189/279}
16b. 1 of {189} must be in R7C8 -> no 8 in R7C8

17. 19(3) cage at R2C6 = {379/469/478/568} (cannot be {289} because R3C7 only contains 3,4,5), no 2
17a. R3C7 = {345} -> no 3,4,5 in R23C6

18. 45 rule on N3 3 outies R123C6 = 22 = {679} (only remaining combination), no 8, clean-up: no 2 in R12C7 (step 14b), no 5 in R3C7 (step 15)
18a. Naked triple {679} in R123C6, locked for C6 and N2 -> R67C6 = [24], R6C5 = 9, R6C4 = 6

19. Naked triple {134} in R123C7, locked for C7 and N3 -> R6C7 = 5, R7C9 = 9 (step 16)

20. R89C7 must contain 2 (cannot make 12(3) with other combinations of 6,7,8 in R89C7) -> 2 locked in R89C7 for N9, clean-up: no 7 in R7C78 (step 3) -> R7C78 = [81]
20a. 12(3) cage in N9 = {237/246}, no 5
20b. 3,4 only in R9C8 -> R9C8 = {34}

21. 45 rule on N1 3 innies R123C3 = 21 = {489/678} = 8{49/67}, 8 locked for C3 and N1, clean-up: no 6 in R4C2 (step 10a)

22. 45 rule on N1 3 outies R123C4 = 12 = {138/345} = 3{18/45}, no 2, 3 locked for C4 and N2

23. R7C4 = 2 (hidden single in C4), R7C5 = 7

24. 7 in C4 locked in 12(3) cage at R4C4 = {147} (only remaining combination), locked for N5

25. Naked triple {358} in R4C256, locked for R4

26. R5C3 = 3 (hidden single in C3)

27. 20(3) cage in N8 (step 4a) = {389/569}
27a. 3,6 only in R9C5 -> R9C5 = {36}

28. 21(3) cage in N3 = {579/678}, 7 locked for N3
28a. 9 of {579} locked in R1C8 -> no 5 in R1C8

29. 45 rule on N1 1 innie R3C3 – 1 = 1 outie R1C4 -> R1C4 = {358}, R3C3 = {469}

30. 8 in C3 locked in R12C3 for 20(3) cage at R1C3 -> no 8 in R1C4, clean-up: no 9 in R3C3 (step 29)
30a. 20(3) cage = 8{39/57}, no 4,6

31. 13(3) cage at R2C4 = {148/346} = 4{18/36}, no 5
31a. CPE no 4 in R3C5

32. 1 in C6 locked in R89C6 -> no 1 in R8C5
32a. 12(3) cage in N8 = 1{38/56}
32b. 6 of {156} must be in R8C5 -> no 5 in R8C5

33. 2 in C3 locked in R89C3, locked for N7
[Alternatively Grouped X-wing 2 in 6(3) cage at R1C1 and 16(3) cage at R4C1, locked for C12.]

34. 9 in C7 locked in R45C7, locked for N6

35. 1 in R3 locked in R3C45, locked for N2

36. R123C5 = {128/245}
36a. 1 of {128} must be in R3C5 -> no 8 in R3C5

37. 13(3) cage at R2C4 (step 31) = {148/346}
37a. 1 of {148} must be in R3C4 -> no 8 in R3C4

38. 8 in R3 locked in R3C89, locked for N3, clean-up: no 6 in 21(3) cage (step 28)
38a. 21(3) cage in N3 = {579} (only remaining combination) -> R1C8 = 9
38b. Naked pair {57} in R12C9, locked for C9 and N3

39. R1C6 = 6 (hidden single in R1), clean-up: no 3 in R12C7 (step 14b)

40. R3C7 = 3 (hidden single in C7)

41. 13(3) cage at R2C4 (step 31) = {148/346}
41a. 3 of {346} must be in R2C4 -> no 4 in R2C4

42. R8C8 = 5 (hidden single in C8)
42a. R89C9 = 10 = {46} (only remaining combination)
42b. Naked pair {46} in R89C9, locked for C9 and N9 -> R9C8 = 3, R6C89 = [83], R9C5 = 6, R89C9 = [64], clean-up: no 8 in R89C4 (step 4a)
42c. R89C4 = [95]

43. R1C4 = 3, R2C4 = 8, clean-up: no 7 in R12C3 (step 30a), no 6 in R3C3 (step 29), no 4 in R3C4 (step 31)
43a. R12C3 = [89]
43b. R3C34 = [41]

44. R4C3 = 6 (naked single), R4C2 = 8

45. R8C2 = 4 (hidden single in C2)

46. Naked pair {26} in R23C8, locked for C8 and N3

and the rest is naked singles
Walkthrough by Afmob with no shortcuts:
This assassin was pretty straightforward but it took me quite a while to finish it since I found no obvious shortcuts. So to my surprise the walkthrough for A74 is much longer than the one for M1 although M1 was more difficult.

Walkthrough for A74:

1. N7
a) 7(3) = {124} locked
b) 24(3) = {789} locked
c) Naked triple {356} locked in R7C123 for R7
d) 13(3) @ R6C1: R7C12 = {35/36/56} -> R6C1 = (245)
-> R6C1 <> 5 since R7C12 would be {35}
-> 13(3) = 6{25/34} -> 6 locked for N7

2. N89
a) Innies N8 = 13(3) = 4{18/27} because of step 1c -> 4 locked for R7+N8
b) Killer pair (78) of Innies of N8 blocks {578} of 20(3)
c) 20(3) = 9{38/56} -> 9 locked for N8
d) Innies N9 = 18(3) = 9{18/27} -> 9 locked for N9

3. N6
a) 22(3) = 9{58/67} -> 9 locked
b) 7(3) = {124} locked
c) Innies = 16(3) = 3{58/67} -> 3 locked for R6
d) 14(3): R7C78 must be at least 8 (1+7) because 3 (1+2) is too small -> R6C7 <> 7,8

4. N3
a) Innies = 8(3) = 1{25/34} -> 1 locked for C7+N3
b) Outies = 22(3) = 9{58/67} -> 9 locked for C6+N2
c) 19(3) must have 2,3,4 xor 5 and R3C7 = (2345) -> R23C6 <> 5
d) 19(3) <> 5 since R23C6 would be {68} -> no combo for Outies
e) 11(3) must have 5,6,7 xor 8 and R1C6 = (5678) -> R12C7 <> 5
f) Innies = 8(3) = {134} locked for C7+N3
g) 16(3) = 2{59/68}
h) 11(3) = 1{37/46}
i) Outies = 22(3) = {679} because R1C7 = (67) -> locked for C6+N2

5. N2
a) 11(2) = 2{18/45} -> 2 locked for C5+N2
b) 3 locked in R123C4 for C4

6. N1
a) 6(3) = {123} locked for N1

7. N69
a) 3 locked in R6C89 @ 20(3) -> 20(3) = {389} -> R7C9 = 9, R6C89 = {38} locked for R6+N6
b) 22(3) = {679} locked
c) R6C7 = 5
d) 2,8 locked in R789C7 for N9
e) 14(3) = 5[27/81]
f) 15(3) = 5{37/46} -> 5 locked for N9
g) 1 locked in R79C8 for C8
h) 9 locked in R45C7 for N6

8. N2
a) 1 locked in R3C45
b) 20(3): R12C3 <> 4 since R1C4 <> 7,9

9. C89
a) Innies = 11(3): R5C8 = (67) -> R79C8 <> 6,7
b) R7C8 = 1 -> R7C7 = 8

10. R67
a) Both 15(3) = 2{49/67} -> no 1
b) Naked pair (24) locked in R67C6 for C6
c) 15(3) @ R6C5 = {249} -> R6C5 = 9
d) 15(3) @ R6C4 = {267} -> R6C4 = 6, R7C4 = 2, R7C5 = 7
e) R7C6 = 4 -> R6C6 = 2, R6C1 = 4
f) 13(3) @ R6C2 = {157} -> R7C3 = 5
g) Naked pair (17) locked in R6C23 for N4

11. C45
a) 16(3) = {358} locked for N5
b) 20(3) @ N2 must have 3,4 xor 5 -> only possible @ R1C4 -> R1C4 = (345)
c) 20(3) @ N2: Killer pair (69) of 18(3) @ N1 blocks {569} -> 20(3) <> 6

12. N1
a) 7,8,9 locked in R12C3 + 18(3)
b) 18(3) <> 8 because {468} is blocked by R3C3 = (46)
c) 13(3) = 4{18/36}
d) 8 locked in 20(3) = 8{39/57} -> 8 locked for C3

13. C123
a) 3 locked in R34C3 for N4
b) 16(3) = 2{59/68} -> 2 locked for N4
c) 1 locked in R12C1 for N1
d) 2 locked in R89C3 for N7
e) 17(3) must have 5 xor 8 -> only possible @ R4C2 -> R4C2 = (58)

14. R4
a) Naked triple (358) locked in R4C256
b) Hidden Single: R5C3 = 3 @ N4

15. N8
a) 1 locked in R89C6
b) 20(3) must have 3 xor 6 -> only possible @ R9C5 -> R9C5 = (36)
c) 12(3): R8C5 <> 5 since R89C6 has no 6

16. N2
a) 11(3): R3C5 <> 8 since R12C5 has no 1
b) 11(3): R3C5 <> 4 because 4 locked in 13(3)
c) 13(3): R3C4 <> 8 because R2C4 and R3C3 <> 1

17. N3
a) 8 locked in R3C89
b) 21(3) = {579} -> R1C8 = 9, {57} locked for C9+N3
c) Hidden Single: R1C6 = 6 @ R1, R8C8 = 5 @ N9, R5C8 = 7 @ C8, R4C4 = 7 @ R4
d) 11(3) = {146} -> 1,4 locked for C7
e) R3C7 = 3

18. N69
a) 6 locked in R45C7 for C7
b) 12(3) = {237} -> R9C8 = 3
c) R6C8 = 8, R6C9 = 3
d) R9C5 = 6, R9C9 = 4, R8C9 = 6

19. C4
a) 20(3) @ N8 = {569} -> R8C4 = 9, R9C4 = 5
b) 20(3) @ N2 = {389} -> R1C4 = 3, R1C3 = 8, R2C3 = 9

20. Rest is clean-up and singles.

Rating: 1.0, I might try to tackle this one again to shorten up my WT but I can't promise it :?.
Outline by gary w:
Hi all,

Haven't been through the posted wts in detail but doubt if I've done anything very different.I'm not sure I can rate very accurately but perhaps this was about a 1.0? Took me about 2.5 hours.

A brief outline of my solving path..


Various prelims include

1.r468c5=20
2.r6c7=r7c9-4

from which r6c7=3/5 r7c9=7/9

3. x-wing work on c89 placed r6c7=5 r7c9=9

This leads to a number of placements in r67 and a large number of either/ors in many other cages.Combination work -> r3c3=4/6 ( thus r1c4=3/5) at which point I got stuck for a while.Then noticed that the 6/5 pairing also forced a 5 into r4c2 and hence could not place a 5 in c5.

4.Thus r3c3=4 r1c4=3 etc and then it was straightforward.

Because there was nothing other than x-wings and combination work involved in solving this killer I'd rate it about 1.0.

I notice Ruud likes to use 3 cages but he excelled himself here..every cage was a 3 cage and all but one was L shaped.Interesting.The killersudokuonline "mindbending" series typically employ much larger cages and are certainly easier than the assassin series.Any reason ,Ruud,why 3 cages figure so predominantly in your excellent puzzles??

Like Andrew I suspect that this cage pattern may accommodate some very difficult variants?? Gulp!!

Regards

Gary


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PostPosted: Mon Jul 14, 2008 4:27 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Assassin 74v2 by Ruud (Oct 07)
Puzzle pic:
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Code: Select, Copy & Paste into solver:
3x3::k:3584:3584:5378:5378:2308:5893:5893:2567:2567:3584:2058:5378:4620:2308:4622:5893:3600:2567:2058:2058:4620:4620:2308:4622:4622:3600:3600:4379:3356:3356:3358:4639:4639:3873:3618:3618:4379:4379:3356:3358:3358:4639:3873:3873:3618:3117:5422:5422:3376:3633:3633:3379:4404:4404:3117:3117:5422:3376:3376:3633:3379:3379:4404:5183:1856:1856:3906:4419:4419:3397:4678:4678:5183:5183:1856:3906:3906:4419:3397:3397:4678:
Solution:
+-------+-------+-------+
| 7 2 8 | 4 1 9 | 6 5 3 |
| 5 1 9 | 7 6 3 | 8 4 2 |
| 4 3 6 | 5 2 8 | 7 1 9 |
+-------+-------+-------+
| 2 6 3 | 9 7 5 | 4 8 1 |
| 8 7 4 | 1 3 6 | 9 2 5 |
| 1 9 5 | 2 8 4 | 3 7 6 |
+-------+-------+-------+
| 3 8 7 | 6 5 2 | 1 9 4 |
| 6 4 2 | 8 9 1 | 5 3 7 |
| 9 5 1 | 3 4 7 | 2 6 8 |
+-------+-------+-------+
Quote:
Ruud, lead-in:..requires a few steps which are more advanced than those required for the original, but in total, the solving path is shorter
Afmod: This one required some more complicated combo analysis. I can't say that the walkthrough was shorter than my WT for V1
Andrew: I didn't find A74V2 much harder than A74 so I can't rate it any higher than 1.25..the solving path is shorter than for the original, but not by much
Walkthrough by Afmob:
This one required some more complicated combo analysis. I can't say that the walkthrough was shorter than my WT for V1.
Let's see how devilish the Brick Wall is. :twisted:

Walkthrough for A74 V2:

1. N1
a) Innies = 23(3) = {689} locked for C3+N1
b) 14(3) = 7{25/34} -> no 1
c) 21(3) <> 5 since R12C3 <> 5,7
d) 21(3) = 8{49/67} -> R1C4 = (47), 8 locked for N1

2. C12
a) Innies = 19(3) -> no 1
b) Innies = 19(3) = {289/469/478} because R8C2 = (24)
c) 7(3) = {124} locked for N7 and 1 locked for C3
d) 21(3) <> 4 because R67C3 <> 8,9
e) 21(3) = {579} because R67C3 = {57} -> R6C2 = 9, {57} locked for C3
f) 13(3): R4C2 = (678) because R45C3 = {23/24/34}
g) Innies = 19(3) = 9[64/82]
h) 13(3) = 3{28/46} -> 3 locked for N4
i) 17(3) <> 1 since it has no 9
j) Hidden Single: R6C1 = 1 @ N4

3. N7
a) 12(3) = 1{38/56}
b) 20(3) <> 7 since {578} blocked by R7C3 = (57)
c) Hidden Single: R7C3 = 7 -> R6C3 = 5

4. N3
a) Innies = 21(3) -> no 1,2,3
b) Innies = 21(3) <> 5 since R12C7 <> 5,7
c) Innies = 21(3) = 8{49/67} -> 8 locked for C7+N3 and R3C7 = (47), R1C6 <> 8
d) Outies = 20(3) -> no 1,2
e) Outies = 20(3) = 9{38/47/56} since {578} impossible because of R1C6 = (69)
-> 9 locked for C6+N2

5. R123
a) Naked triple (689) locked in R1C367 for R1
b) 8 locked in R3C46 for N2
c) 18(3) @ R2C4 <> 2 because of Innies+Outies N1:
If 18(3) = {279} -> R3C3 = 9 -> R1C4 = 7 so 18(3) can't be {279}
d) 9(3) = 2{16/34} -> 2 locked for C5

6. N56
a) Innies N6 = 16(3) = 6{28/37} -> 6 locked for R6+N6
b) Innies N5 = 14(3) = 4{28/37} -> 4 locked for N5
c) 13(3) @ R4C4 <> 8 since {238} blocked by Killer pair (23) of Innies of N5
d) 18(3) <> 2 because {279} blocked by Killer pair (27) of Innies of N5
e) Outies N6 = 14(3): has no 6 since {356} blocked by Killer pair (35) of 12(3) @ N7
f) Outies N6 = 14(3): has no 5 since {158} blocked by Killer pair (58) of 12(3) @ N7
g) 13(3) @ R6C7 <> 6 since R7C78 would be {34} -> no combo for Outies of N6
h) 6 locked in 17(3) = 6{29/38/47}

7. N2
a) 18(3) @ R2C6 must have 4 xor 7 since R3C7 = (47) -> R23C6 <> 4,7
b) 7 locked in R123C4 for C4

8. C6789
a) Outies C6789 = R468C5 = 24(3) = {789} locked for C5

9. N58
a) Innies N5 = 14(3) must have 7 xor 8 and R6C5 = (78) -> R6C46 <> 7,8
b) 14(3) must have 7 xor 8 since R6C5 = (78) -> R7C6 <> 8
c) 18(3) <> 3 since {378} blocked by R6C5 = (78) and {369} blocked by Killer pair (36) of 13(3) @ R4C4
d) 14(3) <> 1 because R6C6 <> 1,5,6,7,8
e) 14(3) <> 6 because R6C5 = (78) -> 14(3) = {248/257/347}
f) 7 locked in 17(3) @ N8 -> 17(3) = 7{19/28/46}
g) 18(3) = {189/567} -> R45C6 <> 7 since R4C5 <> 5,6

10. N58
a) 7 locked in R46C5 for C5
b) 7 locked in 17(3) = 7{19/28} because R8C5 = (89)
c) 4 locked in 14(3) = 4{28/37}

11. N6 !
a) ! 17(3) <> 9 since R6C89 would be {26} -> no combo for Outies because R6C7 <> 8
b) 17(3) = 6{38/47}
c) ! Outies N6 = 14(3) = {149/239/248} -> {239} impossible since R7C9 would be 3
and R7C78 would be {29} -> no combo for 13(3)
-> R7C789 <> 3 and 4 locked in R7C789 = 4{19/28} for R7+N9
d) Hidden Single: R6C6 = 4 @ C6
e) 17(3) must have 4 xor 8 and R7C9 = (48) -> R6C89 <> 8
f) Innies = {367} locked for R6+N6
g) R6C4 = 2, R6C5 = 8 -> R7C6 = 2, R8C5 = 9, R4C5 = 7
h) 13(3) = {139} since R6C7 = (37) -> R6C7 = 3 and {19} locked for R7+N9

12. N9
a) Hidden Single: R7C9 = 4
b) 13(3) @ R8C7 = 2{38/56} -> 2 locked
c) Hidden Single: R9C1 = 9 @ R9, R3C7 = 7 @ C7

13. N2
a) 18(3) @ R2C6 = 7[38/56/65]
b) Hidden Single: R1C6 = 9, R2C6 = 3 @ C6 -> R3C6 = 8
c) 9(3) = {126} locked for C5+N2
d) 23(3) = {689} -> 6,8 locked for C7+N3

14. C789
a) 13(3) @ R8C7 = {256} -> R9C8 = 6 and {25} locked for C7+N9
b) R6C8 = 7, R6C9 = 6
c) 15(3) = 9{15/24} since R45C7 have no 2,5,8 -> 9 locked for N6
d) Hidden Single: R3C9 = 9 @ C9
e) R3C3 = 6, R1C3 = 8, R2C3 = 9, R1C7 = 6, R2C7 = 8

15. C456
a) 21(3) = {489} -> R1C4 = 4
b) R3C4 = 5, R2C4 = 7
c) 13(3) @ R4C4 = {139} -> R5C5 = 3 and {19} locked for C4+N5
d) 13(3) @ R6C4 = {256} -> R7C4 = 6, R7C5 = 5
e) R9C5 = 4
f) Hidden Single: R8C1 = 6 @ N7 -> R9C2 = 5
g) R9C7 = 2, R8C7 = 5, R9C3 = 1, R9C6 = 7, R8C6 = 1

16. N13
a) 8(3) = {134} locked, 3 locked for R3
b) 14(3) @ R3C8 = {149} -> 1,4 locked for C8+N3
c) R7C8 = 9, R7C7 = 1

17. N6
a) 15(3) = {249} -> R5C8 = 2

18. Rest is singles.

Rating: 1.25-1.5
Outline by gary w:
Another excellent puzzle.

I solved this one via



Some early combo work enabled r6c123 to be filled in (=195) and -> r7c3=7
This placed a 7 in the 3 cage r12c1r2c1 N1.
In N2 the 9(3) cage must contain a 2 as the combos with the 21(3) cage N12 won't permit a 2 in r23c4 so the 9(3) cage is {126} or {234}
1-O on N3 -> r1c6=6/9 (can't be 8 as this puts an impermissible 6 into r3c7.
The key move for me... if r1c6=6 -> r123c5={234} -> r23c4=1. -> r1c4=7 and then x-wings on the 1,6 and 7 in N1/2 means the 14(3) cage in N3 cannot be filled.
Therefore r1c6=9 r3c7=7


This together with outies r6-9 -> r468c5=24={789} -> r6c5=7/8 lead (eventually) to the solution.


Now I'm boldly off to the brick wall too. :roll:

Regards

Gary

P.S How do you access Ruud's "solving tip"....just in case I should need it!!!
Walkthrough by Andrew:
I didn't find A74V2 much harder than A74 so I can't rate it any higher than 1.25, having rated A74 as 1.0. However, as can be seen from my comment after the Prelims, I missed something while solving A74 which might have made that one easier. Therefore I'll stick at 1.25 for A74V2.

Ruud was right that the solving path is shorter than for the original, but not by much.

Here is my walkthrough for A74V2.

Prelims

a) 8(3) in N1 = 1{25/34}, 1 locked for N1
b) 21(3) cage at R1C3 = {489/579/678}, no 1,2,3
c) R123C5 = {126/135/234}, no 7,8,9
d) 23(3) cage R1C6 = {689}, CPE no 6,8,9 in R1C89
e) 10(3) cage in N3 = {127/136/145/235}, no 8,9
f) 21(3) cage at R6C2 = {489/579/678}, no 1,2,3
g) 20(3) cage in N7 = {389/479/569/578}, no 1,2
h) 7(3) cage in N7 = {124}, locked for N7

There were so many innies and innies/outies on nonets in A74 that I completely forgot to look for innies in columns, so let’s put that right and start with one.

1. 45 rule on C12 3 innies R468C2 = 19 = {289/469/478} (cannot be {379/568} because R8C2 only contains 1,2,4), no 1,3,5
1a. 2,4 must be in R8C2 -> no 2,4, in R46C2

2. 1 in N7 locked in R89C3, locked for C3

3. 45 rule on C6789 3 outies R468C5 = 24 = {789}
3a. Naked triple {789} in R468C5, locked for C5

4. 14(3) cage at R6C5 = {149/158/167/239/248/257/347} (cannot be {356} because R6C5 only contains 7,8,9)
4a. 7,8,9 must be in R6C5 -> no 7,8,9 in R67C6

5. 12(3) cage at R6C1 = {138/156/237/345} (cannot be {129/147/246} because 1,2,4 only in R6C1), no 9
5a. 1,2,4 only in R6C1 -> R6C1 = {124}

6. 45 rule on N7 1 innie R7C3 – 6 = 1 outie R6C1 -> R6C1 = {12}, R7C3 = {78}

7. 21(3) cage at R6C2 = {489/579/678}
7a. 4,5 of {489/579} must be in R6C3 -> no 9 in R6C3

8. 9 in N7 locked in 20(3) cage = {389/569}, no 7

9. 7 in N7 locked in R7C123, locked for R7

10. 45 rule on N1 3 innies R123C3 = 23 = {689}, locked for C3 and N1 -> R7C3 = 7, R6C1 = 1 (step 6), R6C23 = [95] (only remaining permutation)
10a. R468C2 (step 1) = 9{28/46}, no 7
10b. R7C12 = {38/56} (step 5)

11. 3 in C3 locked in R45C3, locked for N4
11a. 13(3) cage at R4C2 = 3{28/46}
11b. 17(3) cage in N3 = 7{28/46}

12. 45 rule on N1 1 innie R3C3 – 2 = 1 outie R1C4 -> R1C4 = {467}

13. 21(3) cage at R1C3 = {489/678}, 8 locked in R12C3, locked for C3, clean-up: no 6 in R1C4 (step 12)

14. 45 rule on N3 3 innies R123C7 = 21 = {489/678} (cannot be {579} because 5,7 only in R3C7) = 8{49/67}, no 1,2,3,5, 8 locked for C7 and N3
14a. 4 of {489} must be in R3C7 -> no 9 in R3C7

15. 45 rule on N3 1 outie R1C6 – 2 = 1 innie R3C7 -> R3C7 = {467}
15a. 8 locked in R12C7, locked for 23(3) cage -> no 8 in R1C6, clean-up: no 6 in R3C7 (step 15)

16. 18(3) cage at R2C6 = {279/378/459/468/567} (cannot be {189/369} because R3C7 only contains 4,7), no 1
16a. 4,7 must be in R3C7 -> no 4,7 in R23C6

17. 45 rule on N5 3 innies R6C456 = 14 = {248/347} = 4{28/37}, no 6, 4 locked for R6 and N5
17a. 7,8 must be in R6C5 -> no 7,8 in R6C4
17b. 6 in R6 locked in R6C789, locked for N6
17c. R6C789 = 6{28/37}

18. 14(3) cage at R6C5 (step 4) = {248/257/347} (cannot be {158/167} because 1,5,6 only in R7C6), no 1,6

19. 13(3) cage at R6C4 = {139/148/238/256/346}
19a. 8,9 of {139/148} must be in R7C4 -> no 1 in R7C4
19b. 8 of {238} must be in R7C4, 2 of {256} must be in R6C4 -> no 2 in R7C4

20. 45 rule on N8 1 outie R6C4 = 1 innie R7C6 -> no 5 in R7C6

21. 14(3) cage at R6C5 (step 18) = {248/347} = 4{28/37}, 4 locked in R67C6, locked for C6

22. 45 rule on N9 1 innie R7C9 – 1 = 1 outie R6C7, R6C7 = {237}, R7C9 = {348}

23. 6 locked in R6C89 -> 17(3) cage at R6C8 = 6{38/47}, no 2

24. 45 rule on N9 3 innies R7C789 = 14 = {149/248} (cannot be {158/356} which clash with R7C12, cannot be {239} because R7C78 = {29} would give 2{29} in 13(3) cage at R6C7) = 4{19/28}, no 3,5,6, clean-up: no 2 in R6C7 (step 22)
24a. 4 locked in R7C789, locked for R7 and N9, clean-up: no 4 in R6C4 (step 20)

25. R6C789 (step 17c) = {367} (only remaining combination)
25a. Naked triple {367} in R6C789, locked for R6 and N6 -> R6C456 = [284], R7C6 = 2 (step 20)
[Forgot to do clean-up for R7C789 using step 24 but that didn’t matter; R7C9 was fixed in step 27.]

26. 13(3) cage at R6C4 (step 19) = 2{38/56}, no 1,9
26a. 8 of {238} must be in R7C4 -> no 3 in R7C4

27. Naked quad {3568} in R7C1245, locked for R7 -> R7C9 = 4, R6C7 = 3 (step 22)
27a. Naked pair {19} in R7C78, locked for N9

28. 13(3) cage in N9 = {256} (only remaining combination, cannot be {238} because 3,8 only in R9C8), locked for N9

29. 45 rule on C1234 3 outies R579C5 = 12 = {156/246/345}
29a. 4 of {345} must be in R9C5 -> no 3 in R9C5

30. 45 rule on C89 3 innies R579C8 = 17 = {269} (only remaining combination, cannot be {458} because R7C8 only contains 1,9) -> R7C78 = [19], R59C8 = [26], R6C89 = [76]

31. Naked pair {25} in R89C7, locked for C7

32. Naked pair {49} in R45C7, locked for C7 and N6 -> R3C7 = 7

33. R3C9 = 9 (hidden single in C9), R3C3 = 6, R1C4 = 4 (step 12)
33a. R3C9 = 9 -> R23C8 = 5 = {14}
33b. Naked pair {14} in R23C8, locked for C8 and N3

34. R12C7 = {68} -> R1C6 = 9, R12C3 = [89], R12C7 = [68]

35. R2C4 = 7 (hidden single in N2), R3C4 = 5, clean-up: no 6 in R7C5 (step 26)

36. R3C7 = 7 -> R23C6 = 11 = [38]

37. R1C5 = 1 (hidden single in R1), R23C5 = [62]

38. R9C5 = 4 (hidden single in C5)

39. 3 in R3 locked in R3C12, locked for N1
39a. 8(3) cage in N1 = {134}, locked for N1

40. 7 in N8 locked in 17(3) cage = {179} (only remaining combination), locked for N8 -> R8C5 = 9, R4C5 = 7
40a. Naked pair {17} in R89C6, locked for C6

41. R7C5 = 5 (hidden single in N8), R7C4 = 6 (cage sum), R5C5 = 3, R5C3 = 4, R45C7 = [49]

42. Naked pair {56} in R45C6, locked for N5 -> R45C4 = [91]

43. R4C3 = 3 (hidden single in C3), R4C2 = 6 (cage sum)

44. R4C1 = 2 (hidden single in R4)

and the rest is naked singles


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PostPosted: Mon Jul 14, 2008 4:35 am 
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Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Assassin 74 Brick Wall by Ruud (Oct 07)
Puzzle pic:
Attachment:
a74BW.JPG
a74BW.JPG [ 104.61 KiB | Viewed 11156 times ]
Code: Select, Copy & Paste into solver:
3x3::k:3840:3840:3840:3843:3843:3843:3846:3846:3846:4873:2826:2826:3852:3853:3853:3343:4368:4368:4873:4873:2826:3852:3852:3853:3343:3343:4368:4123:4636:4636:4382:2591:2591:4897:2594:2594:4123:4123:4636:4382:4382:2591:4897:4897:2594:4909:2862:2862:1584:5681:5681:3635:4660:4660:4909:4909:2862:1584:1584:5681:3635:3635:4660:1599:5184:5184:3906:5187:5187:2373:5190:5190:1599:1599:5184:3906:3906:5187:2373:2373:5190:
Solution:
+-------+-------+-------+
| 5 1 9 | 7 6 2 | 3 8 4 |
| 7 6 3 | 5 8 4 | 1 9 2 |
| 4 8 2 | 9 1 3 | 5 7 6 |
+-------+-------+-------+
| 9 7 5 | 2 4 1 | 8 6 3 |
| 3 4 6 | 8 7 5 | 9 2 1 |
| 8 2 1 | 3 9 6 | 7 4 5 |
+-------+-------+-------+
| 6 5 8 | 1 2 7 | 4 3 9 |
| 1 9 4 | 6 3 8 | 2 5 7 |
| 2 3 7 | 4 5 9 | 6 1 8 |
+-------+-------+-------+
Quote:
Ruud, lead-in: a little off the Assassing scale:..A solving tip: :brickwall:
mhparker: I'm still suffering from a kind of paranoia when it comes to so many "L" shaped cages after our experience with TJK18! :pallid: .. the second half of the puzzle would have been paradise for me
gary w: I've made a little bit of progress but am now stuck in a morass of either/ors which just don't want to seem to yield..I really ran into a featureless wall of rock
Afmob: What a monster! That was the most difficult Killer Sudoku I've solved so far. But I got no idea about the rating since the hardest I've solved was about 1.75...
Para:...some cracks and a few holes but it is still not falling down..[Edit]Now got 12 digits placed.[Edit].. Now 13 digits placed...[Edit]...Now 81 digits placed ;)
gary w: A privilege to go thro' Afmob's and Para's wts...Great to see two masters at work
goooders: c'est magnifique! well done para i got a long way last weekend but could not bust the top three nonets
Para: It is probably a high 2.0. ...It took me 3 days to solve (officially 4 days as i had tried it once when Ruud posted but gave up pretty quickly)
mhparker: the Brick Wall can be solved quite elegantly, as Para has just proved so well
Afmob, 4 months later: I finally decided to solve it again in an appropiate way without resorting to long contradiction chains...Rating: 2.0. I used lots of forcing chains and combo analysis (but not as heavy as in A60 RP) to solve this monster
Andrew, 9 months later: This is by far the hardest Assassin that I've ever done by myself. The rating for the way I solved it must be at least 2.0. It's got far more combination and permutation analysis than in the walkthroughs by Afmob and Para but less chains
Walkthrough by Para:
Hi

This is what i have done so far on the brick wall, some cracks and a few holes but it is still not falling down. About the same as Afmob's progress i think by quickly checking his walkthrough.

[Edit] Some moves added. Now got 12 digits placed.

[Edit] Another few moves added. Now 13 digits placed.

[Edit] Another set of moves added. Now 81 digits placed :wink:

Walk-through Assassin 74 V3 "Brick Wall"

1. 19(3) at R2C1, R4C7 and R6C1 = {289/379/469/478/568}: no 1

2. 11(3) at R2C2 and R6C2 = {128/137/136/236/245}: no 9

3. 10(3) at R4C5 and R4C8 = {127/136/145/235}: no 8,9

4. 22(3) at R6C5 = {589/679}: no 1,2,3,4

5. 20(3) at R8C2, R8C5 and R8C8 = {389/479/569/578}: no 1,2

6. 9(3) at R8C7 = {126/135/234}: no 7,8,9

7. 6(3) at R8C1 = {123} -> locked for N7

8. 6(3) at R6C4 = {123} -> pointing eliminates {123} from R89C4

9. 45 on N7: 1 innie and 1 outie: R6C1 = R7C3: R6C1: no 2,3,9
9a. 3 outies: R6C123 = 11 = {128/137/146/236/245}
9b. 3 innies: R7C123 = 19 = {469/478/568}

10. 45 on N8: 1 innie and 1 outie: R6C4 + 4 = R7C6: R7C6: no 8,9
10a. 3 outies: R6C456 = 18 = {189/279/369/378}
10b. 3 innies: R7C456 = 10 = {127/136/145/235}

11. 9 in 22(3) at R6C5 locked within R6C56 -> locked for R6 and N5
11a. 22(3) = {89}[5]/{679}: R6C56: no 5
11b. R6c456: {378} blocked

12. 9 in N6 locked within 19(3) cage at R4C7: 19(3) = {289/379/469}: no 5

13. 45 on N9: 1 innie and 1 outie: R6C7 + 2 = R7C9: R6C7: no 8; R7C9: no 1,2
13a. 3 outies: R6C789 = 16 = {178/268/349/358/367/457} = {1/2/3/7..}
13b. 3 innies: R7C789 = 16 = {169/178/259/268/349/358/367/457}

14. R6C4789 needs at least 2 of {1237} -> R6C123: {137} blocked: no 7
14a. Clean up: R7C3: no 7

15. 45 on C6: 1 innie + 4 outies: R1C6 + 22 = R2468C5: R1C6: no 9

16. 45 on C4: 1 innie + 4 outies: R1C4 + 8 = R3579C5: R1C4: no 1

17. 17(3) at R4C4 = {278/368/458/467}: no 1

18. Hidden Pair {12} in R8C17: R8C17 = {12}
18a. 3 in N7 locked for R9

19. 9(3) at R8C7 = {126}(last combo) -> locked for N9
19a. 6 in N9 locked for R9
19b. Clean up: R6C7: no 4

20. 3 in R8 locked within 20(3) cages at R8C5 and R8C8: one of these cages is {389}
20a. 3 20(3) cages in R89: One is {389} and both others need one of {89}; the 3 20(3) cages in R89 need 4 of {89}: no {89} anywhere else in R89
This would probably have been easier if i has spotted the hidden pair in R7C45 instead, but it looks nicer.

21. Both {89} in N8 locked within 20(3) cage at R8C5: 20(3) = {389} -> locked for N8
21a. R6C4 = 3(hidden in 6(3) at R6C4)
21b. R7C6 = 7(step 10); R8C4 = 6(hidden)
21c. 3 in N8 locked for R8
21d. Naked Pair {12} in R7C45 -> locked for N8
21e. Naked Pair {45} in R9C45 -> locked for R9
21f. Clean up: R6C56 = {69} -> locked for R6 and N5; R6C7: no 5; R7C9: no 5,8; R7C3: no 6

22. 11(3) at R6C2 = {12}[8]/245}: R6C23: no 8; 2 locked within R6C23 -> locked for R6 and N4
22a. Clean up: R7C9: R7C9: no 4

23. 7 in R6 locked in N6
23a. Clean up: 19(3) in R4C7 = {289/469}: no 3

24. 3 in N6 locked in 10(3) at R4C8: 10(3) = {136/235}: no 4

25. 9 in C4 locked for N2

26. 19(3) at R6C1 = [4]{69}/{568}: R7C12: no 4

27. 10(3) = [7]{12}/{145}: R4C5: no 2

28. 45 on C4: 2 innies + 3 outies: R17C4 + 5 = R359C5: Min R17C4 = 3 -> Min R359C5 = 8: R359C5 = 8 = [125] blocked by R7C5
28a. Min R359C5 = 9 -> Min R17C4 = 4: R1C4: no 2

Ok realised this a bit late.
29. 15(3) cages can have max 1 of {123}.
29a. 3 15(3) cages in R1 need one of {123}: {456} blocked in all 3
29b. 3 15(3) cages in N2 {456} blocked through same reasoning

Some more reasoning between 3 15(3) cages in one Nonet.
30. 1 in a 15(3) cage = {159/168} = {5/8..}
30a. 3 15(3) cages in R1 or N2 can't be {258}

31. 45 on C4: 3 innies and 3 outies: R123C4 = R579C5 + 7
31a. Analysis
Valid combos: R579C5/R123C4
214=7 - 14 = {149}=[4]19
425=11 - 18 = {279}=[9]27
524=11 - 18 = {279}=[9]27
725=14 - 21 = {579}=[9]57/[7]59
824=14 - 21 = {489}=[9]48
825=15 - 22 = {589}=[8]59
Blocked by C4 + R3C5
215=8 - 15 = {159} ---
415=10 - 17 = {179}=[7]19 --
514=10 - 17 = {179}=[7]19 --
724=13 - 20 = {479}=[7]49 --
Blocked by C4
--714=12 - 19 = {478}=[7]48
--715=13 - 20 = {578}=[8]57
--814=13 - 20 = {479}=[7]49
--815=14 - 21 = {579}=[9]57
31b. Conclusions: R1C4: no 5; R23C4 = {19/27/48/57/59} -> R3C5 = {1356}
31c. 15(3) at R2C4 = {159/267/348/357}
31d. 15(3) at R1C4 = [4]{38}/[7]{26}/[8]{34}/[9]{24}/[9]{15}: [7]{35}/[8]{25} blocked by 15(3) at R2C4: R1C5: no 7

32. 15(3) at R2C5: [4]{38} blocked by R89C6: R2C5: no 4

33. R123C4 = [4]{19} -> R2C5 = 7(hidden): R3579 = [5214] blocked by R4C5
33a. R1C4: no 4; R3C5: no 5
33b. R123C4 = [9]{27}/[9]{57}/[9]{48}/[7]{59}/[8]{59}: no 1
33c. R7C4 = 1(hidden); R7C5 = 2
33d. Clean up: R1C56: no 8(step 31d)

34. 11(3) at R2C2 = {128/137/146/236/245} = {2/6/7..};{3/4/8..}
34a. 15(3) at R1C1 = {159/168/249/357} = {1/5/9..}: {267/348} blocked by 11(3) at R2C2
34b. 15(3) at R1C4 = [9][42]/[8]{34}/[762]: [9]{15} blocked by 15(3) at R1C1: no 1,5; R1C6: no 6
34b. 15(3) at R1C7: {159} blocked

35. 1's in N2: R3C5 = 1 or 15(3) at R2C5 = {168}: R3C5: no 6

36. 15(3) at R2C4 = {59}[1]/{48}[3]/{57}[3]= {3/5..}: R23C4: no 2
36a. 2 in N2 locked for C6

37. 10(3) at R4C5 = {145} -> locked for N5

38. 15(3) at R2C5 = {168/267/348}: {357} blocked by 15(3) at R2C4: no 5
38a. 15(3): [1]{68} blocked by R689C6: R2C5: no 1

39. 5 in N2 locked for C4
39a. R9C45 = [45]
39b. 15(3) at R1C4: [843] blocked by R34C5: R1C6: no 3

40. 15(3) at R2C4 = {59}[1]/{57}[3]: no 8

41. 15(3) at R1C7 = {168/267/348/357} = {2/3/8..},{2/7/8..},{3/4/6..},{4/6/7..}: {249} blocked by R1C6: no 9
41a. 13(3) at R2C7 = {139/148/157/247/256}: {238/346} blocked
41b. 17(3) at R2C8 = {179/269/359/368/458}: {278/467} blocked

42. 15(3) at R1C1 = {159/168/357} = {5/6..},{1/7..}: {249} blocked by R1C6: no 2,4
42a. 19(3) at R2C1 = {289/379/469/478}: {568} blocked: no 5
42b. 11(3) at R2C2 = {128/146/236/245}: {137} blocked: no 7

43. 13(3) at R2C7:[9]{13} blocked by R3C5: R2C7: no 9
43a. 13(3): {17}[5] blocked by R6C7 and {26}[5] blocked by R89C7: R3C8: no 5

44. 2 and 6 in C9 either in 10(3) at R4C8 or R123C9. 10(3) can't have both {26} so R123C9 needs one of {26}
44a. 13(3) at R2C7 = {139/148/157/247} = {1/7..} {256} blocked by R123C9: no 6

45. 17(3) at R2C8 = {269/359/368/458} = {3/6/8..} {179} blocked by 13(3) at R2C7: no 1,7

46. 17(3) at R2C8 = {3/6/8..}
46a. 17(3) has 3 -> R7C7 = 3(hidden) -> R6C7 <> 1
46b. 17(3) has 6/8 -> R1C789 <> {168}: no 1 -> R456C9 = 1 -> R6C7<>1
46c. Conclusion: R6C7: no 1
46d. R6C7 = 7; R7C9 = 9

47. R7C78 = {34}(last combo) -> locked for R7 and N9
47a. Clean up: R6C1: no 4; R6C23: no 5

48. Naked Triple {568} in R7C123 -> locked for N7

49. 5 in C7 locked for N3

50. 17(3) at R2C8 = {269/368}: no 4; 6 locked for N3

51. 15(3) at R1C7 = {348/357}: no 1,2: 3 locked for R1 and N3
51a. R1C6 = 2(hidden)
51b. R1C45 = [76/94]

52. 15(3) at R2C5 = {168/348}: no 7
52a. R5C5 = 7(hidden)

53. 17(3) at R2C8 = {269}: R2C8 = 9; R23C9 = {26} -> locked for N3 and C9

54. 15(3) at R1C1 = {159/168} = {5/6..}: no 7; 1 locked for N1

55. 11(3) at R2C2 = {236/245} = {5/6..}: no 8; 2 locked for N1
55a. Killer Pair {56} in 15(3) at R1C1 and 11(3) at R2C2 -> locked for N1

56. 1 in C9 locked for N6

57. 10(3) at R4C8 = [2]{35}/[6]{13}: R4C8: no 3,5; 3 locked in R45C9 for C9

58. R6C89 = {45}/[81]: R6C9: no 8

59. 2 in C1 locked for N7

60. Killer xy-wing: Pivot cell(s): R1C45 = {47}; Wings: R1C789 = {45}, R2C4 = {57} -> Common Peers can't have 5: R2C7: no 5

61. 15(3) at R1C7 = [537]/[3]{48}/[438/843]: R1C8: no 7

62. 7's in N3: 15(3) at R1C7 = [537] or R3C8 = 7
62a. 45 on C7: 1 innie and 4 outies: R1C7 + 10 = R3579C8
62b. Valid combos: [3]-[7231]/[4]-[7241]/[5]-[8241]/[5]-[1842]/[8]-[7641](other combos blocked by step 61 and 62 and by R4C8)
62c. R3C8 = {178}; R5C8 = {268}; R9C8 = {12}
62d. R9C7 = 6(hidden)

63. 19(3) at R4C7 = {49}[6]/{2[9]8}: [9]{28} blocked by R5C4: R5C7: no {28}

64. ER on 4: R4C5 = 4 or R1C5 = 4 -> R23C7 = 4: R4C7: no 4

65. Combination analysis 19(3) at R4C7 + 10(3) at R4C8: R4C78 = [26/86/92] = {2/8..},{6/9..}
65a. Killer Pair {28} in R4C4 + R4C78 -> locked for R4

66. R6C5: no 6, the following chain explains how.
66a. R1C5 = 6 -> R6C5 <> 6
66b. R1C5 = 4 -> 15(3) at R1C7 = [537] -> R9C9 = 8 -> R9C6 = 9 -> R6C6 = 6 -> R6C5<>6
66c. R6C56 = [96]

67. Hidden Pair {26} in R3C39: R3C3 = {26}

68. 18(3) at R4C2 = {19}[8]/{37}[8]/[9]{45}/{49}[5]/{36}[9]/{39}[6]/{57}[6]/{67}[5]: {45}[9] blocked by R4C56, [5]{49} blocked by R89C3, {69}[3] blocked by R4C78: R5C3: no 1,3
68a. {19}[8] blocked by following chain: R5C3 = 8 -> R6C8 = 8 -> R4C7 = 9 -> R4C23 <> 9: 18(3): {19}[8] blocked: no 1

69. Hidden Killer Pair {69} in R4C123 + R4C78: R4C123 needs one of {69}
69a. 16(3) at R4C1: [1]{69} blocked by steps 68 and 69; [1]{78} not possible: R4C1: no 1

70. 8 in R23 locked within cages 15(3) at R2C5 and 19(3) at R2C1 or 13(3) at R2C7
70a. When 19(3) = {478}, 13(3) has no 8, so 13(3) = [157] -> 19(3) = [7]{48}: R2C1: no {48}

71. 11(3) at R2C2 = {23}[6]/{36}[2]/{45}[2] = {3/5..}
71a. Killer Triple {357} in R2C1 + R2C23 + R2C4 -> locked for R2
71b. 3 in R2 locked for N1

72. 15(3) at R2C5 = [843]/[6]{18}: R3C6: no 4

73. 13(3) at R2C7 = {1[4]8}/[157]: [4]{18} blocked by R3C56: R2C7: no 4; R3C7: no 1,8

74. 16(3) at R4C1 = [6]{19}/[9]{16}/[781]/{349}/[763]/[7]{45}: [718] blocked by R289C1, [736] blocked by R2C1: R4C1: no 5; R5C2: no 8

75. 5's in R3: R3C4: no 7
75a. R3C4 = 5 : R3C4 <> 7
75b. R3C7 = 5 -> R3C8 = 7: R3C4 <> 7

76. R9C1: no 3
76a. R9C2 = 3: R9C1 <> 3
76b. R9C2 = 1 -> R3C8 = 1 -> R3C5 = 3 -> R2C4 = 7 -> R2C1 = 3: R9C1 <> 3
76c. R9C2 = 3(hidden)
76d. Naked Pair {12} in R89C1 -> locked for C1

77. 11(3) at R2C2 = {2[3]6}/{45}[2]: R2C3: no 2,6

78. 16(3) at R4C1 = {69}[1]/[781]/[439]/[934]/[7]{45}: [739] blocked by R2C1; [3]{49} blocked by R5C7: R4C1: no 3; R5C2: no 6

79. 15(3) at R1C1 = [5]{19}/[6]{18}/[8]{16}/[9]{15}
79a. 45 on C1: 1 innie and 3 outies: R1C1 + 12 = R357C2
79b. [5]-[458/746/845]
79c. [6]-[495/756/846/945]: [918] blocked by 15(3) at R1C1
79d. [8]-[758/956]
79e. [9]-[498/795]
79f. R5C2: no 1

80. Hidden Pair {12} in N4 in R6C23 = {12} -> locked for R6
80a. Clean up: R6C8: no 8

81. R6C1 = 8(hidden); R7C3 = 8(hidden)

82. R6C89 = {45} -> locked for N6
82a. R5C7 = 9
82b. Clean up: R5C8: no 6

83. R4C8 = 6(hidden)

84. 16(3) at R4C1 = [934]/[7]{45}: no 6; R4C1: no 4; 4 locked for N4 and R5
84a. R5C3 = 6(hidden); R3C3 = 2; R23C9 = [26]; R6C23 = [21]
84b. R1C2 = 1(hidden); R3C2 = 8(hidden)

85. R1C13 = {59}(last combo in 15(3)) -> locked for R1 and N1

And the rest is naked singles.

greetings

Para
Analysis of Para's step 46 (Killer XY-Chain) by mhparker in M1 thread:
Para wrote:
You've been talking about AIC's etc. a lot. Maybe you know this. I was just wondering something about my Brick Wall chain. I used a link i can't really place. I think there should be a third type of link for Killer Sudoku.
Normally you have strong and weak links.
Strong link: If A is wrong, B is right.
Weak Link: If A is right, B is wrong.
In Killer Sudoku we can also have: If A is right, B is right or if A is wrong, B is wrong. The second, which i used in my chain, is probably more likely to happen. This can happen because certain values only occur with another value in a cage.
Don't know if you mentioned this before. But this doesn't really fit into the strong/weak link view of AIC's.
Yes, I've discussed this before here, where I reached the same conclusion that you did, in that a new link type is needed. I called it a direct link at the time, and introduced the comma notation. However, I'm now thinking about calling them neutral links instead, because (unlike strong and weak links) they don't change the truth state of the premise at the current end of the chain.
Para wrote:
How would you qualify the chain i used in my Brick Wall WT at the end(step 46)
Yes, I'd already noticed that. Excellent move! Here's my analysis:
Quote:
46. Killer XY-Chain with 9 links (4 strong, 3 weak, 2 direct) on 7 as follows:

(7=1)r6c7-(1)r456c9=(1)r1c9,(68)r1c78-(68=3)r2c89|r3c9-(3)r123c7=(3)r7c7,(7)r6c7 => r6c7=7

This can be explained in verbose form as follows:
(i) Either r6c7 = 7 or...
(ii) ...r6c7 <> 7
(ii) => r6c7 = 1 (strong link, bivalue cell r6c7)
(iii) -> r456c9 <> 1 (weak link, n6)
(iv) => r1c9 = 1 (strong link, c9), r1c78 = {68} (direct link, combinations 15(3))
(v) -> 17(3) at r2c89+r3c9 <> {(6/8)..} (weak link, n3)
(vi) => 17(3) at r2c89+r3c9 = {3..} (strong link, combinations 17(3))
(vii) -> r123c7 <> {3..} (weak link, n3)
(viii) => r7c7 = 3 (strong link, c7), r6c7 = 7 (direct link, combinations 14(3))
In other words, "if r6c7 is not a 7, then ... it must be a 7" (contradiction)
Conclusion: r6c7 = 7

Notes:
  1. Nomenclature: "XY-Chain" because not all links are on the same digit, "Killer XY-Chain" because some links are based on cage combinations (Note: JSudoku uses the term "Complex" instead of "Killer" here).
  2. Chain does not make use of side-effects of previous links, and thus is fully bidirectional.
  3. Chain contains 1 (more complex) link that is based on 2 digits ({68}) rather than the usual 1.
Para wrote:
(well i really think it is the middle because there doesn't seem to be an end in sight...).
I'm really impressed with how far you've managed to get already. Afmob's doing really well, too. BTW, I gave up after taking a peek your WT, where I realized that you'd already found everything that I had, and more besides. Maybe I'm still suffering from a kind of paranoia when it comes to so many "L" shaped cages after our experience with TJK18? :pale:

BTW, if you and Afmob get completely stuck on the Brick Wall, maybe we should merge yours and Afmob's progress and convert it to a team (tag) effort? I guess that's what you would do anyway. I personally would have preferred it to be a team solution right from the start, but you and Afmob have come so far now, I'm rather hoping that one of you can carry on and claim victory. Good luck!
Alternative to Para's step 46 (Hidden Killer Pair Type 2:0) by mhparker:
Hi folks,
I wrote:
Without knowing it, you've given me enough work for the next few days just trying to analyze and categorize all those great moves you made! :wink: :scratch:

OK, let's get the ball rolling...

Actually, I'm already regretting having given up on this puzzle too early. All that early combination crunching was driving me up the wall (literally!). Little did I know at the time that the second half of the puzzle would have been paradise for me, with all those opportunities for "advanced" techniques (as Andrew always refers to them, with the word advanced in quotes :wink:). Ah well, can't win 'em all. But at least sitting back and analysing Para's WT (will look at Afmob's next) allows me to learn some new techniques, rather than simply using what I already know.

As many of you will have already seen, on the Maverick 1 thread, Para asked me how I would categorize his step 46 for the Brick Wall, which turned out to be representable as a Killer XY-Chain, although one of the links was more complicated than usual, because it was based on a digit pair rather than the usual single digit. The chain was very useful, because it resulted in an immediate placement at R6C7.

However, I've since found out that the same result (and more) can be achieved without a chain, as presented below. (BTW, hope you don't mind me doing this, Para!)

Firstly, for reference, here's the grid state after Para's step 45:

Code:
.--------------------------------.--------------------------------.--------------------------------.
| 12356789   12356789   12356789 | 789        346        24       | 12345678   12345678   12345678 |
:----------.---------------------+----------.---------------------+----------.---------------------:
| 2346789  | 12345678   12345678 | 579      | 3678       123468   | 1234578  | 23456789   23456789 |
|          '----------.          |          '----------.          |          '----------.          |
| 2346789    2346789  | 12345678 | 579        13       | 123468   | 12345789   1234789  | 23456789 |
:----------.----------'----------+----------.----------'----------+----------.----------'----------:
| 13456789 | 13456789   13456789 | 278      | 14         145      | 24689    | 12356      12356    |
|          '----------.          |          '----------.          |          '----------.          |
| 13456789   13456789 | 13456789 | 278        78       | 145      | 24689      24689    | 12356    |
:----------.----------'----------+----------.----------'----------+----------.----------'----------:
| 458      | 1245       1245     | 3        | 69         69       | 17       | 14578      14578    |
|          '----------.          |          '----------.          |          '----------.          |
| 5689       5689     | 458      | 1          2        | 7        | 34589      34589    | 39       |
:----------.----------'----------+----------.----------'----------+----------.----------'----------:
| 12       | 45789      45789    | 6        | 389        389      | 12       | 45789      45789    |
|          '----------.          |          '----------.          |          '----------.          |
| 123        123      | 789      | 4          5        | 89       | 126        126      | 789      |
'---------------------'----------'---------------------'----------'---------------------'----------'

From this position, we can basically use exactly the same type of move that Para had already used in his step 44, as follows:

Quote:
46. {35} in C7 only available in R1237C7
46a. -> R123C7 must contain at least 1 of {35}
46b. -> {359} combo blocked for 17(3) at R2C8 = {269/368/458} = {(6/8)..}

47. 17(3) at R2C8 (step 46b) blocks {168} combo for 15(3) at R1C7 = {267/348/357} (no 1)

48. 1 in C9 locked in N6 -> not elsewhere in N6

49. Naked single at R6C7 = 7
...

One reason for mentioning this (apart from the fact that it's a natural follow-up to my other post mentioned above) is that, despite being generally very powerful, SudokuSolver missed the above step 46, as well as missing Para's step 44. Hope you're reading this, Richard! :wink:

I'm not sure what one would call the above move. It's a bit like a hidden killer pair, except that the distribution of the two digits can be 2:0 rather than 1:1. JSudoku picks up this type of move using AICs, although that seems like overkill in comparison to the much simpler logic I presented for step 46 above. Anyone else got any ideas on how best to categorize this type of move?
New shorter Walkthrough by Afmob (mar 08):
This was a project I wished to finish for quite some time but I didn't find the time or energy to tackle this Assassin again. But after being encouraged by Andrew who will also post his wt for A74 Brick Wall, I finally decided to solve it again in an appropiate way without resorting to long contradiction chains (which more match Killers of rating 2.5+) like in my original walkthrough.

The new wt is shorter than the first walkthrough since I mangaged to place candidates faster and there is nearly no endgame. After the last difficult steps there are only few sub-steps and then it's over which was quite surprising.

A74 Brick Wall Walkthrough (rewritten and improved):
1. R789
a) 6(3) @ N7 = {123} locked for N7
b) Innies+Outies N7: R6C1 = R7C3 -> R6C1 <> 2,3,9
c) 11(3): R6C23 <> 7,8 because R7C3 >= 4
d) Innies N8 = 10(3) <> 8,9
e) 22(3) = 9{58/67} -> 9 locked for R6+N5
f) 6(3) @ N8 = {123} locked between C4+N8 -> R89C4 <> 1,2,3
g) Hidden pair (12) in R8C17 for R8 -> R8C17 = {12}
h) 6(3) @ N7 = {123} -> 3 locked for R9
i) 9(3) = {126} locked for N9, 6 locked for R9
j) 1,2 locked in 6(3) + 9(3) for R89

2. R789
a) 15(3) = {456} -> R8C4 = 6, {45} locked for R9+N8
b) 20(3) @ N8 = {389} locked for N8, 3 locked for R8+N8
c) 6(3) @ N8 = {123} -> R6C4 = 3
d) R7C6 = 7 -> 22(3) = {679} -> 6 locked for R6+N5
e) Innies+Outies N7: R6C1 = R7C3 = (458)
f) 11(3) = 2{18/45} -> 2 locked for R6+N4
g) Innies+Outies N9: -2 = R6C7 - R7C9 -> R6C7 = (17), R7C9 = (39)
h) 19(3): R7C12 <> 4 because R6C1 <> 6,9

3. N56
a) 7 locked in R6C789 for N6
b) 9 locked 19(3) @ N6 = 9{28/46}
c) 3 locked in 10(3) @ N6 = 3{16/25}
d) 10(3) @ N5 = 1{27/45} -> 1 locked for N5
e) 10(3) @ N5: R4C5 <> 2 since 7 only possible there

4. R123
a) 9 locked in R123C4 for N2
b) All 15(3) @ R1 + N2 <> 5{28/46} since they are Killer triples (of each other)
c) 15(3) @ R2C4: R3C5 <> 7,8 because R23C4 <> 3,6
d) 15(3) @ R2C5: R2C5 <> 2,5 because 7 only possible there
e) 15(3) @ R2C5: R2C5 <> 4 because 4{38} blocked by R89C6

5. R123
a) 15(3) @ R1C1 <> {267} since it's a Killer triple of 11(3)
b) 15(3) @ R1C1 <> {348} since it's a Killer triple of 19(3)
c) 15(3) @ R1C4, R1C7 <> {159} because it's a Killer triple of 15(3) @ R1C1
d) 13(3) <> 3{28/46} since they are Killer triples of 15(3) @ N3
e) 17(3) <> 7{28/46} because they are Killer triples of 15(3) @ N3

6. R789 !
a) ! Hidden Killer pair (35) in R123C7 for C7 since only other place possible is R7C7
b) 17(3) <> {359} since it's blocked by Killer pair (35) of R123C7
c) 15(3) <> 1 because {168} is a Killer triple of 17(3)
d) ! Hidden Killer pair (26) in R123C9 for C9 because 10(3) can't have both of them
e) 13(3) <> 6 because {256} blocked by Killer pair (26) in R123C9
f) 17(3) <> 1,7 because {179} blocked by Killer pair (17) of 13(3)
g) 1 locked in R456C9 for N6
h) R6C7 = 7 -> 14(3) = 7{34} -> {34} locked for R7+N9
i) R7C9 = 9 -> 18(3) = 9{18/45}; R6C9 <> 8
j) 5 locked in R123C7 for N3

7. N7
a) Naked triple (568) locked in R7C123
b) 19(3) = {568}
c) 11(3) must have 5 xor 8 and R7C3 = (58) -> R6C23 <> 5

8. R123+C6 !
a) 17(3) = 6{29/38} -> 6 locked for N3
b) 13(3) <> 3,9 because {139} blocked by Killer pair (39) of 15(3) @ N3
c) 1 locked in 13(3) @ N3 = 1{48/57}
d) 15(3) @ R1C4 <> {348} because of Killer pair (34) of 15(3) @ N3
e) 15(3) @ R2C4, R2C5 <> {267} since it's a Killer triple of 15(3) @ R1C4
f) 15(3) @ R2C5 = {168/348/357} <> 2
g) ! Hidden Killer pair (24) in R123C6 for C6 since 10(3) can only have one of them
h) 15(3) <> 2 because {249} blocked by Killer pair (24) of R123C6
i) 2 locked in 15(3) @ R1C4 = 2{49/67} for R1
j) 15(3) @ N3 = 3{48/57} -> 3 locked for R1+N3
k) 15(3) @ N1 = 1{59/68} -> 1 locked for N1

9. R123+C19
a) 17(3) = {269} -> R2C8 = 9, {26} locked for C9
b) 10(3): Hidden Killer pair (26) in R4C8 -> R4C8 = (26)
c) 10(3) = 3{16/25} -> 3 locked for C9
d) 11(3) = 2{36/45} -> 2 locked for N1
e) 7 locked in 19(3) @ N1 = 7{39/48}
f) 2 locked in R89C1 for N7
g) 15(3) @ R2C4 <> 4 because {348} blocked by Killer pair (38) of 15(3) @ R2C5

10. C456 !
a) ! Innies+Outies C6: 22 = R2468C5 - R1C6, R1C6 = (246) -> R4C5 <> 7 because:
- R2468C5 = 24/26/28(4), now consider all combos with 7 in R4C5 = 7{359/368/458/469/489/568}
- <> 7{359/458/469/568/489} because 4,5 only possible @ R4C5
- <> {3678} because 7 in R4C5 forces 10(3) = 7{12} -> no 2 in R1C6

b) 10(3) = {145} locked for N5
c) Hidden Single: R1C6 = 2 @ C6 -> 15(3) @ R1C4 = [76/94]2
d) Hidden Single: R9C4 = 4 @ C4, R9C5 = 5
e) 10(3) = {145} -> 5 locked for C6
f) 15(3) @ R2C5 = 8{16/34} -> 8 locked for N2
g) Hidden Single: R5C5 = 7 @ C5
h) 17(3) = {278} -> 2 locked for C4
i) R7C4 = 1, R7C5 = 2
j) 15(3) @ R2C4 = 5{19/37}
k) Outies C6 = 24(4) = 89{16/34}: Outies must have 1 xor 4 and R4C5 = (14) -> R2C5 <> 1

11. R123 !
a) 19(3): R3C12 <> 3 because 7{39} blocked by Killer pair (39) of 15(3) @ R2C4
b) ! Consider both candidates of R1C5 = (46) -> R6C5 <> 6:
- i) R1C5 = 4 -> 15(3) @ R1C7 = [537] -> R9C9 = 8 -> R9C6 = 9 -> R6C6 = 6 -> R6C5 <> 6
- ii) R1C5 = 6 -> R6C5 <> 6
c) R6C5 = 9, R6C6 = 6
d) Hidden pair (26) in R3C39 for R3 -> R3C3 = (26)
e) 3 locked in R123C2 for C2
f) Consider combos of 11(3) -> R2C1 = (37):
- i) 11(3) = {236} -> 15(3) @ N1 = {159} -> 15(3) @ R1C4 = [762] -> 15(3) @ R2C5 = [843] -> R2C1 = 7
- ii) 11(3) = {245} -> 19(3) = {379} -> R2C1 = 3
g) ! Consider placement of R2C1 -> R9C2 = 3:
- i) R2C1 = 3 -> R9C2 = 3 (HS @ N7)
- ii) R2C1 = 7 -> R2C4 = 5 -> R3C7 = 5 (HS @ R3) -> 13(3) = [157] -> R9C8 = 1 (HS @ N9) -> R9C2 = 3

12. C123
a) 6(3) = {123} -> 1 locked for C1
b) 16(3) <> {358} since it's blocked by R6C1 = (58)
c) 16(3): R5C2 <> 8 because R45C1 <> 1
d) 16(3): R5C2 <> 6 because R45C1 <> 1 and [736] blocked by R2C1 = (37)
-> 16(3) = {169/178/349/457} (because R5C2 = (1459))
e) Killer pair (14) locked in 16(3) + 11(3) for N4
f) 16(3) <> 6 because {69}1 together with R67C1 leaves no candidate for R1C1

13. C123 !
a) 6 locked in 18(3) = 6{39/57}
b) 8 locked in R456C1 for C1
c) Killer pair (37) locked in R2C1 + 16(3) for C1
d) 19(3) @ N1 must have 4 xor 9 and R3C1 = (49) -> R3C2 <> 4,9
e) 16(3): R5C2 <> 9 because {34}9 blocked by Killer pair (34) of 19(3) @ N1
f) ! R1C1 <> 9 because either 19(3) @ N1 = [397] or 19(3) = [748] -> 16(3) = {39}4
g) 15(3) @ N1 must have 5 xor 6 and R1C1 = (56) -> R1C23 <> 5,6
h) Naked pair (56) locked in R17C1 for C1
i) R6C1 = 8

14. R456
a) 16(3) = 4{39/57} -> 4 locked for N4
b) 11(3) = {128} -> R7C3 = 8; 1 locked for R6
c) 18(3) @ N6 = {459} -> {45} locked for N6
d) 10(3) @ N6 = {136} -> R4C8 = 6

15. Rest is singles.
Rating: 2.0. I used lots of forcing chains and combo analysis (but not as heavy as in A60 RP) to solve this monster.
Walk-through by Andrew with summaries (Jan 2009):
This is by far the hardest Assassin that I've ever done by myself. The rating for the way I solved it must be at least 2.0. It's got far more combination and permutation analysis that in the walkthroughs by Afmob and Para but less chains although I now realise that my combination analysis includes implied chains for some of the clashes.

Here is my walkthrough. I've included summaries at the end of the very heavy analysis steps. I'm not sure that I'd recommend anyone to work right through it although I think some of the hidden killers are interesting and the later ones may not be in the other posted walkthroughs.

Prelims

a) 19(3) cage in N1 = {289/379/469/478/568}, no 1
b) 11(3) cage in N1 = {128/137/146/236/245}, no 9
c) 10(3) cage in N5 = {127/136/145/235}, no 8,9
d) 19(3) cage in N6 = {289/379/469/478/568}, no 1
e) 10(3) cage in N6 = {127/136/145/235}, no 8,9
f) 19(3) cage at R6C1 = {289/379/469/478/568}, no 1
g) 11(3) cage at R6C2 = {128/137/146/236/245}, no 9
h) 6(3) cage at R6C4 = {123}, CPE no 1,2,3 in R89C4
i) 22(3) cage at R6C5 = 9{58/67}
j) 6(3) cage in N7 = {123}, locked for N7
k) 20(3) cage in N7 = {479/569/578}
l) 20(3) cage in N8 = {389/479/569/578}, no 1,2
m) 9(3) cage in N9 = {126/135/234}, no 7,8,9
n) 20(3) cage in N9 = {389/479/569/578}, no 1,2

1. Hidden pair {12} in R8 -> R8C17 = {12}
1a. 3 in N7 locked in R9C12, locked for R9
1b. 9(3) cage in N9 = {126} (only remaining combination), locked for N9
1c. 6 in N9 locked in R9C78, locked for R9
1d. Hidden pair {12} in R7C45, locked for N8 and 6(3) cage -> R6C4 = 3
1e. 3 in R7 locked in R7C789, locked for N9

2. 45 rule on N8 1 remaining innie R7C6 = 7
2a. R6C56 = {69}, locked for R6 and N5
2b. 17(3) cage in N5 = {278/458}, no 1

3. 15(3) cage at R8C4 = {456} (only remaining combination) -> R8C4 = 6, R9C45 = {45}, locked for R9 and N8

4. 9 in C4 locked in R123C4, locked for N2
4a. One of the 15(3) cages at R1C4 or R2C4 must be 9{15/24}
4b. 15(3) cage at R2C5 = {168/267/348/357} (cannot be {258/456} which clash with the 15(3) cage containing 9)
4c. 7 of {267/357} must be in R2C5 -> no 2,5 in R2C5
4d. 15(3) cage at R2C4 = {159/168/249/267/348/357} (cannot be {258/456} which clash with the 15(3) cage containing 9 and, if it contains 9 it clearly cannot contain either of those combinations)
4e. 3,6 of {168/267/348/357} must be in R3C5 -> no 7,8 in R3C5
4f. 3,6 must be in different 15(3) cages and neither in the one containing 9 -> one of the two cages in step 4b must be {168/267} and the other one must be {348/357}

5. 45 rule on N7 1 outie R6C1 = 1 innie R7C3, no 2,7 in R6C1, no 6 in R7C3

6. 45 rule on N9 1 innie R7C9 = 1 outie R6C7 + 2, no 4,5,8 in R6C7, no 5,8 in R7C9

7. 11(3) cage at R6C2 = {128/245}, no 7, 2 locked in R6C23 for R6 and N4, clean-up: no 4 in R7C9 (step 5)
7a. 8 of {128} must be in R7C3 -> no 8 in R6C23
7b. 7 in R6 locked in R6C789, locked for N6
7c. R6C1 = R7C3 (step 5) -> R6C123 = {128/245}

8. 19(3) cage at R6C1 = {469/568}
8a. 4 of {469} must be in R6C1 -> no 4 in R7C12
8b. R6C1 = R7C3 (step 5) -> R7C123 = {469/568}

9. 10(3) cage in N5 = {127/145}
9a. 7 of {127} must be in R4C5 -> no 2 in R4C5

10. 9 in N6 locked in 19(3) cage = {289/469}, no 3,5
10a. 3 in N6 locked in 10(3) cage = {136/235}, no 4

11. 9 locked in R123C4, 45 rule on C4 4 outies R3579C5 = 1 innie R1C4 + 8, min R3579C5 = 10 -> min R1C4 = 2
11a. If R1C4 = 2 => R3579C5 = 10 = {1234}, R7C4 = 1, R7C5 = 2, R9C5 = 4 -> {1234} blocked by R5C5 -> no 2 in R1C4
11b. If R1C4 = 4 => R3579C5 = 12 = {1236/1245}, R9C4 = 5, R9C5 = 4 blocks {1236} but {1245} can be [5214] (cannot be [1524/2514] because 15(3) cage at R2C4 must be {19}5 to avoid clash with R9C4)
11c. If R1C4 = 5 => R3579C5 = 13 = {1237/1246/1345}, R9C4 = 4, R9C5 = 5 blocking {1237/1246}, 3 of {1345} can only be at R3C5 and that clashes with 15(3) cage at R2C4 which can only be {29}4 -> no 5 in R1C4
[Nothing useful was obtained at this stage from analysing R1C4 = 7,8,9]

12. For the same reasons as in step 4, one of the 15(3) cages in R1 must be 9{15/24} and the other two must be {168/267} and {348/357}
12a. R1C123 = {159/168/249/357} (cannot be {267/348} which clash with the 11(3) cage, they also clash with the 19(3) cage)
12b. R1C456 and R1C789 cannot be {159} which clash with R1C123

13. 1 in C4 must be in R23C4 or in R7C4
13a. If 1 in R7C4, R7C5 = 2 -> no 2 in R3C5
13b. If 1 in R23C4, 15(3) cage at R2C4 = 1{59/68} -> no 2 in R3C5
13c. -> no 2 in R3C5

14. 45 rule on C6 4 outies R2468C5 = 1 innie R1C6 + 22
14a. R2468C5 cannot be {6789}
14aa. If R2468C5 = [6798] => R45C6 = {12}, R23C6 = {18} (step 4b) clashes with R45C6
14ab. If R2468C5 = [8769] => R45C6 = {12}, R89C6 = [38], R23C6 = {16/34} (step 4b) clashes with R45C6 + R8C6
14ac. -> no 8 in R1C6

15. Hidden killer quad 3,6,8,9 in R123C6, R6C6 and R89C6 for C6 -> R123C6 contains one of 3,6,8
15a. 15(3) cage at R2C5 (step 4b) = {168/267/348/357}
15b. R23C6 cannot be {68} (step 15) -> no 1 in R2C5
15c. R23C6 cannot be {38} (step 15) -> no 4 in R2C5
Consider now the implications of step 15 when the 15(3) cages at R1C4 and R2C5 interact
15d. 15(3) at R2C5 = {168} => no 3 in R1C6 (step 15) => R1C456 = [735]/9{24}
15e. 15(3) at R2C5 = {267} => no 3 in R1C6 (step 15) => R1C456 = [834]
15f. 15(3) at R2C5 = {348} => no 6 in R1C6 (step 15) => R1C456 = [762]
15g. 15(3) at R2C5 = {357} => no 6 in R1C6 (step 15) => R1C456 = [861]/9{24}
15h. -> no 4 in R1C4, no 1,5,7,8 in R1C5, no 3,6 in R1C6
15i. R1C456 = [735/762/834/861/924/942]

16. 15(3) cage at R2C4 (step 4d) = {159/168/249/267/348/357} contains one of 7,8,9 in R23C4
16a. Hidden killer triple 7,8,9 in R1C4, R23C4 and R45C4 for C4 -> R45C4 must contain one of 7,8
16b. 17(3) cage in N5 (step 2b) = {278/458}
16c. R45C4 cannot be {78} -> no 2 in R5C5

17. R2468C5 (step 14) = R1C6 + 22, 9 in C5 locked in R68C5
17a. If R1C6 = 1 => R1C5 = 6 (step 15i) => R2468C5 = 23 = {3479} (cannot be {1589} because 1,5 only in R4C5, cannot be {1679/3569} which clash with R1C5)
17aa. {3479} can only be [7493] => R45C6 = {15} clashes with R1C6 -> no 1 in R1C6
17b. If R1C6 = 2 => R1C5 = {46} (step 15i) => R2468C5 = 24 = {1689/3489/3579} (cannot be {4569} which clashes with R1C5)
17ba. {1689} can be [6198/8169]
17bb. {3489} can be [3498/8493]
17bc. {3579} can only be [7593]
17c. If R1C6 = 4 => R2468C5 = 26 = {4679} (cannot be {3689} because R4C5 only contains 1,4,5,7, cannot be {4589} because 4,5 only in R4C5)
17ca. {4679} can only be [7469] => R23C6 = {26} (cannot be {35} which clashes with R45C6 = {15}) -> R1C456 cannot be [924]
17d. If R1C6 = 5 => R1C456 = [735] (step 15i) => R2468C5 = 27 = {4689/5679} (cannot be {3789} which clashes with R1C5)
17da. 4 of {4689} can only be in R4C5 => R45C6 = {15} clashes with R1C6 -> cannot be {4689}
17db. 7 of {5679}can only be in R2C5 which clashes with R1C456 -> cannot be {5679}
17dc. -> no 5 in R1C6
17e. Summary no 1,5 in R1C6, R1C456 = [762/834/942], no 2 in R1C5, R2468C5 = [6198/8169/3498/8493/7593/7469], no 7 in R4C5

18. R7C5 = 2 (hidden single in C5), R7C4 = 1
18a. 10(3) cage in N5 = {145} (only remaining combination), locked for N5
18b. 2 in N5 locked in R45C4, locked for C4

19. 15(3) cage at R2C4 (step 4d) = {159/348/357} (cannot be {168} because 1,6 only in R3C5), no 6
19a. 1,3 only in R3C5 -> R3C5 = {13}

20. R1C123 (step 12a) = {159/168/357} (cannot be {249} which clashes with R1C456), no 2,4
20a. 11(3) cage in N1 = {128/146/236/245} (cannot be {137} which clashes with R1C123), no 7
20b. 19(3) cage in N1 = {289/379/469/478} (cannot be {568} which clashes with R1C123), no 5

21. R3579C5 = R1C4 + 8 (step 11), R7C5 = 2 -> R359C5 = R1C4 + 6
21a. R1C4 = {789} -> R359C5 = 13,14,15
21b. If R1C4 = 7 => R45C4 = {28} => R5C5 = 7 => R359C5 = 13 = [175]
21c. If R1C5 = 8 => R45C4 = {27} => R5C5 = 8 => R359C5 = 14 = [185]
21d. If R1C6 = 9 => R1C5 = 4 (step 17e), R359C5 = 15 = [375] (cannot be [384] which clashes with R1C5)
21e. -> R359C5 = [175/185/375] -> R9C5 = 5, R9C4 = 4

22. 5 in C4 locked in R23C4, locked for N2
22a. 15(3) cage at R2C4 (step 19) = {159/357}, no 8

23. R1C789 = {168/267/348/357} (cannot be {249} which clashes with R1C456), no 9
23a. 13(3) cage in N3 = {139/148/157/247/256} (cannot be {238/346} which clash with R1C789
23b. R3C78 cannot be {13} which clashes with R3C5 -> no 9 in R2C7
23c. 17(3) cage in N3 = {179/269/359/458} (cannot be {278/368/467} which clash with R1C789)

24. 10(3) cage in N6 (step 10a) = {136/235}
24a. R45C9 may contain one, but not both, of 2,6
24b. Hidden killer pair 2,6 in R123C9 and R45C9 for C9 -> R123C9 must contain at least one of 2,6
24c. 13(3) cage in N3 = {139/148/157/247} (cannot be {256} which clashes with R123C9), no 6
24d. 5 of {157} must be in R23C7 because R23C7 = {17} clashes with R6C7 -> no 5 in R3C8
24e. 17(3) cage in N3 (step 23c) = {269/359/458} (cannot be {179} which clashes with 13(3) cage), no 1,7
[Alternatively can use hidden killer triple because the three cages in N3 each require at least one of 7,8,9 so can each only have one of 7,8,9. I saw that before the clash with the 13(3) cage but gave the clash as step 24e because it’s simpler.]

25. R7C7 may contain one, but not both, of 3,5
25a. Hidden killer pair 3,5 in R123C7 and R67C7 for C7 -> R123C7 must contain at least one of 3,5
25b. 17(3) cage in N3 (step 24e) = {269/458} (cannot be {359} which clashes with R123C7), no 3
25c. 13(3) cage in N3 = {139/148/157} (cannot be {247} which clashes with 17(3) cage), no 2, 1 locked for N3

26. 1 in R1 locked in R1C123, locked for N1
26a. R1C123 = {159/168}, no 3,7
26b. 11(3) cage in N1 (step 20a) = {236/245}, no 8, 2 locked for N1
26c. Killer pair 5,6 in R1C123 and 11(3) cage, locked for N1
26d. 19(3) cage in N1 (step 20b) = {379/478}

27. 1 in C9 locked in R456C9, locked for N6 -> R6C7 = 7, R7C9 = 9 (step 6)
27a. R6C7 = 7 -> R7C78 = 7 = {34}, locked for R7 and N9, clean-up: no 4 in R6C1 (step 5)
27b. Naked triple {568} in R7C123, locked for N7
27c. R7C9 = 9 -> R6C89 = 9 = {45}/[81], no 8 in R6C9
27d. Killer pair 5,8 in R6C1 and R6C89, locked for R6
[Alternatively can eliminate 5 from R6C23 because 5 of {245} must be in R7C3]

28. 5 in C7 locked in R123C7, locked for N3, clean-up: no 4,8 in 17(3) cage (step 25b)
28a. 17(3) cage = {269} -> R2C8 = 9, R23C9 = {26}, locked for C9 and N3

29. R1C789 (step 23) = {348/357}, 3 locked for R1 and N3, clean-up: no 8 in R1C4, no 4 in R1C6 (both step 17e) -> R1C6 = 2

30. 8 in C4 locked in R45C5, locked for N5 -> R5C5 = 7

31. 10(3) cage in N6 (step 10a) = {136/235}
31a. 2,6 only in R6C8 -> R6C8 = {26}
31b. 3 locked in R45C9, locked for C9

32. R1C789 (step 29) = {348/357}
32a. 7 of {357} must be in R1C9 -> no 7 in R1C8

33. 16(3) cage in N4 = {169/178/349/367/457} (cannot be {358} which clashes with R6C1)
33a. 7 of {178} must be in R4C1 -> no 8 in R4C1

34. 2 in C1 locked in R89C1, locked for N7

35. 11(3) cage in N1 (step 26b) = {236/245}
35a. R2C23 cannot be {26} which clashes with R2C9 -> no 3 in R3C3

36. 19(3) cage in N6 (step 10) = {289/469}
36a. {289} = [298/892] (cannot be 9{28} which clashes with R5C4) -> no 2,8 in R5C7
36b. {469} => R4C8 = 2
36c. Killer pair 2,8 in R4C4 and R4C78, locked for R4

37. 18(3) cage in N4 = {189/369/378/459/567} (cannot be {468} which clashes with R6C123)
37a. 8 of {189} must be in R5C3 -> no 1 in R5C3

38. 1 in C8 locked in R39C8
38a. 5 in C7 locked in R123C7
38b. If 5 in R23C7 => R23C7 = {15}, R89C7 = [26], R3C8 = 7, R9C8 = 1
38c. 45 rule on C7 4 outies R3579C8 = 1 innies R1C7 + 10
38d. If R1C7 = {348} => R3579C8 = 13,14,18 = [7231/7241/7641] (R39C8 must be [71] (step 38b), cannot be {1278} because R7C8 only contains 3,4)
If R1C7 = 5 => R3579C8 = 15 = {1248} (cannot be {1347} because 13(3) cage in N3 can only be {148} when R1C7 = 5, cannot be {2346} which clashes with R4C8) = [1842/8241]
38e. -> R3579C8 = [1842/7231/7241/7641/8241], no 4 in R35C8, no 6 in R9C8

39. R9C7 = 6 (hidden single in R9)

40. R1C5 = {46}
40a. If R1C5 = 4 => R1C789 (step 29) = [537] => R9C9 = 8 => R9C6 = 9 => R6C6 = 6 => no 6 in R6C5
40b. If R1C5 = 6 => no 6 in R6C5
40c. -> R6C5 = 9, R6C6 = 6

41. Hidden pair {26} in R3C39
41a. 11(3) cage in N1 = {23}6/{36}2/{45}2

42. 1 in C5 locked in R34C5
42a. If R3C5 = 1 => R2C7 = 1 => R9C8 = 1 => R8C1 = 1 => no 1 in R4C1
42b. If R4C5 = 1 => no 1 in R4C1
42c. -> no 1 in R4C1

43. 16(3) cage in N4 (step 33) = {169/178/349/367/457}
43a. 3 of {349} must be in R5C12 (cannot be 3{49} which clashes with R5C7), 7 of {367} must be in R4C1 -> no 3 in R4C1
43b. 7 of {457} must be in R4C1 -> no 5 in R4C1

44. 4 in C5 locked in R14C5
44a. If R1C5 = 4 => 4 in N3 locked in R23C7 => no 4 in R4C7
44b. If R4C5 = 4 => no 4 in R4C7
44c. -> no 4 in R4C7

45. Hidden killer quad 1,3,4,5 in R4C123, R4C56 and R4C9 for R4 -> R4C123 must have one of 1,3,4,5
45a. 7 in R4 locked in R4C123
45b. 18(3) cage in N4 (step 37) = {189/369/378/459/567}
45c. 3 of {369} must be in R4C23 (from hidden killer quad because R4C1 cannot be 4 when 18(3) cage = {369}, steps 43 and 43b), 8 of {378} must be in R5C3 -> no 3 in R5C3

46. R2C4 = {57}
46a. If R2C4 = 5 => no 5 in R2C7
46b. If R2C4 = 7 => R1C45 = [94] => R1C789 (step 29) = [537] => no 5 in R2C7
46c. -> no 5 in R2C7

47. Hidden killer triple 2,6,8 in R5C123, R5C4 and R5C8 for R5 -> R5C123 must contain one of 6,8
47a. 16(3) cage in N4 (step 33) = {169/178/349/367/457}
47b. 18(3) cage in N4 (step 37) = {189/369/378/459/567}
47c. 7 in R4 locked in R4C123
47d. If 18(3) = {189} => R6C123 = {245} (step 7c) => R4C1 = 7 => R5C12 = {36} would place both of 6,8 in R5C123
47e. 18(3) cage in N4 = {369/378/459/567}, no 1
47f. If {369/459}, 7 must be in R4C1
47g. If {378} => R5C3 = 8 => R6C123 = 5{24} => 16(3) = {169} => no 6 in R5C12 (step 47) => R4C1 = 6
47h. If {567} => R6C123 = 8{12} => 16(3) = {349}, 6 must be in R5C3 (step 47), R4C23 = {57} => R4C1 = 9 (cannot be 4 because of step 45)
47i. -> R4C1 = {679}, no 4

48. 2 in C2 locked in R26C2
48a. 45 rule on C3 4 outies R2468C2 = 1 innie R1C3 + 15
48b. If R1C3 = 1 => R2468C2 = 16 = {1249/1267/2347} (cannot be {2356} because R8C2 only contains 4,7,9)
48c. If R1C3 = 5 => R2468C2 = 20 = {2369/2459/2567}
48ca. Cannot be {2459} because R26C2 = {24} => R8C2 = 9, R89C3 = [47], R4C2 = 5, R45C3 = {49/67} clash with R89C3
48cb. 5 of {2567} must be in R4C2
48d. If R1C3 = 6 => R3C3 = 2, R2C23 = {45}, R2468C2 = 21 = {2469} (cannot be {2379} because R2C2 only contains 4,5)
48e. If R1C3 = 8 => R1C12 = {16}, R3C3 = 2, R2C23 = {45}, R6C2 = 2, R2468C2 = 23 = {2579}
48ea. Cannot be {2579} because R2C2 = 5, R23C3 = [42], R6C2 = 2 (step 48), R67C3 = [18/45] clashes with R12C3
48f. If R1C3 = 9 => R2468C2 = 24 = {2679}

Summary of step 48.
From steps 48e and 48ea, no valid combinations with R1C3 = 8
From steps 48b, 48cb, 48d and 48f, no valid combinations with R2C2 = 5
-> no 8 in R1C3, no 5 in R2C2, clean-up: no 4 in R2C3 (step 41a)
R2468C2 = {1249/1267/2347/2369/2469/2567/2679}

49. 8 in C3 locked in R57C3
49a. R6C1 = R7C3 (step 5) -> 8 in N4 locked in R5C3 + R6C1 -> no 8 in R5C12

50. 45 rule on C1 4 outies R3579C2 = 1 innie R1C1 + 15
50a. If R1C1 = 1 => R9C2 = 1, R3579C2 = 16 = {1348/1357/1456}
50aa. {1348} must be [4381] (cannot be [3481] because R23C1 = [79], R45C1 = [75/93] clashes with R23C1)
50ab. Cannot be {1357} because R9C2 = 1, R89C1 = [23], R7C2 = 5, R67C1 = [86], R3C2 = 7, R23C1 = [39]/{48} clashes with R67C1 or R89C1
50ac. Cannot be {1456} because R3C2 = 4, R23C1 = {78}, R7C2 = {56}, 8 in R67C1 clashes with R23C1
50b. If R1C1 = 5 => R7C2 = 5, R3579C2 = 20 = {1568/3458} = [8453/8651]
50c. If R1C1 = 6 => R7C2 = 6, R3579C2 = 21 = {1569/3468/3567}
50ca. Cannot be {1569} because R9C2 = 1, R89C1 = [23], R3C2 = 9, R23C1 = {37} clashes with R9C1
50cb. {3468/3567} = [7563/8463]
50d. If R1C1 = 8 => R7C2 = 8, R3579C2 = 23 = {1589/3578} (cannot be {4568} because R9C2 only contains 1,3)
50da. Cannot be {1589} because R9C2 = 1, R89C1 = [23], R5C2 = 5, R3C2 = 9, R23C1 = {37} clashes with R9C1
50db. {3578} = [7583]
50e. If R1C1 = 9 => R3579C2 = 24 = {1689/3489/3579/3678} (cannot be {4569/4578} because R9C2 only contains 1,3)
50ea. Cannot be {3489/3579} because R9C2 = 3, R89C1 = {12}, R5C2 = 9, R45C1 = [61] clashes with R89C1
50eb. {1689/3678} = [7683/8961]

Summary of step 50
The only combination for R3579C2 with both of 1,3 is {1348} in step 50a when 1 must be in R9C2 -> no 1 in R5C2
3 of {1348} must be in R5C2 (step 50aa) -> no 3 in R3C2
Cannot be {1569/1589} (steps 50ca and 50da), all other combinations with 9 are for R1C1 = 9 -> no 9 in R3C2
R3579C2 = [4381/7563/7583/7683/8453/8463/8651/8961]

51. 16(3) cage in N4 (step 33) = {169/349/367/457}
51a. 1 of {169} must be in R5C1, 9 of {349} must be in R4C1 -> no 9 in R5C1

52. 19(3) cage in N1 (step 26d) = {379/478}
52a. 9 of {379} must be in R3C1 -> no 3 in R3C1
52b. 3 in R3 locked in R3C56, locked for N2

53. 15(3) cage at R2C5 (step 4b) = {168/348}
53a. 3 of {348} must be in R3C6 -> no 4 in R3C6

54. 11(3) cage in N1 (step 26b) = {236/245}
54a. If {236} => naked triple {236} in R2C239, locked for R2 => R2C5 = 8, R2C6 = 4 (step 53) => R2C1 = 7
54b. If {245} => 19(3) cage = {389} => R2C1 = 3
54c. -> R2C1 = {37}

55. 19(3) cage in N1 (step 26d) = {379/478}
55a. 7 of {379} must be in R3C2, 7 of {478} must be in R2C1 -> no 7 in R3C1

56. 16(3) cage in N4 (step 51) = {169/349/367/457}
56a. 6 of {169} must be in R4C1 (step 47g), 6 of {367} must be in R5C1 (cannot be [736] which clashes with R2C1) -> no 6 in R5C2
56b. 18(3) cage in N4 (step 47e) = {369/378/459/567}
56c. If {369} => 16(3) = {457} => 6 must be in R5C3 (step 47)
56d. If {567} => 5 must be in R4C23 (step 45) => 6 must be in R5C3
56e. Combining steps 56c and 56d -> no 6 in R4C23
56f. If {459} => 9 must be in R4C23 (cannot be {45}9 which clashes with R4C56)
56g. Combining steps 56c and 56f -> no 9 in R5C3

57. R2468C2 (step 48 summary) = {1249/2347/2369/2469/2567/2679} (cannot be {1267} because 1,2,6 only in R26C2)
57a. For {2369/2469/2567/2679} 6 must be in R2C2
57b. {1249} must have 1 in R6C2 and 2 in R2C2
57c. If {2347} => R1C3 = 1 (step 48b), {2347} = [2347/3724] (cannot be [3427/4327] because R89C3 = [49], R67C3 = [18/45] clashes with R1C3 or R89C3)
57d. Combining steps 57a, 57b and 57c -> no 4 in R2C2, clean-up: no 5 in R2C3 (step 41a)

58. Naked triple {236} in 11(3) cage in N1, locked for N1 -> R2C1 = 7, R2C4 = 5, clean-up: no 8 in R1C12 (step 26a)
58a. Naked triple {159} in R1C123, locked for R1 and N1 -> R1C4 = 7, R1C5 = 6 (step 17e), R3C4 = 9, R2C5 = 8, R8C5 = 3, R3C5 = 1, R23C6 = [43], R4C5 = 4, R2C7 = 1, R8C7 = 2, R9C8 = 1, R8C1 = 1, R9C12 = [23]
58b. Naked pair {48} in R3C12, locked for R3 -> R3C78 = [57]

59. 7 in R4 locked in R4C23, 18(4) cage (step 47e) = {378/567}, no 4,9
59a. 6,8 only in R5C3 -> R5C3 = {68}

60. 9 in N4 locked in 16(3) cage (step 51) = {349} (only remaining combination), locked for N4 -> R4C1 = 9

and the rest is naked singles


Last edited by Ed on Mon Jan 12, 2009 8:40 am, edited 2 times in total.

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PostPosted: Mon Jul 14, 2008 4:39 am 
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Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Assassin 75 by Ruud (Nov 07)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:2816:3841:3841:4355:4355:3333:3333:2055:2055:2816:1034:3841:4355:5645:3333:4367:4367:2577:3858:1034:5645:5645:5645:5399:5912:2577:2577:3858:3858:4381:4381:5399:5399:5912:4386:4386:5668:3877:3877:4381:4381:2601:5912:5912:4386:5668:5668:3877:4144:4144:2601:2601:4148:4148:3894:3894:3877:4144:3898:3898:3898:2877:4148:3894:3136:3136:4930:3898:3652:2885:2877:2375:2632:2632:4930:4930:3652:3652:2885:2885:2375:
Solution:
+-------+-------+-------+
| 7 2 8 | 1 9 4 | 6 3 5 |
| 4 1 5 | 7 6 3 | 9 8 2 |
| 6 3 9 | 5 2 8 | 4 1 7 |
+-------+-------+-------+
| 2 7 1 | 6 4 9 | 3 5 8 |
| 5 6 3 | 2 8 1 | 7 9 4 |
| 9 8 4 | 3 5 7 | 2 6 1 |
+-------+-------+-------+
| 3 4 2 | 8 1 6 | 5 7 9 |
| 8 5 7 | 9 3 2 | 1 4 6 |
| 1 9 6 | 4 7 5 | 8 2 3 |
+-------+-------+-------+
Quote:
CathyW: I'm struggling with it :? :( ..... I feel a bout of combo crunching coming on..Finally got there. :) ..Total time about 4 hours and I haven't done a WT!
sublue: My first placement was ...... But I'll be darned if I can figure out how I did it! Note to self: write this stuff down the *first* time!
gary w: After the wall this one wasn't too bad...took me about 2.5 hours
Afmob: That one was tougher than I thought.... so rating should be about 1.25..And I thought I (would) get some relaxation after the pain that was the Brick Wall. :twisted:
Andrew: On what I've done so far it feels like a 1.25..I particularly liked Susan's (sublue) use of innies/outies that are in the same columns
azpaull: I'm glad to see that this gave (or is giving) others problems, too.....I think this will go into my growing bank of "ones to come back to" for now!
Brief outline by gary w:
After the wall this one wasn't too bad.Couldn't match Sue's time..took me about 2.5 hours.As per the others couldn't see where the 4s particularly entered into the solution..briefly outlined.


1. r4679c2=28=89 (4/7 or 5/6)
2. r158c2=13=2(4/7 or 5/6)
3. Thus r8c2=4/5/7.... combos in N7 and cells at r3c13(=15) -> 15(3) cage N7 does not contain a 9.
4. So r9c12=19 thus 8 @ r67c2
5. Further combo work utilising r3c1+r7c3=r4c3+7 shows r1c2=2 and r4c1-2
6.So r79c3={26}..using 5. above and combos for 15(4) cage N47 -> R79C3=26
7.R7C349=19..Innies of R789 -> r7c49={89} -> HS r6 r6c1=9 and r6c2=8.r5c1=5 r4c2=7
8.In N9 9 not in r8-> in r7 so r7c9=9 r7c4=8
9.Now deduce r4c2=5/7 thus in r456c3 1 cannot be in the 15(4) cage..would not be able to complete it.Thus r4c3=1
10.With r4c3=1 and r7c3=8 -> r3c6+r6c7=10

Mop up now

Look out for the variants!

Regards

Gary
Walkthrough by sublue: less-intuitive, defensable:
After spending several hours trying to recreate the incredibly fast way I solved this puzzle, I am now convinced that I made an intuitive leap and correctly guessed my first placement at R3C3. Everything fell out from there. I have re-solved it, and can't figure out where I got my original placement from, so I went with what I can defend.

Editted once for corrections and clarifications. Thanks Andrew!
1) Prelims:
a) N1 11(2) no 1.
b) N1 4(2) = {13} locked.
c) N25 21(3) no 1,2,3.
d) N3 8(2) no 4,8,9.
e) N3 17(2) = {89} locked.
f) N3 10(3) no 8,9.
g) N4 22(3) no 1,2,3,4. 9 locked to N4 22(3).
h) N56 10(3) no 8,9.
i) N7 12(2) no 1,2,6
j) N7 10(2) no 5.
k) N78 19(3) no 1.
l) N9 11(3) no 8
m) N9 11(2) no 1
n) N9 9(2) no 9.

Solving:
2) Cleanup from 1b), 1e) and 1g).
a) N1 11(2) no 8.
b) N7 12(3) no 9 R8C3.
c) N7 10(2) no 7,9 R9C1.
d) N1 11(2) no 2 R1C1.

3) N1 2 innies R3C13 = 15 -> no 2,4,5.

4) N3 2 innies R13C7 = 10 -> no 1,2,5.

5) N7 2 innies R79C3 = 8 -> no 4,8,9. No 7 at R7C3.

6) N9 2 innies R7C79 = 14 -> no 1,2,3,4,7.

7) C1: 4 outies: R4679C2 = 28 -> no 2 in R479C2.
a) Cleanup: R9C1 no 8
b) 8 and 9 are locked into R4679C2
c) R8C3 no 3,4.

8) R12 3 innies R2C259 = 9 -> no 7 at R2C59.

9) C89 3 innies R259C8 = 19 -> no 1 at R59C8.

10) R789 3 innies R7C349 = 19 -> no 1 R7C34. No 7 at R9C3.

11) N89 4 innies R7C49 and R89C4 = 30 -> R789C4 no 2,3.

12) C3 has locked 9 in R13C3 since n/e.
a) R2C1 no 2, R3C3 no 6.

13) N14 2 innies and 1 outie: R34C3 = R7C3 +8 -> R3C3 <> 8 and R4C3 <>7 or 8.
a) Cleanup: R3C1 <> 7.
b) N14 15(3) R3C1 = {68} -> R4C1 no 6,7,8.

14) N69 1 outie and 2 innies: R3C7 + 3 = R67C7 ->R6C7 no 3,5,6,7.

15) N1: 8 must be in either R1C3 or R3C1. 9 locked in R13C3 (step 12) -> R1C3 = {89}

16) N1 15(3) has locked 2 since n/e.

16b) N1 15(3) R1C2 and R2C3 = {245}

17) Deleted. Bwahahaha!

18) N1: 6 locked in R123C1 since n/e. 6 locked for C1.
a) Cleanup: R9C2 no 4.
b) R6C2 no 7.

19) N7: 1 locked to R789C1 since n/e. Locked for C1.

20) deleted

21) N14 15(3) no 6, 8 at R4C2.

22) N89 15(4): R7C7 = {5689} -> R7C56 and R8C5 min 6, max 10 -> no 8,9.

23) C12 3 innies R158C2 = 13 -> R15C2 no 5.

24) N8: 1 innie and 2 outies: R7C4 + 3 = R7C7 + R9C3 -> R7C4 no 6 or 9, R9C3 no 3.

25) N78 19(3): no 7 at R89C4.

26) N7 2 innies: R79C3 = 8 -> R7C3 <> 5.

27) R789 3 innies: R7C349 =19 -> R7C9 no 6.

28) N9 2innies: R7C79 = 14 -> R7C7 no 8.

29) R123: 3 innies R349C3 = 16 -> R4C3 no 6.

30) C789: 3 innies R167C7 = 13 -> R1C7 no 4.

31) N3: 2 innies R13C7 =10 -> R3C7 no 6.

32) N23 13(3): R12C6 no 7.

33) R123: 3 innies R349C3 = 16 -> R3C6 no 4.

34) N8: 1 innie and 2 outies: R7C4 + 3 = R7C7 + R9C3
a) N78 19(3) if R9C3 = 2, then R89C4 = {89} which means R7C4 <> 8.
b) Therefore, no combo can have 9 at R7C7.

35) N9:2 innies R7C79 = 14 -> R7C9 no 5.

36) N9: R7C7 = {56} -> N9 11(2) R78C8 cannot be 5,6.

37) N69 16(3) R6C89 no 8,9.

38) C1: 4 outies: R4679C2 = 28 which must include 8 and 9. R67C2 no 5, since the 6 the 5 would have to have would eliminate either an 8 or 9, and we need both.

39) R6789: 4 outies R5C1236 = 15 -> R5C36 no 6 or8.

40) C6789: 4 outies R4789C5 = 15 -> R9C5 no 9.

41) C12: 3 innies R158C2 = 13, and 2 is locked in this split, hidden 13(3) since n/e.
a) Determine whether R15C2 contains the 2. Assume R5C5 = 2. Cleanup as you go hoping to force a contradiction, or work through to end of puzzle.
b) Then R1C2 = 4
c) N1 11(2) = {56}
d) R3C1 = 8.
e) R1C3 = 9
f) R2C3 = 2
g) R3C3 = 7
h) N14 15(3) has R3C1 = 8, and R4C12 = {34/57}. I can’t make a 15 out of this, there R5C5 cannot be 2.

42) R1C2 = 2.
a) Cleanup R1C89 no 6.

43) N3 10(3) locked 2s since n/e. -> no 4 in R2C9 and R3C89.

44) HS R3C7 = 4.

45) N46 23(4) : R45C7 no 1.

46) R123 2 innies: R3C16 = 14 -> {68} locked pair for R3.

47) N3: 1 innies R1C7 = 6.
a) Cleanup R2C1 <> 5.

48) NS R7C7 = 5.
a) Cleanup R89C9 no 4.

49) N9: 1 innie R7C9 = 9.
a) Cleanup R6C89 no 7.
b) R78C8 no 2.

50) N9 4 locked in R789C8 for N9 and C8.
a) Cleanup R6C9 no 3.

51) N6 1 innie R6C7 = 2.
a) Cleanup: R6C89 no 5.

52) N9 11(3) R9C8 <> 6 since R89C7 cannot make a 5. -> 6 is locked in N9 9(2)

53) N9 9(2) = {3,6} locked pair for N9 and C9.
a) Cleanup: R78C8 no 8. -> R78C8 = {4,7} NP locked for N9 and C8.
b) Cleanup: R6C8 no 1.
c) R1C8 no 5
d) R1C9 no 1.

54) HS R9C8 = 2.

55) N7 2 innies R79C3 = 8 -> R7C3 no 6.

56) N3 has locked 3 in R13C8 locked for N3 and C8.
a) Cleanup: R6C8 = 6 -> R7C9 = 1

57) N36 23(4) Has locked 3 in R45C7. Remaining 2 cells sum to 16 -> must be 7 and 9. No 5,8.
a) NS R5C8 = 9.
b) NS R2C8 = 8
c) NS R2C7 = 9.
d) NS R4C8 = 5

58) NP R45C7 = {3.7}

59) HS R8C2 = 5.

60) And the rest are naked and hidden singles.
Walkthrough by Afmob: forcing chains:
That one was tougher than I thought. I had to use some forcing chains (Considering placement with 2 possibilites) to solve this one so rating should be about 1.25.

A75 Walkthrough:

1. C123
a) 4(2) = {13} locked for C2+N1
b) Innies C12 = 13(3) = 2{47/56} -> 2 locked for C2
c) Innies N1 = 15(2) = {69/78}
d) 15(3) @ R1C2 <> 7 because {267} is blocked by Killer pair (67) of Innies of N1
e) 11(2) <> 8
f) 12(2) = [48/57/75]
g) 10(2): R9C1 <> 7,8,9
h) Innies N7 = 8(2) = {17/26/35}, R7C3 <> 7

2. N14
a) 22(3) = 9{58/67} -> 9 locked for N4
b) 9 locked in R123C3 for N1
c) 11(2) = {47/56}
d) Killer pair (67) locked in 11(2) + Innies of N1 for N1
e) Innies N1 = 15(2): R3C3 <> 6

3. C789
a) 17(2) = {89} locked for R2+N3
b) Innies N3 = 10(2) = {37/46}
c) 10(3) @ N3 <> 6 because {136} blocked by Killer pair (36) of Innies of N3
d) Innies N9 = 14(2) = {59/68}
e) 11(2) <> 5,6 since {56} blocked by Killer pair (56) of Innies of N9
f) Innies C89 = 19(3) -> no 1
g) Innies C89 = 19(3) <> 3 because {379} blocked by Killer triple (379) of 11(2)
h) Innies C789 = 13(3): R6C7 <> 5,6,7 since sum would be > 13
i) 11(3): R89C7 <> 7 since R9C8 <> 1,3

4. C123
a) 6 locked R123C1 for C1
b) 15(3) @ R1C2 must have 8 xor 9 -> only possible @ R1C3 -> R1C3 = (89)
c) 22(3): R6C2 <> 7 because R56C1 <> 6
d) 10(2): R9C2 <> 4
e) Innies C12 = 13(3): R5C2 <> 5 since R18C2 <> 6
f) 15(3) @ R3C1: R4C1 <> 7,8 because R3C1+R4C2 is at least 10

5. N789
a) Innies N89 = 30(3+1) -> R7C9 <> 5 since R789C4 would be 25
b) Innies N89 = 30(3+1) -> R789C4 <> 1,2,3 because it's at least 21
c) 15(4): R7C56+R8C5 <> 8,9 because R7C7 >= 5
d) Innies N9 = 14(2): R7C7 <> 9
e) Innies N789 = 19(3) -> no 1

6. N7
a) Innies N7 = 8(2) = {26/35}
b) 1 locked in R789C1 for C1
c) 7,8,9 only possible @ 15(3), 12(2), 10(2) but none of them can have both -> 10(2) must have 7,8 xor 9
-> 10(2) = [19/28/37]

7. C123
a) Innies C123 = 16(3): R4C3 <> 8 since R39C3 >= 9
b) 15(3) @ R3C1: R4C2 <> 8 because R34C1 >= 8
c) 15(3) @ N7 <> {456} since it's blocked by Killer pair (56) of Innies of N7
d) 2 possibilites of (123) locked in R789C1 for C1 and R4C1
is the only place @ C1 where one candidate of (123) is possible -> R4C1 = (23)
e) Innies C12 = 13(3): R1C2 <> 5 because R8C2 <> 2,6
f) Innies C123 = 16(3): R4C3 <> 7 since R39C3 would be >= 10

8. R6789
a) 14(3) <> 9 because 9{14/23} blocked by Killer pairs (14,23) of 15(4)
b) 9 locked in R789C4 for C4
c) Outies = 15(4) must have 1 because {2346} impossible since R5C1 <> 2,3,4,6
-> 1 locked for R5

9. R12
a) Innies = 9(3) -> no 7
b) 17(3): R1C5 <> 1 because R12C4 <> 9
c) 13(3): R2C6 <> 7 because R1C2 blocks {24} and R1C7 <> 1,5

10. N9
a) Consider placement of 9 in N9 -> 11(3) <> 5:
Either Innies N9 = [59] -> no {245} in 11(3) or 11(2) = {29} -> no {245} in 11(3)

11. N7+C2 !
a) Consider placement of 6 in N7 -> 10(2) <> 2,8:
- i) 6 in 15(3) = 6{18/27} -> Innies 8(2) = {35} -> 12(2) = {48} -> 15(3) = {267} -> 10(2) = {19}
- ii) 6 in Innies 8(2) = {26} -> 10(2) = {19/37} -> 15(3) = {159/348/357}
-> 10(2) <> 2,8 and 15(3) = {159/267/348/357}
b) ! Consider placement of 8 in C2 -> R2C3 <> 2:
- i) 8 in 22(3) = {589} -> R56C1 = {59} -> 11(2) = {47} -> R1C2 = 2 -> R2C3 <> 2
- ii) 8 in 15(3) @ N7 = {348} -> Innies N7 = {26} -> R2C3 <> 2
c) 15(3) @ R1C2 = 2{49/58} -> R1C2 = 2

12. N36
a) 8(2) <> 6
b) 2 locked in 10(3) @ N3 = 2{17/35}
c) 4 locked in Innies N3 = 10(2) = {46} -> locked for C7
d) 13(3) <> 9 since R1C7 = (46)
e) 7 locked in R45C7 for N6
f) 17(3) <> 1 since it has no 7
g) 7 locked in 23(4) -> 23(4) <> 5 because R3C7 = (46)
h) Hidden Single: R7C7 = 5 @ C7

13. N9
a) Innies = 14(2) = [59] -> R7C9 = 9
b) 11(2) <> 2
c) 9(2) <> 4
d) 11(3) <> 4 since R89C7 <> 4,6
e) 4 locked in 11(2) = {47} locked for C8+N9
f) 9(2) <> 2
g) 16(3) = 9{16/25/34}, R6C9 <> 3

14. N8
a) 4 locked in R9C456 for N8
b) 15(4) = 5{127/136} -> 1 locked for N8
c) 9 locked in 19(3) = 9{28/37/46}
d) 5 locked in 14(3) = 5{27/36}
e) Hidden Single: R9C4 = 4
f) 19(3) = {469} -> R9C3 = 6, R8C4 = 9
g) Hidden Single: R7C4 = 8, R6C2 = 8 @ C2

15. C123
a) 22(3) = {589} -> {59} locked for C1+N4
b) 11(2) = {47} locked for C1+N1
c) 15(3) @ R1C2 = {258} -> R1C3 = 8, R2C3 = 5
d) 15(3) @ R3C1 = {267} -> R3C1 = 6, R4C1 = 2, R4C2 = 7
e) 15(4) = {2346} -> R5C2 = 6, R7C3 = 2 -> {34} locked for C3+N4
f) R3C3 = 9, R3C7 = 4, R1C7 = 6, R4C3 = 1, R7C2 = 4, R7C8 = 7, R8C8 = 4
g) R8C2 = 5, R8C3 = 7, R9C2 = 9 -> R9C1 = 1, R7C1 = 3, R8C1 = 8

16. N2
a) 13(3) = 6{25/34}
b) 9 locked 17(3) = 9{17/26/35} -> R1C5 = 9
c) 17(3) <> 3,5 since (35) is a Killer pair of 13(3)
d) 17(3) = {179} -> {17} locked for C4+N2
e) 6 locked in 22(4) = 69{25/34} -> R2C5 = 6, {25} locked for R3+N2
f) 4 locked in 13(3) = {346} -> {34} locked for C6
g) 21(3) = {489} -> R3C6 = 8, R4C5 = 4, R4C6 = 9

17. N89
a) 15(4) = {1356} -> R7C5 = 1, R7C6 = 6, R8C5 = 3
b) 11(3) = {128} -> R8C7 = 1, {28} locked for R9+N9
c) R8C9 = 6, R9C9 = 3, R8C6 = 2

18. N36
a) Hidden Single: R5C7 = 7 @ N6
b) 23(4) = {3479} -> R4C7 = 3, R5C8 = 9
c) 10(3) @ N6 = {127} -> R6C7 = 2, R5C6 = 1, R6C6 = 7
d) 5 locked in 8(2) @ R1 -> 8(2) = [35] -> R1C8 = 3, R1C9 = 5

19. Rest is singles.

And I thought I get some relaxation after the pain that was the Brick Wall. :twisted:
Walkthrough by Andrew: Interesting interactions between split cages sharing a common cell:
It looks like Susan's intuitive leap, if that's what it was, must have been an inspired one. Solving any Assassin in 45 minutes is excellent! I'm not sure if I've ever done that; maybe on one of the very early ones.

I've only had a glance at the posted walkthroughs, I'll go through them properly later, but I think my solving method was different.

On going through the posted walkthroughs I particularly liked Susan's use of innies/outies that are in the same columns, C3 for N14 and C7 for N69.

I must admit I missed Gary's first step; that would probably have made my solving path quicker. On checking while editing typos, I found that step 10 gave the same result.

My main technique for this puzzle was the one outlined in my previous message. Once I realised it was there and I reworked some of the earlier stages more rigorously, the puzzle fell out fairly quickly. However I'll still rate it 1.25 because the technique was hard to spot.

Here is my walkthrough for A75 (corrections in red, original step 31 delete as unnecessary). Thanks Ed for your feedback, added after step 6.

Prelims

a) R12C1 = {29/38/47/56}, no 1
b) R1C89 = {17/26/35}, no 4,8,9
c) R23C2 = {13}, locked for C2 and N1, clean-up: no 8 in R12C1
d) R2C78 = {89}, locked for R2 and N3, clean-up: no 2 in R1C1
e) R78C8 = {29/38/47/56}, no 1
f) R8C23 = {48/57}/[93], no 1,2,6, no 9 in R8C3
g) R89C9 = {18/27/36/45}, no 9
h) R9C12 = [19/37]/{28/46}, no 5, no 7,9 in R9C1
i) 22(3) cage in N4 = 9{58/67}, 9 locked for N4
j) 10(3) cage at R5C6 = {127/136/145/235}, no 8,9
k) 19(3) cage at R8C4 = {289/379/469/478/568}, no 1
l) 11(3) cage in N9 = {128/137/146/236/245}, no 9
[I missed 21(3) cage at R2C6 = {489/579/678}, no 1,2,3]

1. 45 rule on R12 3 innies R2C259 = 9 = {126/135/234}, no 7

2. 45 rule on R789 3 innies R7C349 = 19 = {289/379/469/478/568}, no 1
2a. 1 in N7 locked in R789C1, locked for C1

3. 45 rule on C89 3 innies R259C8 = 19 = {289/379/469/478/568}, no 1

4. 45 rule on N1 2 innies R3C13 = 15 = {69/78}

5. 45 rule on N3 2 innies R13C7 = 10 = {37/46}, no 1,2,5
5a. 10(3) cage in N3 = {127/145/235} (cannot be {136} which clashes with R13C7), no 6

6. 45 rule on N7 2 innies R79C3 = 8 = {26/35}, no 4,7,8,9
6a. 9 in C3 locked in R13C3, locked for N1, clean-up: no 2 in R2C1, no 6 in R3C3 (step 4)
6b. 15(3) cage in N7 = {159/168/249/267/348/357} (cannot be {258/456} which clash with R79C3)
[Ed. I went a step further with this one: {168} clashes with h8(2) & 10(2) -> 1 in 15(3) must have 9. 1 in 10(2) -> must have 9. -> no 9 in 12(2). You get rid of it pretty soon anyway, so not much of a short cut.
When I discussed this clash with Ed, he pointed out the use of "combining cages". It's a technique I've used occasionally but haven't yet reached the stage of instinctively looking for them.]


7. 2 in N1 locked in 15(3) cage = 2{49/58} (cannot be {267} which clashes with R12C1), no 6,7
7a. 6 in N1 locked in R123C1, locked for C1, clean-up: no 7 in R6C2, no 4 in R9C2

8. 45 rule on N9 2 innies R7C79 = 14 = {59/68}
8a. R78C8 = {29/38/47} (cannot be {56} which clashes with R7C79), no 5,6

9. R7C349 (step 2) = {289/379/469/568} (cannot be {478} because no 4,7,8 in R7C3)
9a. 2,3 of {289/379} must be in R7C3 -> no 2,3 in R7C4
9b. 6 of R7C349 = {568} must be in R7C3, here’s how
9ba. If R7C3 = 5 => R7C49 = {68} clashes with R7C79 = {68}
9bb. -> no 5 in R7C3, clean-up: no 3 in R9C3 (step 6)
[Note that R7C349 = [685] is still valid but [658] gives clash between R7C3 and R7C7.]

10. 45 rule on C12 3 innies R158C2 = 13 = {247/256} = 2{47/56}, no 8,9, 2 locked for C2, clean-up: no 3,4 in R8C3, no 8 in R9C1
10a. 5 on {256} must be in R8C2 -> no 5 in R15C2

11. 15(3) cage in N1 (step 7) = 2{49/58}
11a. 8,9 only in R1C3 -> R1C3 = {89}

12. 45 rule on R123 3 innies R3C167 = 18 = {468/567} (cannot be {189} because no 1,8,9 in R3C7, cannot be {279} because 2,9 only in R3C6, cannot be {369} because R3C167 = [693] clashes with R1C13 = [69], cannot be {378} because 7/8 in R3C67 clashes with R3C13 = {78}, cannot be {459} because no 4,5,9 in R3C1) = 6{48/57}, no 1,2,3,9, 6 locked for R3, clean-up: no 7 in R1C7 (step 5)
12a. 5 of {567} must be in R3C6 -> no 7 in R3C6
[If I’d included the 21(3) in the Prelims, then I wouldn’t have needed to eliminate {279} from R3C167 which wouldn’t contain a 2.]

13. 45 rule on C123 3 innies R349C3 = 16 = {169/259/367/457} (cannot be {178/349} because R9C3 only contains 2,5,6, cannot be {268} because R49C3 = {26} clashes with R79C3 = {26}, cannot be {358} because R49C3 = [35] clashes with R79C3 = [35]), no 8, clean-up: no 7 in R3C1 (step 4)
13a. 7 of {367/457} must be in R3C3 -> no 7 in R4C3
13b. 1,3 of {169/367} must be in R4C3 -> no 6 in R4C3

14. 45 rule on C789 3 innies R167C7 = 13 = {139/148/157/238/256/346} (cannot be {247} because no 2,4,7 in R7C7)
14a. 1,2 of {157/256} must be in R6C7
14b. 6 of {346} must be in R7C7
14c. -> no 5,6,7 in R6C7
14d. 3 of {139/238/346} must be in R1C7 (3 of {346} in R6C7 would make R13C7 = [46] clash with R7C7 = 6), no 3 in R6C7

15. 15(3) cage at R3C1 = {258/267/348/456} (cannot be {357} because R3C1 only contains 6,8)
15a. 8 of {258/348} must be in R3C1 -> no 8 in R4C12
15b. 2 of {267} must be in R4C1 -> no 7 in R4C1
15c. 6 of {267/456} must be in R3C1 -> no 6 in R4C2

16. 15(4) cage at R5C2 = {1248/1347/2346} (cannot be {1257} because {157} in N4 clashes with 22(3) cage, cannot be {1356} because 6 must be in R7C3 to avoid clash with 22(3) cage and then there’s no 1,3,5 in R5C2) = 4{128/137/236), no 5, 4 locked for N4 because there’s no 4 in R7C3

17. 15(3) cage at R3C1 (step 15) = {258/267} = 2{58/67} -> R4C1 = 2, clean-up: no 8 in R9C2

18. Killer pair 5,7 in R4C2 and 22(3) cage, locked for N4

19. 15(4) cage at R5C2 (step 16) = {1248/2346} = 24{18/36} -> R7C3 = 2, R9C3 = 6 (step 6), clean-up: no 9 in R8C8, no 3 in R8C9, no 4 in R9C1
19a. R9C3 = 6 -> R34C3 (step 13) = 10 = {19/37}
19b. R89C4 = 13 = {49/58}, no 2,3,7

20. R1C2 = 2 (hidden single in C2), clean-up: no 6 in R1C89

21. 45 rule on C3 R12C3 = 13, R34C3 = 10, R79C3 = 8 -> R568C3 = 14 = {158/347}
21a. 5,7 only in R8C3 = {57}, no 8, clean-up: no 4 in R8C2
21b. Naked pair {57} in R8C23, locked for R8 and N7 -> R9C2 = 9, R9C1 = 1, clean-up: no 4 in R7C8, no 4 in R8C4 (step 19b), no 8 in R8C9, no 8 in R9C4 (step 19b), no 2,4 in R9C9
21c. Naked pair {57} in R48C2, locked for C2, clean-up: no 8 in R56C1

22. R7C3 = 2 -> R7C49 = {89} (step 9)
22a. Naked pair {89} in R7C49, locked for R7 -> R7C2 = 4, R78C1 = [38], R7C8 = 7, R8C8 = 4, R8C4 = 9, R9C4 = 4 (step 19b), R7C4 = 8, R7C9 = 9, R7C7 = 5 (step 8), clean-up: no 1 in R1C9, no 2 in R8C9

23. R3C1 = 6 (naked single), R3C3 = 9 (step 4), R4C2 = 7, R8C23 = [57], clean-up: no 5 in R12C1

24. R1C3 = 8 (naked single), R2C3 = 5

25. R5C2 = 6 (naked single), R6C2 = 8, R56C3 = {34} (step 19)
25a. R4C3 = 1 (hidden single in C3)

26. R1C7 = 6 (hidden single in N3), R3C7 = 4 (step 5), R6C7 = 2 (step 14)
26a. R12C6 = 7 = [34/43/52], no 1,7,9

27. 11(3) cage in N9 = {128} (only remaining combination) -> R8C7 = 1, R9C78 = [82], R89C9 = [63], R2C78 = [98], R45C7 = [37], R5C8 = 9 (cage sum), R45C1 = [59], clean-up: no 5 in R1C8

28. R7C7 = 5, R7C56 = {16} -> R8C5 = 3 (cage sum), R8C6 = 2, clean-up: no 5 in R1C6 (step 26a)

29. Naked pair {34} in R12C6, locked for C6 and N2 -> R5C6 = 1, R6C6 = 7, R7C56 = [16], R9C56 = [75], R34C6 = [89], R4C5 = 4

30. Naked pair {56} in R4C48, locked for R4 -> R4C9 = 8, R5C9 = 4, R4C8 = 5, R4C4 = 6, R6C45 = [35], R5C45 = [28], R56C3 = [34]

31. R1C5 = 9 (naked single), R12C4 = 8 = {17} (only remaining combination)
31a. Naked pair {17} in R12C4, locked for C4

and the rest is naked singles and simple cage sums


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PostPosted: Mon Jul 14, 2008 5:00 am 
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Location: Sydney, Australia
Copy of A50-75 Ratings post @ sudocue.net http://www.sudocue.net/forum/viewtopic.php?p=5001#5001


http://www.sudocue.net/forum/viewtopic.php?p=3182#3182
mhparker's rating post:
0.5: Typical newspaper "Deadly". Intended to be done using only limited pencilmarks.

0.75: Easy Assassin, like some of the very early ones, such as A1. Rarely seen now: all recent Assassins would have at least a 1.0 rating on thiscale.

1.0: "Average" V1 Assassin (looking back over a longer period of time). Something like A57, perhaps.
1.25: Harder Assassin. Actually, most recent Assassins seem to have become more difficult than they traditionally used to be. So a rating of "1.25" would be considered the norm now. Typical example: A59.

1.5: Hard Assassin, having a significantly longer and/or narrower solution path, and/or requiring more advanced techniques. The A60 was definitely one of these.

1.75: Very hard Assassin, but still not hard enough to require a team effort to solve. Does not require any hypotheticals. The A60RP-Lite could maybe deserve such a rating.

2.0: Traditional "V2" standard, typically requiring a team effort and maybe (but not necessarily) involving limited use of hypotheticals. Example: A55V2.

2.5: Requires a team effort and several short to medium length hypotheticals. The TJK18 and A48-Hevvie would probably fall into this category.

3.0: "Ruudiculous", requiring a team effort and massive hypotheticals to solve, if it can be solved at all. The A50V2 and (possibly) A60RP could be considered examples of this.

4.0: Puzzles with unique solutions, but which can only realistically be solved by computer programs using backtracking (brute force).


This is my interpretation of Mike's excellent ratings ideas. Comments, criticisms, corrections and suggestions please! I plan to regularly update this list.

Puzzles in each rating category are arranged according to the number of steps taken by rcbroughton's Sudoku Solver & Helper w/o singles (number in brackets next to puzzle name).

A (mostly) chronological list. NOTE: many ratings no longer apply. See the Archive Tables for up-to-date ratings.
Hidden Text:
Assassin 1 (Rating 0.75)
Assassin 1V2 (Rating 1.25)

A48-Hevvie (Rating 2.5)

Assassin 50 (Rating 1.75)
Assassin 50 V2 (Rating 3.0)
Assassin 50 V0.2 (Rating 0.75)

Assassin 51 (Rating 1.25)

Assassin 52 (Rating 1.25)
Assassin 52 V2 (Rating 2.0)

Assassin 53 (Rating 1.0)
Assassin 53V2 (Rating 1.25)
Assassin 53V2.5 (Rating 1.25)
Assassin 53V3 ( (Rating 1.75)
Assassin 53 V0.1 (Rating 2.0)

Assassin 54 (Rating 1.25)
Assassin 54 Version 2 (Rating 1.75)

Assassin 55 (Rating 1.25)
Assassin 55 V2 (Rating 2.0)

Assassin 56 (Rating 1.25)
Assassin 56 V2 (Rating 1.75)

Assassin 57 (Rating 1.0)
Assassin 57 V1.5 (Rating 1.0)
Assassin 57V2X (Rating 1.75)

Assassin 58 (Rating 1.0)
Assassin 58 V1.5 (Rating 1.5)

Assassin 59 (67) (Rating 1.25)
Assassin 59 V1.5 (Rating 1.5)

Assassin 60 (84) (Rating 1.5)
Assassin 60 RP (Rating 2.50)
Assassin 60 RP-Lite (Rating 1.75)

Special X Killer 4 V2 (Rating 4.0)

Assassin 61 (Rating 1.25)
Assassin 61X (Rating 1.50)
Assassin 61X V3 (Rating 4.0)

Assassin 62 (Rating 0.75)
Assassin 62V2 (Rating 2.0)

Assassin 63 (Rating 0.75)
Assassin 63 V1.5 (Rating 1.0)
Assassin 63 V2 (Rating 1.5)

Assassin 64 (Rating 1.25)
Assassin 64V2 (Rating 1.75)

Assassin 65 (Rating 1.25)
Assassin 65 V2 (Rating 1.75)
Assassin 65 V3 (Rating 1,75)

Assassin 66 (Rating 1.0)
Assassin 66 V1.5 (Rating 1.5)

Assassin 67 (Rating 0.75)

Vortex X (Rating 1.75)
Vortex X Lite (Rating 1.25)

Transformer Killer X (Rating 1.75)
Transformer Killer X Lite (Rating 1.25)

Assassin 68 (Rating 1.00)
Assassin 68 V2 (Rating 1.75)
Assassin 68 V3 (Rating 3.00)
Assassin 68 V1.5 (Rating 1.25)

Assassin 69 (Rating 1.25)
Assassin 69 V1.5 (Rating 1.50)

Assassin 70 (Rating 0.75)
Assassin 70 V2 (Rating 1.75)
Assassin 70 V3 (Rating 1.25)

Assassin 71 (Rating 1.75)
Assassin 71 (V2) - Full Border (Rating 1.50)
Assassin 71 V1.5 (Rating 1.25)

Concentric Squares (CS) Killer by mhparker (Rating 1.25)

Assassin 72 (Rating 1.0)
Old School Assassin 72V2 (Rating 1.75)

Assassin 73 (Rating 1.0)

Maverick 1 (Rating 1.75)

Assassin 74 (Rating 1.0)
Assassin 74 V2 (Rating 1.25)
Assassin 74 Brick Wall (Rating 2.0)

Assassin 75 (Rating 1.25)


Assassin 50-75 & Forum Killers' (& Killer X) Ratings (number in brackets is the number of steps taken by Sudoku Solver w/o singles)
___________________________________________________________
Rating 4.0

Hidden Text:
Special Killer X4 V2 (Did Not Solve: DNS 8 steps No progress) http://www.sudocue.net/forum/viewtopic.php?p=3174#3174
Para wrote:
But i don't think there is any proper way of solving this puzzle.


Assassin 61X V3 (DNS 17 steps No progress) http://www.sudocue.net/forum/viewtopic.php?p=3202#3202
mhparker wrote:
A60RP looks like child's play in comparison to this one
Para wrote:
Another horrible creation while trying to make a suitable V2 for an assassin

___________________________________________________________
Rating 3.0

Hidden Text:
Assassin 68 V3
code: http://www.sudocue.net/forum/viewtopic.php?p=3590#3590
pic: http://www.sudocue.net/forum/viewtopic.php?p=3599#3599
Ruud wrote:
estimated rating 3-4
mhparker wrote:
it looks it's going to be a strong candidate for the Unsolvables list!
Jean-Christophe in JSudoku thread this forum: Proud to announce JSudoku could also solve Ruud's Assassin 68V3.
Quote:
no walk-through


Assassin 50 V2 (DNS 24 No progress) http://www.sudocue.net/forum/viewtopic.php?p=2624#2624
Quote:
mhparker wrote:
rating 3.0: "Ruudiculous", requiring a team effort and massive hypotheticals to solve, if it can be solved at all. The A50V2 and (possibly) A60RP could be considered examples of this.
Ruud wrote:
could be one of the toughest killers I made so far.
Glyn wrote:
I am struggling with it here. Tried making a huge implication chain round the outside, knocks out a few candidates but nothing worth reporting.


__________________________________________________________
Rating 2.5

Hidden Text:
Assassin 60 RP (DNS 28 No progress) http://www.sudocue.net/forum/viewtopic.php?p=3099#3099
mhparker wrote:
3.0: "Ruudiculous", requiring a team effort and massive hypotheticals to solve, if it can be solved at all. The A50V2 and (possibly) A60RP could be considered examples of this.
rcbroughton wrote:
This is a real tough nut.
mhparker wrote:
My only real suggestions are that we document the misery, be thankful for every candidate we've managed to pick off, pack our bags and go home**!
Ruud wrote:
A60RP may be unsolvable at this moment, but a lot of progress has been made in the Killer community, so I expect this puzzle to fall at the hands of a skilled player at some time in the future.
Afmob wrote:
This one was definitely harder than A74 Brick Wall since even finding those hypotheticals was difficult especially those moves between step 9 and 14 took me a long time to find...Rating: Hard 2.5. I had to use some hypotheticals and massive combo analysis but those hypotheticals were of medium length
Quote:
Walk-through by Afmob with obvious moves left out http://www.sudocue.net/forum/viewtopic.php?p=4324#4324



A48-Hevvie (157) http://www.sudocue.net/forum/viewtopic.php?p=2509#2509
mhparker wrote:
2.5: Requires a team effort and several short to medium length hypotheticals. The TJK18 and A48-Hevvie would probably fall into this category.
sudokuEd wrote:
Very
rcbroughton wrote:
not an easy one by any means
Quote:
Condensed/simplified walk-through by sudokuEd
http://www.sudocue.net/forum/viewtopic.php?p=2636#2636


______________________________________________________
Rating 2.0

Hidden Text:
Assassin 55V2 (DNS 30 No progress) http://www.sudocue.net/forum/viewtopic.php?p=2825#2825
mhparker wrote:
2.0: Traditional "V2" standard, typically requiring a team effort and maybe (but not necessarily) involving limited use of hypotheticals. Example: A55V2.
sudokuEd wrote:
can't resist trying the lollie. But will need lots of help. Any other suckers
Quote:
Tag solution by sudokuEd, CathyW, mhparker
http://www.sudocue.net/forum/viewtopic.php?p=2835#2835


Assassin 62V2 (DNS 42 No progress) http://www.sudocue.net/forum/viewtopic.php?p=3221#3221
mhparker wrote:
not so much of an Assassin, this one. More like a Terminator!
mhparker wrote:
I could eventually solve without hypotheticals, but only by using several grouped AICs..I rated the A62V2 at 2.0
Quote:
Long, optimized Walk-through by Grandmaster mhparker and uses several AICs, and some other creative moves http://www.sudocue.net/forum/viewtopic.php?p=4204#4204



Assassin 53 V0.1 (DNS 46 No progress) http://www.sudocue.net/forum/viewtopic.php?p=2763#2763
Para wrote:
53V0.1 i still have no clue on how to advance. I did the basics and am stuck.
mhparker wrote:
Had to use a hypothetical to continue
Quote:
tag solution by Para and mhparker. Starts at
http://www.sudocue.net/forum/viewtopic.php?p=2794#2794


Assassin 74 Brick Wall http://www.sudocue.net/forum/viewtopic.php?p=3868#3868
Ruud wrote:
a little off the Assassing scale:..A solving tip: Brick wall
mhparker wrote:
I'm still suffering from a kind of paranoia when it comes to so many "L" shaped cages after our experience with TJK18! pale.. the second half of the puzzle would have been paradise for me
gary w wrote:
I've made a little bit of progress but am now stuck in a morass of either/ors which just don't want to seem to yield..I really ran into a featureless wall of rock
Afmob wrote:
What a monster! That was the most difficult Killer Sudoku I've solved so far. But I got no idea about the rating since the hardest I've solved was about 1.75...
Para wrote:
...some cracks and a few holes but it is still not falling down..[Edit]Now got 12 digits placed.
[Edit].. Now 13 digits placed...[Edit]...Now 81 digits placed Wink
gary w wrote:
A privilege to go thro' Afmob's and Para's wts...Great to see two masters at work
gooders wrote:
c'est magnifique! well done para i got a long way last weekend but could not bust the top three nonets
Para wrote:
It is probably a high 2.0. ...It took me 3 days to solve (officially 4 days as i had tried it once when Ruud posted but gave up pretty quickly)
mhparker wrote:
the Brick Wall can be solved quite elegantly, as Para has just proved so well
over 4 months later Afmob wrote:
I finally decided to solve it again in an appropiate way without resorting to long contradiction chains...Rating: 2.0. I used lots of forcing chains and combo analysis (but not as heavy as in A60 RP) to solve this monster
Quote:
Walk-through by Afmob including a "last big contradiction move on R2C1" http://www.sudocue.net/forum/viewtopic.php?p=3897#3897
Walk-through by Para http://www.sudocue.net/forum/viewtopic.php?p=3904#3904
Solving outline using "hypos" by gary w http://www.sudocue.net/forum/viewtopic.php?p=3907#3907
Analysis of Para's step 46 (Killer XY-Chain) by mhparker http://www.sudocue.net/forum/viewtopic.php?p=3916#3916
Alternative to Para's step 46 (Hidden Killer Pair Type 2:0) by mhparker http://www.sudocue.net/forum/viewtopic.php?p=3922#3922
new shorter Walk-through by Afmob (mar 08) http://www.sudocue.net/forum/viewtopic.php?p=4782#4782



Assassin 52 V2 (92) http://www.sudocue.net/forum/viewtopic.php?p=2688#2688
Para wrote:
doesn't seem i am going to solve this one by myself.
mhparker wrote:
.. the puzzle was not that difficult - certainly not "terrifying", and easily within range of ordinary mortals.
Quote:
Tag solution by Para, mhparker, Jean-Christophe
http://www.sudocue.net/forum/viewtopic.php?p=2694#2694
full walkthrough for the V2, based on tag solution.
http://www.sudocue.net/forum/viewtopic.php?p=2743#2743


_________________________________________________________
Rating 1.75

Hidden Text:
Assassin 60 RP-Lite (159) http://www.sudocue.net/forum/viewtopic.php?p=3140#3140
mhparker wrote:
1.75: Very hard Killer, but still not hard enough to require a team effort to solve. Does not require any hypotheticals. The A60RP-Lite could maybe deserve such a rating.
CathyW wrote:
Brick wall It's no good. I'm not getting any further
sudokuEd wrote:
Finally found a nice solution to RP Lite - after nearly 3 weeks.
4 months later Para wrote:
I solved the A60RP-Lite with "only" those (normal Killer) techniques. That doesn't mean it isn't hard. Using those techniques can make a puzzle awfully difficult as well. You just need the right insight to use those techniques appropriately
4 months later in November 07 Andrew wrote:
It's easy to forget that each of these ratings represent a range. Obviously, from what people say about A60RP-Lite, it must be at the very top of the 1.75 rating range

Quote:


Old School Assassin 72V2 http://www.sudocue.net/forum/viewtopic.php?p=3809#3809
Para wrote:
it opens up some interesting moves from the the original pattern that weren't needed to solve the puzzle before. It rates about a V1.75 the way i solved it
mhparker wrote:
In particular, there's one high-level (but simple and very powerful) move that effectively killed the puzzle off without having to resort to a lot of low-level combination crunching ..correspond to a rating of around 1.5
sudokuEd wrote:
Have given up...Wow. What a brute......Took me forever .... - but not for Mike! I really enjoyed the JSudoku log.... Really easy to follow and many, many clever things
Andrew wrote:
I don't think I'm going to be able to finish...
Quote:
Walk-through by mhparker http://www.sudocue.net/forum/viewtopic.php?p=3811#3811
"android" Walk-through (i.e., automated solver ..Jsudoku.. dressed up in human WT form) by mhparker http://www.sudocue.net/forum/viewtopic.php?p=3818#3818


Assassin 65 V3 http://www.sudocue.net/forum/viewtopic.php?p=3389#3389
Ruud wrote:
hot hot hot, probably needs some creative moves (guesses)
Para wrote:
That V3 is really deceiving, you think you're doing pretty well, placing digits, making eliminations and then all of the sudden you hit a dead end and there's seems to be no way out.
Caida wrote:
I've been pounding away at it for quite sometime and I think I'm going in circles. I've resorted to trial and error
Afmob wrote:
Rating: 1.75 it wasn't as difficult as A74 Brick Wall but a bit more complicated than M1, it's solvable without guesses or T&E
gary w wrote:
after a tough battle..rather more than 5 hours....managed to crack it
Quote:
Wrong answer walk-through by Caida http://www.sudocue.net/forum/viewtopic.php?p=3977#3977
No contradiction moves Walk-through by Afmob http://www.sudocue.net/forum/viewtopic.php?p=4000#4000
Beginning solution outline by gary w without any t&e http://www.sudocue.net/forum/viewtopic.php?p=4019#4019


Assassin 53V3 (124) http://www.sudocue.net/forum/viewtopic.php?p=2752#2752
Jean-Christophe wrote:
Grouping some cages... make it real hard to solve. ...
sudokuEd wrote:
Took hours to see some 'obvious' contradiction moves.
Para wrote:
It wasn't as hard as the line "the new JSudoku can solve it" make it look
Quote:


Assassin 56 V2 (117) http://www.sudocue.net/forum/viewtopic.php?p=2882#2882
Para wrote:
It's a tough one, but once you know where to look it will break slowly.
sudokuEd wrote:
A very, very difficult puzzle with lots of contradiction moves and extensive combination conflicts. Had to restart many times to get a valid solution. Must have spent 15 hours on this one
Quote:


Assassin 50 (117)
mhparker wrote:
As far as difficult V1 Assassins go... add A50V1 to the list... In terms of techniques, the A50V1 was harder than this one (A55).
Andrew wrote:
A tough challenge
Para wrote:
I spent a while looking for a nicer way ... But can't find anything.
Quote:


Assassin 54 Version 2 (106) http://www.sudocue.net/forum/viewtopic.php?p=2787#2787
mhparker wrote:
It should be harder than the original, but is definitely still solvable via logic
sudokuEd wrote:
It is a real good one too -lots of combining "45" moves to see contradictions.
Quote:


Assassin 57V2X (65) http://www.sudocue.net/forum/viewtopic.php?p=2916#2916
mhparker wrote:
The latest released version (of JSudoku 0.6b1) only manages 2 placements before giving up.
Andrew wrote:
Mike's step 30 - I'll settle for the stiff drink after working through it.
Quote:
tag solution by rcbroughton, Andrew, mhparker
http://www.sudocue.net/forum/viewtopic.php?p=2922#2922
sudokuEd simplified walk-through
http://www.sudocue.net/forum/viewtopic.php?p=2975#2975
mhparker alternate ending to simplified walk-through
http://www.sudocue.net/forum/viewtopic.php?p=2994#2994


Assassin 64V2 http://www.sudocue.net/forum/viewtopic.php?p=3316#3316
CathyW wrote:
completely stumped after 26 steps.
mhparker wrote:
it was no monster. I would give it a clear rating of 1.75
Quote:
tag solution by CathyW, mhparker, Howard S, rcbroughton, Para, Glyn & goooders!
http://www.sudocue.net/forum/viewtopic.php?p=3319#3319
Alternative ending to tag solution by mhparker
http://www.sudocue.net/forum/viewtopic.php?p=3354#3354
Missed moves by mhparker
http://www.sudocue.net/forum/viewtopic.php?p=3356#3356
Consolidated tag walkthrough by Andrew
http://www.sudocue.net/forum/viewtopic.php?p=3401#3401


Assassin 65 V2 http://www.sudocue.net/forum/viewtopic.php?p=3389#3389
Ruud wrote:
Tough, but no hypotheticals (guesses) needed.
CathyW wrote:
Hmmph! Confused. Can't say that the V2 is a fun puzzle.
Howard S wrote:
Learnt a lot
Quote:
tag solution by Howard S and Para - moral support from CathyW and mhparker
http://www.sudocue.net/forum/viewtopic.php?p=3414#3414
Alternative to tag solutions' step 29 by mhparker
http://www.sudocue.net/forum/viewtopic.php?p=3445#3445


Transformer Killer X by Para http://www.sudocue.net/forum/viewtopic.php?p=3543#3543
Para wrote:
It contains a little trick, that could help you in solving..Rating-wise i think .. a 1.75.
mhparker wrote:
Standard moves exhausted and a huge forest of candidates still remaining! Looks like I'll need to find that trick Para was talking about..
mhparker wrote:
.a very enjoyable Killer-X!..some advanced moves ...so I think a 1.75 rating is not a bad estimate.
Quote:


Assassin 68 V2
code: http://www.sudocue.net/forum/viewtopic.php?p=3590#3590
pic: http://www.sudocue.net/forum/viewtopic.php?p=3594#3594
Para wrote:
It is probably a high 1.75 because it uses no hypotheticals, mostly creative combination work.
mhparker wrote:
I would rate it around 1.75 (i.e., roughly A60RP level)
sudokuEd wrote:
lots of combination pecking....Still no-where near A60 RP Lite in difficulty. But a very nice 1.75!
Quote:

Vortex Killer X by mhparker http://www.sudocue.net/forum/viewtopic.php?p=3470#3470
mhparker wrote:
Est. rating: 1.75
Andrew wrote:
Assassin 66V1.5 and Vortex Killer ...Vortex Killer was definitely the easier and more enjoyable of these two puzzles
I would rate Vortex Killer between 1.5 and 1.75. Ed currently has Vortex Killer as 1.75 and A66V.15 as 1.5. Maybe he should consider swapping those ratings?
Quote:


Assassin 70 V2 http://www.sudocue.net/forum/viewtopic.php?p=3673#3673
sudokuEd wrote:
I'm still stuck on both V2 & V3
gary w wrote:
Obviously this one turned out to require afearsome amount of combination work
mhparker wrote:
I discovered that this puzzle could be unlocked without an awful lot of combination crunching
Quote:
tag walk-through by sudokuEd, Afmob, goooders, Para http://www.sudocue.net/forum/viewtopic.php?p=3718#3718
Alternate ending by mhparker http://www.sudocue.net/forum/viewtopic.php?p=3731#3731


Assassin 71
CathyW wrote:
This is definitely a tough one. 45 steps (about 3 hours) and counting. Shocked..Finally! Took about 4 hours in total. At least 1.5 rating. I can't say I particularly want to go through it again
gary w wrote:
this was a tough one..sure was..took me 5 hrs plus Exclamation
Afmob wrote:
What a monster. I didn't find a nice way to solve to puzzle so be prepared for some contradiction moves. I think it was more difficult than A69 V1.5 so I guess rating is about 1.75
Andrew wrote:
A71 must be one of the hardest ever V1s!... I'll go along with Afmob's rating of 1.75. I think this is the first time that a V1 has been harder than the V2
sudokuEd wrote:
I'd rate the puzzle a 1.5 since it took me less than 10 hours to get a nice solution
About A71 On A74 thread mhparker wrote:
there's been a tendency for people to overrate puzzles recently. The A71 was a good example of this...Sure, it was very tough. But does it really deserve a 1.75 rating?
About A71 on A74 thread sudokuEd wrote:
I agree (about overrating puzzles) - especially about A71
Quote:


Maverick 1 (M1) by mhparker
mhparker wrote:
(Est. rating: 1.5) This puzzle .... should provide plenty of opportunity for creativity and individualism, as its name implies
gary w wrote:
I'm finding this one tough going!!... Finally cracked it
Afmob wrote:
Definitely a fun assassin with lots of cool moves
Para wrote:
all this talk about x-wing and x-cycles going on... It is also solvable by just sticking to the basic killer techniques as 45-test cage combos and Killer Subsets
Andrew wrote:
It took me a week, on and off .. If I hadn't received encouragement off-forum from Mike and then seen that Para had posted his partial walkthrough from my position, now expanded to a full walkthrough, I might well have given up on this one. Maverick 1 felt to me at least as hard as any of the other 1.75s that I've done. I spent longer on it than on any of those others. It's definitely my longest walkthrough yet. Therefore I've no hesitation in rating Maverick 1 as 1.75.
Para wrote:
This puzzle felt more like a 1.5 rating to me. But that is mostly because it fell fairly quickly compared to say A60RP-Lite which i rated a 1.75. For me it wasn't in the same league as that puzzle.
gary w wrote:
it had a rather lovely solving path (which I "sort of" used myself but could never have expressed it as well as the other two (Afmob & mhparker) did)
on sat Nov 24 Afmob wrote:
M2 was more difficult than M1 so... now I would rate M1 with a 1.5
Quote:


_______________________________________________________________
Rating 1.5

Hidden Text:
Assassin 66 V1.5 (SSscore 1.52) http://www.sudocue.net/forum/viewtopic.php?p=3460#3460
CathyW wrote:
Edit: Definitely much harder - at least a 1.5. ..Edit 2: ... scratch Rating up to 2 probably. Either needs hypotheticals or I'm missing something....Edit 3: Give up ..just checked through Para's WT. Nothing short of brilliant imho!
Para wrote:
That was a good puzzle somewhere between 1.50 and 1.75. Some fancy combination work and/with 45-tests did the trick.
Andrew wrote:
I would rate A66V1.5 as a solid 1.75; possibly a bit higher for my solving path with 1.75 for Para's slightly more direct route.
Quote:


Assassin 61X (99) http://www.sudocue.net/forum/viewtopic.php?p=3178#3178
mhparker wrote:
(Est. difficulty: r1.75 level)
CathyW wrote:
I found it easier than the A61
Andrew wrote:
I found Mike's A61X a real struggle.. 1.75 ... 1.5... ratings look right
Quote:


Assassin 58 V1.5 (94) http://www.sudocue.net/forum/viewtopic.php?p=2989#2989
mhparker wrote:
It should be slightly harder than the original was intended to be, but still very do-able.
Quote:
no walk-through


Assassin 60 (84)
mhparker wrote:
1.5: Hard Assassin, having a significantly longer and/or narrower solution path, and/or requiring more advanced techniques. The A60 was definitely one of these.
CathyW wrote:
Ruud has certainly ramped up the difficulty this week
Andrew wrote:
I particularly liked Para's (walk-through) which was so direct.
Quote:


Assassin 59 V1.5 (78) http://www.sudocue.net/forum/viewtopic.php?p=3088#3088
CathyW wrote:
I'm stuck
Quote:


Assassin 63 V2 http://www.sudocue.net/forum/viewtopic.php?p=3282#3282
Mike wrote:
(Estimated rating: 1.75
Quote:


Assassin 69 V1.5 http://www.sudocue.net/forum/viewtopic.php?p=3641#3641
mhparker wrote:
Est. rating: 1.5
Para wrote:
a typical Mike Killer.The rating seems to fit. One really tricky move
Afmob wrote:
V1.5 was definitely harder than the original because it didn't fall that fast and I needed several contradiction moves

Quote:


Assassin 71 (V2) - Full Border http://www.sudocue.net/forum/viewtopic.php?p=3738#3738
Andrew wrote:
It still seems easier than A71
mhparker wrote:
Overall, I would rate the A71V2 at around 1.5
gary w wrote:
Took me less than 1.5 hours...So there Ruud..I reckon this one was much easier than V1 !!!
Afmob wrote:
Another difficult V2 though it was a bit easier than V1
Quote:


____________________________________________________
Rating 1.25

Hidden Text:
Assassin 75
CathyW wrote:
I'm struggling with it Confused Sad ..... I feel a bout of combo crunching coming on..Finally got there. Smile..Total time about 4 hours and I haven't done a WT!
sublue wrote:
My first placement was ...... But I'll be darned if I can figure out how I did it! Note to self: write this stuff down the *first* time!
gary w wrote:
After the wall this one wasn't too bad...took me about 2.5 hours
Afmob wrote:
That one was tougher than I thought.... so rating should be about 1.25..And I thought I (would) get some relaxation after the pain that was the Brick Wall.Twisted Evil
Andrew wrote:
On what I've done so far it feels like a 1.25..I particularly liked Susan's (sublue) use of innies/outies that are in the same columns
azpaull wrote:
I'm glad to see that this gave (or is giving) others problems, too.....I think this will go into my growing bank of "ones to come back to" for now!
Quote:
solution briefly outlined by gary w http://www.sudocue.net/forum/viewtopic.php?p=3947#3947
Walk-through by sublue: less-intuitive, defensable http://www.sudocue.net/forum/viewtopic.php?p=3949#3949
Walk-through by Afmob: forcing chains (Considering placement with 2 possibilites) http://www.sudocue.net/forum/viewtopic.php?p=3954#3954
Walk-through by Andrew: Interesting interactions between split cages sharing a common cell http://www.sudocue.net/forum/viewtopic.php?p=3958#3958



Concentric Squares (CS) Killer by mhparker http://www.sudocue.net/forum/viewtopic.php?p=3799#3799
gary w wrote:
this turned out to be a rather lovely puzzle
Afmob wrote:
It required lots of litte steps but nothing to complicated
Andrew wrote:
I'll agree with your rating of 1.25
Quote:


Assassin 69
CathyW wrote:
A69 is proving extremely tricky!..estimated rating 1.5
mhparker wrote:
This was a nice puzzle. ... Rating probably around 1.25
gary w wrote:
Enjoyed going through Cathy's wt too. Solving path seemed very similar to Mike's... the path is quite tightly constrained.....I really appreciate the effort in putting the wts on
Andrew wrote:
My solving path was quite a lot different than the others. ..I'll agree with Mike's estimated rating of 1.25
Quote:


Assassin 71 V1.5 http://www.sudocue.net/forum/viewtopic.php?p=3768#3768
gary w wrote:
I for one thoroughly enjoyed renewing my acquaintance with this cage...Slightly easier than v1 but...about 3 hours,in fact
Andrew wrote:
A lot easier than V1 ..I'll rate it at least a 1.25. Maybe it should be rated higher because it was a fairly narrow solving path and a lot of work after the breakthrough
Afmob wrote:
was the easiest of the bunch. It didn't need any complicate or long contradiction moves so given rating of 1.25 should be right. By the way, it was the most fun to solve
Quote:

mhparker on Rating Thread A71 (V1.5)- 1.25 1.75
1.25 rating is possibly too low. Agree with upgrade to 1.5.


Assassin 61 (90)
CathyW wrote:
Tougher than it looked from the preliminaries but got there eventually
Andrew wrote:
I found this one fairly straightforward and didn't need any wizard moves
Quote:


Assassin 53V2.5 (88)

pic: http://www.sudocue.net/forum/viewtopic.php?p=3234#3234
code: http://www.sudocue.net/forum/viewtopic.php?p=2746#2746&#41;
Para wrote:
properly solvable (typical assassin difficulty)... Solved that one just sitting back, relaxing and enjoying the end result.
Quote:


Assassin 56 (74)
Andrew wrote:
Assassin 56 was only the 3rd V1 that didn't have any 2-cell cages
Quote:


Assassin 54 (74)
Para wrote:
This one went quickly for me. Not many difficult moves but maybe my definition of difficult is a bit off for other people.
Andrew wrote:
I don't think any of the posted walkthroughs needed many advanced moves
Quote:


Assassin 59 (67)
mhparker wrote:
1.25: Harder Assassin. Actually, most recent Assassins seem to have become more difficult than they traditionally used to be. So a rating of "1.25" would be considered the norm now. Typical example: A59
CathyW wrote:
Strangely, I found this one easier than 58.
Quote:


Assassin 51 (67)
Jean-Christophe wrote:
It was enjoyable to solve. Just the right difficulty level for me. Definitely does not need T&E or big combination crushing like some others.
Andrew wrote:
A tough challenge.
CathyW wrote:
was definitely hard enough for me!
Quote:


Assassin 52 (60)
CathyW wrote:
relatively straightforward.
Para wrote:
straightforward. Nothing spectacular
Quote:


Assassin 55 (58)
CathyW wrote:
Shocked Confused Exclamation
Ruud has certainly ramped up the difficulty level this week.
Para wrote:
What a work to fill 81 little cells.
mhparker wrote:
This V1 wasn't too bad. There was quite a narrow solving path at the beginning... There weren't any really difficult techniques required.
Quote:


Assassin 1V2 (57) http://www.sudocue.net/forum/viewtopic.php?p=2754#2754
sudokuEd wrote:
Rating? About average Assassin one year on - an early placement, then steady progress with that extra trick to finally break it.
Andrew wrote:
I'll rate A1V2 as a solid 1.25
Quote:


Assassin 53V2 (46) http://www.sudocue.net/forum/viewtopic.php?p=2745#2745
Andrew wrote:
Initially I'd got stuck
Quote:


Assassin 65
CathyW wrote:
Excellent puzzle - kept me occupied most of this afternoon... Was stuck for quite a while
Para wrote:
Was a fun puzzle
Andrew wrote:
not ..... particularly difficult..I rate this Assassin as 1.25..also 1.25 for the ways that Cathy and Para solved it.
Quote:


Assassin 64
Para wrote:
Was having some fun with this one. Also used a technique we don't get to use much in Assassins. Guess this assassin rates somewhere between 1.00 and 1.25
Andrew wrote:
I agree with Para that it's rated between 1.0 and 1.25
CathyW wrote:
Hmm - more a 1.5 in my book - quite a challenge
Quote:


Vortex Lite X by mhparker http://www.sudocue.net/forum/viewtopic.php?p=3479#3479
mhparker wrote:
Est. rating: 1.25..the Vortex Lite is really no more difficult than a typical Assassin!
Andrew wrote:
I'll agree with that(rating of 1.25) although at one time I was struggling a bit... No "advanced techniques"
Ruud wrote:
the Vortex Lite was very enjoyable
Quote:


Assassin 68 V1.5 http://www.sudocue.net/forum/viewtopic.php?p=3594#3594
CathyW wrote:
nothing majorly advanced required but it was quite a slog...I would rate this puzzle as 1.25 - 1.5. It took me a couple of hours on the 1st attempt
Quote:


Transformer Killer X "Lite" by Para http://www.sudocue.net/forum/viewtopic.php?p=3543#3543
Para wrote:
Rating-wise i think .. about a 1.00-1.25
CathyW wrote:
Had to have a big hint from Para about "The Trick" but have now solved the Transformer Lite. "The Trick" is clever - seems obvious once you know!! I would agree with 1 - 1.25 for the Lite.
Andrew wrote:
An interesting puzzle with a fairly difficult cage pattern and, of course, a neat trick by Para..Even with "The Trick" I rate it a solid 1.25. No way it's a 1.0!
Quote:


Assassin 70 V3 http://www.sudocue.net/forum/viewtopic.php?p=3683#3683
gary w wrote:
Didn't find it too bad..no worse than version 1 ..I noted .. the two totally different soving pathways in v1 and v3 just determined by the broken cage at r4c258. Killers are fascinating!!
Afmob wrote:
it was nearly as difficult as V2 though the moves were less complicated. I guess rating would be 1.25
sudokuEd wrote:
Really good solution Afmob. 9c is a ripper! Good call on the rating - once you find one of the keys it falls very easily

Quote:


Assassin 74 variant 2 http://www.sudocue.net/forum/viewtopic.php?p=3868#3868
Ruud wrote:
..requires a few steps which are more advanced than those required for the original, but in total, the solving path is shorter
Afmod wrote:
This one required some more complicated combo analysis. I can't say that the walkthrough was shorter than my WT for V1
Andrew wrote:
I didn't find A74V2 much harder than A74 so I can't rate it any higher than 1.25..the solving path is shorter than for the original, but not by much
Quote:



_____________________________________________________
Rating 1.0

Hidden Text:
Assassin 74
Andrew wrote:
This one flowed easily for quite a time, then got a bit stubborn so I'll rate it at 1.0..There was certainly plenty of pattern repetition giving repeating themes for the solving path
CathyW wrote:
13 placements during lunch break
Afmob wrote:
This assassin was pretty straightforward but it took me quite a while to finish it since I found no obvious shortcuts..Rating: 1.0,
gary w wrote:
perhaps this was about a 1.0? Took me about 2.5 hours..I notice Ruud likes to use 3 cages but he excelled himself here.. and all but one was L shaped.
Quote:
Walk-through by sublue including Venn Diagram logic and algebra http://www.sudocue.net/forum/viewtopic.php?p=3851#3851
Walk-through with no short-cuts by Afmob http://www.sudocue.net/forum/viewtopic.php?p=3858#3858
Solving outline by gary w http://www.sudocue.net/forum/viewtopic.php?p=3861#3861


Assassin 73
Andrew wrote:
Thank goodness for another fairly easy one. I liked the way that one theme kept repeating itself ... I'll rate this as 1.0
gary w wrote:
pretty straightforward one and no combo crunching required
Afmob wrote:
Although this Assassin was "just" of rating 1.0 it kept me busy
Quote:


Assassin 68
CathyW wrote:
(took a couple of hours including doing the WT..a reasonable challenge...Estimated rating 1-1.25
Para wrote:
It was a really fun puzzle. I enjoyed solving it. I agree with Cathy about the rating.
Andrew wrote:
I'll rate it as 1.25. I found it a difficult cage pattern because I didn't find any innies/outies that helped
Quote:


Assassin 66 (SSscore 1.25)
Howard S wrote:
One of the easier ones - I am torn between 0.75 and 1.0
Andrew wrote:
I think I'll rate this as 1.0. Step 32 isn't a difficult one but I found it was hard to spot
CathyW wrote:
0.5 because I only used Innies, Outies, Outies-Innies, cage combinations, killer combos and combination analysis and because it only took me just over an hour including writing down my steps as I did them
azpaull wrote:
this was the first Assassin in several weeks that I have been able to do on my own....I'll give it a 0.75....let me thank you all for your walk-throughs and your commentary
gary w wrote:
both a66 and a67 took me about 1.5-2 hrs to do.A "deadly" killer in The Times normally takes me about 0.5 hrs so i'ld rate both of these as significantly harder
Quote:
Walk-through by Andrew (SSscore 1.32)
http://www.sudocue.net/forum/viewtopic.php?p=3436#3436
Walk-through by Cathy (SSscore 0.98)
http://www.sudocue.net/forum/viewtopic.php?p=3437#3437


Assassin 53 (85)
Para wrote:
This was a quick puzzle. But as this is the first of the new assassin year, this one could get some newer players excited.
Quote:


Assassin 63 V1.5 (80) http://www.sudocue.net/forum/viewtopic.php?p=3272#3272
Para wrote:
1.5 seems overrated. Didn't have any more trouble with this one than with the V1. Nothing special needed
Andrew wrote:
would probably be rated as 1.0 for Para's solving path
Quote:


Assassin 58 (78)
CathyW wrote:
Struggling with this one! Confused
mhparker wrote:
The V1 had a (probably unintentional) design weakness that was admittedly not easy to spot
herschko wrote:
I did not find this one hard at all.
Quote:


Assassin 57 (43)
mhparker wrote:
1.0: "Average" V1 Assassin (looking back over a longer period of time). Something like A57, perhaps.
Jean-Christophe wrote:
It isn't as hard as usual.
CathyW wrote:
I thought more combination analysis would be required from Ruud's comment on the puzzle page. Still fun to solve!
Andrew wrote:
A bit easier than some recent ones and definitely less combination work than suggested by Ruud's introduction
Quote:


Assassin 57 V1.5 (43) http://www.sudocue.net/forum/viewtopic.php?p=2902#2902
CathyW wrote:
Plenty of combination analysis required .... methinks!
Quote:


Assassin 72
frank wrote:
It is nice to claim victory for a change
Andrew wrote:
Fairly straightforward but I did need some hidden killers, expressed directly or indirectly so I can't rate it lower than 1.0
Afmob wrote:
I think the problem with this assassin was not to solve it but to make the solving path not too long so I tried to keep it as small as possible. Rating: 0.75 - 1.0 but more 1.0 than 0.75
CathyW wrote:
Enjoyed this one. I'd agree with the 1.0 rating
gary w wrote:
A nice easy one after last week's horror!
Quote:


_________________________________________________________
Rating 0.75

Hidden Text:
Assassin 67
Howard S wrote:
This seemed straight forward - certainly easier than 66
CathyW wrote:
I can't say I found it easier than A66 but would agree with the 0.75 rating
Andrew wrote:
I solved in one session, apart from a break for dinner, so that makes it easier than average Assassins over the last few months
gary w wrote:
a67 took me about 1.5-2 hrs to do.A "deadly" killer in The Times normally takes me about 0.5 hrs so ....significantly harder

Quote:


Assassin 62 (73)
Para wrote:
Somewhere between 0.5-0.75 probably
Quote:


Assassin 63 (59)
goooders wrote:
isnt this very easy?
Andrew wrote:
This was a smooth puzzle except right at the end..about 0.75 which is probably about right
herschko wrote:
found this one relatively easy.... I just wouldn't call it an "assassin."
Quote:


Assassin 50 V0.2 (46) http://www.sudocue.net/forum/viewtopic.php?p=2638#2638
Ruud wrote:
This version 0.2 has the same difficulty rating as a recent Moderate on http://www.sudoku.org.uk
Glyn wrote:
I did it before I had the beer though.
Andrew wrote:
Don't know about that (Ruud's rating). It was definitely routine so V0.2 is a fair rating. However as someone who still does the killers on the other website it took me longer than any daily killer there.
Quote:


Assassin 62
Para wrote:
Somewhere between 0.5-0.75 probably
Quote:


Assassin 70
Afmob wrote:
This one was a bit strange since there were many solving paths you could go, but I tried to keep it as short as possible. Overall, a rather easy assassin
mhparker wrote:
Rating? 0.75? It was probably significantly easier than Ruud intended it to be
sudokuEd wrote:
Definitely only a 0.75 rating - maybe even 0.5 - except I used 1 little contradiction move. Maybe that speeded things up
Andrew wrote:
I did miss something important. .... However it still comes out and would only be rated between 1.0 and 1.25 that way. An excellent solving path by Afmob!
azpaull wrote:
I didn't think it was doable without that key, but since it was difficult for (most of) us to find that key, I think we need to give it at least a 1.25..Edit: Make that a 1.5, I just reviewed the rating scale
Quote:


Assassin 1 (37)
mhparker wrote:
0.75: Easy Assassin, like some of the very early ones, such as A1.

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