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Author Message
Ed
PostPosted: Tue Jul 15, 2008 8:07 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
This is Part C of the Assassin Forum Archive. Please read the first part of the Archive Index to get the background to this archive including Mike (mhparker)'s original post about ratings.
Old SSv3.2.1 scores: 
Killer rating table      

Rounded Score from SSv3.2.1 
! = 0.10+ change from previous Score
pg# on this thread - PART C
(E) = Easy  (H) = Hard
======================================================================
|A ##      Rate   Score|A ##      Rate   Score|A ##      Rate   Score|
|----------------------+----------------------+----------------------|
|DS        1.25    1.10|A.77v2    1.25    0.95|A.79      1.00    0.95|
|A.76      1.00    1.00|M2        1.75    1.70|A.79RP    1.50    1.55|
|A.76X     1.25    1.30|A.78      1.25    1.10|                      |
|A.77      1.00    0.88|A.78V2   H1.50   !2.25|                      |
|====================================================================|
                              page #1


======================================================================
|A ##      Rate   Score|A ##      Rate   Score|A ##      Rate   Score|
|----------------------+----------------------+----------------------|
|A.80      1.50    1.35|A.83      1.50    1.45|A.85      1.25    1.40|
|A.81      1.00    0.90|A.84      1.25    1.30|A.85V2    2.50   !2.50|
|A.82      1.25    1.10|A.84V2    1.50   !2.20|                      |
|A.82V2x   1.50   !1.25|Radial   H1.25    1.45|                      |
|====================================================================|
                              page #2


======================================================================
|A ##      Rate   Score|A ##      Rate   Score|A ##      Rate   Score|
|----------------------+----------------------+----------------------|
|A.86      1.25    0.90|Bored89-E 1.25    1.15|M.3       1.25    0.95|
|A.87     H1.00    1.20|Bored89  H1.50   !1.95|M.4      H1.50   !1.70|
|A.88     H1.25    1.45|A.90     H1.75    1.95|                      |
|A.89      1.25    1.05|A.91     H1.25    1.10|                      |
|====================================================================|
                              page #3


======================================================================
|A ##      Rate   Score|A ##      Rate   Score|A ##      Rate   Score|
|----------------------+----------------------+----------------------|
|No A.92               |uA.95     1.25    1.10|uA96v1.5 E1.25    1.25|
|uA.93     1.00    0.90|nd's#9   H1.50   !1.65|uA.97     1.00    0.85|
|uA.94    H1.25    1.50|uA.96    E1.00    0.95|                      |
|YAK94    H1.25    1.25|uA.96v2   1.75    2.30|                      |
|====================================================================|
                              page #4


======================================================================
|A ##      Rate   Score|A ##      Rate   Score|A ##      Rate   Score|
|----------------------+----------------------+----------------------|
|uA.97v1.5 1.25    1.20|uA.99     1.00    0.85|                      |
|uA.97v2  H1.25    1.25|uA99v1.5 H1.25    1.50|                      |
|uA.98     1.25    1.05|uA99.5   E1.50    1.35|                      |
|uA.98v2  E1.50    1.35|uA100     1.50   !1.65|                      |
|====================================================================|
                              page #5
old Rounded Score from SSv3.3.0: 
! = 0.10 change from previous Score
pg# on this thread - PART C
(E) = Easy  (H) = Hard
======================================================================
|A ##      Rate   Score|A ##      Rate   Score|A ##      Rate   Score|
|----------------------+----------------------+----------------------|
|DS        1.25    1.15|A.77v2    1.25    0.90|A.79      1.00    1.00|
|A.76      1.00   !0.90|M2        1.75   !1.95|A.79RP    1.50   !1.45|
|A.76X     1.25   !1.20|A.78      1.25   !1.20|                      |
|A.77      1.00    0.90|A.78V2   H1.50   !2.60|                      |
|====================================================================|
                              page #1


======================================================================
|A ##      Rate   Score|A ##      Rate   Score|A ##      Rate   Score|
|----------------------+----------------------+----------------------|
|A.80      1.50    1.40|A.83      1.50    1.50|A.85      1.25   !1.50|
|A.81      1.00   !1.15|A.84      1.25   !1.20|A.85V2    2.00   !4.60|
|A.82      1.25    1.10|A.84V2    1.50   !2.40|                      |
|A.82V2x   1.50   !1.35|Radial   H1.25    1.45|                      |
|====================================================================|
                              page #2


======================================================================
|A ##      Rate   Score|A ##      Rate   Score|A ##      Rate   Score|
|----------------------+----------------------+----------------------|
|A.86      1.25   !1.35|Bored89-E 1.25   !1.40|M.3       1.25   !1.10|
|A.87     H1.00    1.20|Bored89  H1.50   !2.30|M.4      H1.50   !1.85|
|A.88     H1.25   !1.65|A.90     H1.75   !2.30|                      |
|A.89      1.25   !1.15|A.91     H1.25    1.10|                      |
|====================================================================|
                              page #3


======================================================================
|A ##      Rate   Score|A ##      Rate   Score|A ##      Rate   Score|
|----------------------+----------------------+----------------------|
|No A.92               |uA.95     1.25    1.00|uA96v1.5 E1.25    1.25|
|uA.93     1.00   !1.05|nd's#9   H1.50   !1.85|uA.97     1.00   !0.95|
|uA.94    H1.25   !1.65|uA.96    E1.00    0.90|                      |
|YAK94    H1.25   !1.10|uA.96v2   1.75   !2.45|                      |
|====================================================================|
                              page #4


======================================================================
|A ##      Rate   Score|A ##      Rate   Score|A ##      Rate   Score|
|----------------------+----------------------+----------------------|
|uA.97v1.5 1.25    1.20|uA.99     1.00    0.90|                      |
|uA.97v2  H1.25    1.20|uA99v1.5 H1.25    1.55|                      |
|uA.98     1.25   !1.35|uA99.5   E1.50    1.55|                      |
|uA.98v2  E1.50   !1.45|uA100     1.50    1.70|                      |
|====================================================================|
                              page #5
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|
|-----------------------------+-----------------------------+-----------------------------|
|DS      Ruud    1.25     1.05|A.77v2  Ruud    1.25     1.05|A.79    Ruud    1.00     1.05|
|A.76    Ruud    1.00     1.10|Mav2    mhp     1.75     1.70|A.79RP  Ruud    1.50     1.45|
|A.76X   mhp     1.25     1.35|A.78    Ruud    1.25     1.30|                             |
|A.77    Ruud    1.00     1.10|A.78V2  mhp    H1.50     2.30|                             |
|=========================================================================================|
                                         page #1


===========================================================================================
|A ##     by     Rate    Score|A ##     by     Rate    Score|A ##     by     Rate    Score|
|-----------------------------+-----------------------------+-----------------------------|
|A.80    Ruud    1.50     1.30|A.83    Ruud    1.50     1.55|A.85    Ruud    1.25     1.40|
|A.81    Ruud    1.00     1.05|A.84    Ruud    1.25     1.20|A.85V2  Ruud    2.50     3.85|
|A.82    Ruud    1.25     1.10|A.84V2  Ruud    1.50     2.05|                             |
|A.82V2x Ruud    1.50     1.30|Radial  mhp    H1.25     1.40|                             |
|=========================================================================================|
                                         page #2



===========================================================================================
|A ##     by     Rate    Score|A ##     by     Rate    Score|A ##     by     Rate    Score|
|-----------------------------+-----------------------------+-----------------------------|
|A.86    Ruud    1.25     1.25|Bord89E Nasen   1.25     1.30|Mav.3   Nasen    1.25    1.10|
|A.87    Ruud   H1.00     1.25|Bord89H Nasen  H1.50     1.95|Mav.4   Nasen   H1.50    1.65|
|A.88    Ruud   H1.25     1.60|A.90    Ruud   H1.75     1.95|                             |
|A.89    Ruud    1.25     1.20|A.91    Ruud   H1.25     1.30|                             |
|=========================================================================================|
                                         page #3



===========================================================================================
|A ##     by     Rate    Score|A ##     by     Rate    Score|A ##     by     Rate    Score|
|-----------------------------+-----------------------------+-----------------------------|
|No A.92                      |uA.95   Ed      1.25     1.20|uA96v15 mhp    E1.25     1.15|
|uA.93   mhp     1.00     1.15|nd's#9  nd     H1.50     1.60|uA.97   Afmob   1.00     1.15|
|uA.94   mhp    H1.25     1.50|uA.96   JC     E1.00     1.10|                             |
|YAK94   JC     H1.25     1.25|uA.96v2 JC      1.75     2.00|                             |
|=========================================================================================|
                                         page #4



===========================================================================================
|A ##     by     Rate    Score|A ##     by     Rate    Score|A ##     by     Rate    Score|
|-----------------------------+-----------------------------+-----------------------------|
|uA97v1.5 JC     1.25     1.20|uA.99   Afmob   1.00     0.95|                             |
|uA.97v2  JC    H1.25     1.25|uA99v15 afmob  H1.25     1.50|                             |
|uA.98    Ed     1.25     1.45|uA99.5  frank  E1.50     1.45|                             |
|uA.98v2  mhp   E1.50     1.30|uA100   mhp     1.50     1.45|                             |
|=========================================================================================|
                                         page #5




Diagonal Surprise by Ruud (Nov 07)
Puzzle pic: Thanks to Børge for the coloured pic:
Image

Image
Code: Select, Copy & Paste into solver:
3x3::k:2816:4609:1538:5379:5124:5379:5124:1799:3336:5385:2816:4609:1538:5379:5124:1799:3336:3601:4370:5385:2816:4609:1538:1799:3336:3601:2330:3611:4370:5385:4894:2335:2592:3601:2330:5155:4370:3611:4894:4391:2592:2335:2592:5155:3628:3611:1838:3631:4894:4391:2592:4659:3628:5155:1838:3631:3384:3129:5690:4923:2620:4659:3628:3631:3384:3129:4674:3139:5690:4923:2620:4659:3384:3129:4674:3139:4674:3139:5690:4923:2620:
Solution: 
+-------+-------+-------+
| 7 6 2 | 4 5 8 | 9 1 3 |
| 8 1 5 | 3 9 6 | 4 2 7 |
| 9 4 3 | 7 1 2 | 8 6 5 |
+-------+-------+-------+
| 6 7 9 | 5 2 3 | 1 4 8 |
| 1 5 8 | 9 4 7 | 2 3 6 |
| 3 2 4 | 6 8 1 | 5 7 9 |
+-------+-------+-------+
| 5 8 6 | 2 7 4 | 3 9 1 |
| 2 3 1 | 8 6 9 | 7 5 4 |
| 4 9 7 | 1 3 5 | 6 8 2 |
+-------+-------+-------+
Quote:
Ruud: Not a V2, but... with unorthodox (unorthogonal) cage shapes
Caida: This looks really cool
mhparker: not too difficult. Rating probably around 1.25
goooders: just like a normal killer once it started to crack it fell over very quickly i thought it wouldnt because of the weird cage structure
Andrew: I agree with Mike's rating of 1.25. Diagonal cages are always harder for human solvers so, for that reason, I won't rate it any lower
Caida: I quite liked this puzzle - but kept slowing down looking to use 45 rules
Walkthrough by mhparker:
Hi folks,

Good job Caida's got no internet access at the moment. Allows me to get my WT in first! :-)

It was a very enjoyable puzzle, although not too difficult. Rating probably around 1.25.

Thanks to Ruud for another interesting new idea. BTW, Para's toroidal killer looks fascinating (albeit mind-boggling!), too. Nothing like being kept on one's toes... :D

Edit: Couple of typos fixed. Thanks, Andrew!

Diagonal Surprise Walkthrough

Prelims:

a) 11(3)n1 = {128/137/146/236/245} (no 9)
b) 6(3)n12 = {123} -> no 1,2,3 in r1c456 (CPE)
c) 21(3)n2 = {489/579/678} (no 1..3)
d) 20(3)n23 = {389/479/569/578} (no 1,2)
e) 7(3)n23 = {124} -> no 1,2,4 in r3c789 (CPE)
f) 21(3)n14 = {489/579/678} (no 1..3)
g) 9(2)n36 = [36/54/63/72/81]
h) 17(2)n5 = {89}, locked for n5
i) 19(3)n45 = {379/469/478/568} (no 1,2) (Note: {289} unplaceable due to no 8,9 in r6c4)
j) 10(4)n56 = {1234} -> no 1..4 in r5c6 (CPE)
k) 9(2)n5 = [27/36/45] (no 1,5..9 in r4c5)
l) 20(3)n6 = {389/479/569/578} (no 1,2)
m) 7(2)n47 = {16/25/34} (no 7..9)
n) 22(3)n89 = {589/679} -> no 9 in r9c456 (CPE)
o) 19(3)n89 = {289/379/469/478/568} (no 1)
p) 10(3)n9 = {127/136/145/235} (no 8,9)

1. Hidden triple (HT) at r46c4+r5c6 = {567} (no 3,4)
1a. -> 19(3)n45 = {568} (last combo)
1b. -> r5c3 = 8
1c. r46c4 = {56}, locked for c4 and n5

2. 17(2)n5 = [98]

3. Naked single (NS) at r5c6 = 7
3a. -> r4c5 = 2
3b. cleanup: no 7 in r3c9

4. Hidden single (HS) in 10(4)n56 at r5c7 = 2
(Note: also derivable as outie, n5)

5. 13(3)n3 = {139/157/238/256/346} = {(1/2/4)..}
(Note: {148/247} combos blocked by r1c8+r2c7)
5a. -> r1c8, r2c7 and 13(3)n3 form killer triple on {124} within n3
5b. -> no 1,2,4 elsewhere in n3

6. 14(3)n36 = {158/167/347/356} (no 9)
6a. min. r2c9+r3c8 = 8
6b. -> no 7,8 in r4c7

7. HS in r4/n6 at r4c9 = 8
7a. -> r5c8+r6c9 = [39/57]
7b. cleanup. no 1 in r4c8

8. {79} in n6 locked in r6 -> not elsewhere in r6

9. Hidden killer triple on {789} in n3 at r1c7, 13(3)n3 and 14(3)n36
9a. -> r1c7 = {789},
9b. {256/346} combos blocked for 13(3)n3 = {139/157/238} (no 4,6), and
9c. {356} combo blocked for 14(3)n36 = {158/167/347} = {(1/4)..}
9d. {14} of 14(3)n36 only available in r4c7
9e. -> r4c7 = {14}
9f. 8 only available in r3c8
9g. -> no 5 in r3c8

10. 13(3)n3 requires 1 of {37} (step 9b)
10a. -> {347} combo blocked for 14(3)n36 (step 9c) = {1(58/67)} (no 3,4)
10b. -> r24c7 = [41]

11. Innie/outie (I/O) diff. n3: r1c7 = r3c6 + r4c8 + 3
11a. -> no 6 in r4c8
11b. cleanup: no 3 in r3c9

12. 3 in n3 locked in 13(3) = {139/238} (no 5,7)

13. 5 in n3 locked in c9 -> not elsewhere in c9

14. NP on {34} at r4c68 -> no 3,4 elsewhere in r4

15. Naked triple (NT) on {123} at r2c4+r3c56 -> no 1,2,3 elsewhere in n2
15a. 3 in n2 locked in 6(3)n12
15b. -> no 3 in r1c3
15c. 2 in 6(3)n12 locked in r1c3+r2c4
15d. -> no 2 in r2c23 (CPE)

16. NP on {12} at r1c38 -> no 1,2 elsewhere in r1

17. Hidden pair (HP) in n3 at r12c8 = {12}, locked for c8

18. 10(3)n9 = {136/145/235} (no 7)
18a. must have 1 of {12}, only available in r9c9
18b. -> r9c9 = {12}

19. 20(3)n23 = [497/569/659/758]
(Note: [587] blocked by 21(3)n2 (Prelim c))
19a. -> no 9 in r1c5, no 8 in r2c6

20. r1c3 blocks {128} combo for 11(3)n1 = {137/146/236/245} (no 8) = {(1/2)..}
20a. r1c3 and 11(3)n1 form killer pair on {12} -> no 1,2 elsewhere in n1

21. HS in r2 at r2c1 = 8
21a. split 13(2) at r3c2+r4c3 = [49/67/76] (no 5)
21b. no 9 in r3c2

22. 2 in n1 locked in c3 -> not elsewhere in c3

23. 21(3)n2 = {489/579/678} (Prelim c)
23a. -> either 21(3)n2 contains a 7, or...
23b. ...both of {48} -> r3c4 = 7
23c. -> 7 in n2 locked in r1c4+r2c5+r3c4
23d. -> no 7 in r1c5
23e. Furthermore, either 21(3)n2 contains a 9, or...
23f. ...both of {78} -> r3c4 = 4
23e. -> 21(3)n2 and r3c4 require at least 1 of {49}
23f. -> 20(3)n23 cannot contain both of {49} within n2
23g. -> (from steps 23d and 23f) 20(3)n23 = [569/659]
23h. -> r1c7 = 9
23i. r1c5+r2c6 = {56}, locked for n2

Rest is just singles and cage sums
Walkthrough by Andrew:
An enjoyable puzzle. As goooders said, it looked as if it might be difficult. There appeared to be very few useful 45s. Fortunately there was one on N3 that mattered, used in slightly different ways by Mike and myself. I felt very early that the interaction between the 21(3) and 20(3) cages in R12 would probably be needed but I delayed using it as long as I could.

I think this is the first time that I've used a Naked Quad as the first step after the Prelims. Mike got the same result with a Hidden Triple as his step 1.

I agree with Mike's rating of 1.25. Diagonal cages are always harder for human solvers so, for that reason, I won't rate it any lower.

Here is my walkthrough for Diagonal Surprise.

Prelims

a) 11(3) cage at R1C1 = {128/137/146/236/245}, no 9
b) 6(3) cage at R1C3 = {123}, CPE no 1,2,3 in R1C456
c) 21(3) cage at R1C4 = {489/579/678}, no 1,2,3
d) 20(3) cage at R1C5 = {389/479/569/578}, no 1,2
e) 7(3) cage at R1C8 = {124}, CPE no 1,2,4 in R3C789
f) 21(3) cage at R2C1 = {489/579/678}, no 1,2,3
g) 9(2) cage at R3C9 = {36}/[54/72/81], no 9, no 5,7,8 in R4C8
h) 19(3) cage at R4C4 = {289/379/469/478/568}, no 1
i) 9(2) cage at R4C5 = {18/27/36/45}, no 9
j) 10(4) cage at R4C6 = {1234}, CPE no 1,2,3,4 in R5C46, clean-up: no 5,6,7,8 in R4C5
k) 20(3) cage at R4C9 = {389/479/569/578}, no 1,2
l) 17(2) cage at R5C4 = {89}, locked for N5, clean-up: no 1 in R4C5
m) 7(2) cage at R6C2 = {16/25/34}, no 7,8,9
n) 22(3) cage at R7C5 = 9{58/67}, CPE no 9 in R9C456
o) 19(3) cage at R7C6 = {289/379/469/478/568}, no 1
p) 10(3) cage at R7C7 = {127/136/145/235}, no 8,9

1. Naked quad {1234} in R4C56 + R5C5 + R6C6, locked for N5
1a) 1 in N5 locked in 10(4) cage -> no 1 in R5C7

2. 19(3) cage at R4C4 = {568} (only remaining combination), cannot be {289/379/469/478} because 2,3,4,8,9 only in R5C3) -> R5C3 = 8, R5C4 = 9, R6C5 = 8
2a. Naked pair {56} in R46C4, locked for C4 and N5 -> R5C6 = 7, R4C5 = 2, clean-up: no 7 in R3C9

3. R5C7 = 2 (only remaining cell for 2 in 10(4) cage)

4. 6(3) cage at R1C3, 2 in R1C3 + R2C4 -> CPE no 2 in R2C23

5. 45 rule on N3 2 innies R1C7 + R3C9 – 11 = 2 outies R3C6 + R4C7
5a. Max R1C7 + R3C9 = 17 -> max R3C6 + R4C7 = 6 -> max R4C7 = 5
5b. Min R3C6 + R4C7 = 2 -> min R1C7 + R3C9 = 13, no 3, clean-up: no 6 in R4C8

6. R4C9 = 8 (hidden single in R4), clean-up: no 1 in R4C8
6a. R5C8 + R6C9 = 12 = [39/57]
6b. 7,9 in R6 locked in R6C789, locked for R6

7. R1C7 + R3C9 – 11 (step 5) = R3C6 + R4C7
7a. Max R1C7 + R3C9 = 15 -> max R3C6 + R4C7 = 4, no 4,5
7b. Min R1C7 + R3C9 = 13 (step 5b) -> min R1C7 = 7
7c. 4 in 7(3) cage at R1C8 locked in R1C8 + R2C7, locked for N3

8. Naked triple {134} in R4C678, locked for R4

9. Naked triple {123} in R2C4 + R3C56, locked for N2
9a. 3 in N2 locked in R2C4 + R3C5 for 6(3) cage -> no 3 in R1C3

10. 14(3) cage at R2C9 = {158/167/239/356} (cannot be {257} because R4C7 only contains 1,3)
10a. 1 of {158/167} must be in R4C7 -> no 1 in R2C9
10b. 2 of {239} must be in R2C9 -> no 9 in R2C9
10c. 3 of {239/356} must be in R4C7 -> no 3 in R2C9 + R3C8

11. 3 in N3 locked in 13(3) cage = 3{19/28}, no 5,6,7

12. Hidden killer triple 7,8,9 for N3 in R1C7, 13(3) cage and 14(3) cage -> 14(3) cage at R2C9 (step 10) must contain 7/8/9 = {158/167/239} (cannot be {356})
12a. 8 of {158} must be in R3C8 -> no 5 in R3C8
12b. 5 in N3 locked in R23C9, locked for C9

13. Hidden killer pair 5,6 for N3 in R3C9 and 14(3) cage -> 14(3) cage at R2C9 (step 12) must contain 5/6 = {158/167} (cannot be {239}), no 2,3,9 -> R4C7 = 1, R2C7 = 4
13a. Naked pair {12} in R1C38, locked for R1

14. 45 rule on R123 2 remaining outies R4C38 – 4 = 1 innie R3C1, min R4C38 = 8 -> min R3C1 = 4

15. 20(3) cage at R1C5 = {479/569/578}
15a. 4 of {479} must be in R1C5
15b. 9 of {569} must be in R1C7
15c. -> no 9 in R1C5

16. 21(3) cage at R1C4 = {489/579/678}
16a. 7 of {579} must be in R1C4 with {59} in R1C6 + R2C5 -> cannot place any of the remaining combinations for 20(3) at R1C5 (step 15)
16b. -> 21(3) cage at R1C4 = {489/678} = 8{49/67}, no 5, 8 locked in R1C46 for R1 and N2
16c. 9 of {489} must be in R2C5 -> no 9 in R1C6

17. 5 in N2 locked in 20(3) cage at R1C5 (step 15) = {569} (only remaining combination) -> R1C7 = 9, clean-up: no 1 in 13(3) cage in N3 (step 11)
17a. Naked pair {56} in R1C5 + R2C6, locked for N2, clean-up: no 7 in 21(3) cage (step 16b) -> R2C5 = 9
17b. Naked pair {48} in R1C46, locked for R1 and N2 -> R3C4 = 7

18. R1C9 = 3 (naked single), R3C7 = 8, R2C8 = 2, R3C8 = 6, R23C9 = [75] , R4C8 = 4, R4C6 = 3, R5C9 = 6, R6C9 = 9, R5C8 = 3 (step 6a), R1C8 = 1, R3C6 = 2, R1C3 = 2

19. Naked pair {57} in R6C78, locked for R6 -> R6C4 = 6, R4C4 = 5, clean-up: no 1,2 in R7C1

20. Naked pair {57} in R68C8, locked for C8

21. R8C6 = 9 (only remaining place in 22(3) cage), R7C5 + R9C7 = {67} (only remaining combination), no 5
21a. CPE no 6,7 in R7C7 + R9C5

22. 10(3) cage at R7C7 = {235} (only remaining combination, cannot be {127/145} because 1,2,4 only in R9C9), locked for N9 -> R9C9 = 2, R8C8 = 5, R7C7 = 3, R6C78 = [57], R7C9 = 1, R8C9 = 4, R7C8 = 9, R9C8 = 8, clean-up: no 4 in R6C2
22a. R9C8 = 8 -> R7C6 + R8C7 = 11 = [47/56]

23. R1C6 = 8 (hidden single in C6), R1C4 = 4

24. R1C1 = 7 (hidden single in R1) -> R2C4 + R3C5 = 4 = {13}
24a. Naked pair {13} in R2C2 + R3C3, locked for N1
24b. Naked pair {56} in R1C2 + R2C3, locked for N1 -> R2C1 = 8

25. R2C1 = 8 -> R3C2 + R4C3 = 13 = [49], R3C1 = 9, R4C12 = [67], R5C1 = 1, R5C5 = 4, R6C6 = 1, R5C2 = 5, R6C1 = 3, R1C2 = 6, R2C3 = 5, R1C5 = 5, R2C6 = 6, R6C2 = 2, R6C3 = 4, R7C2 = 8, R8C1 = 2, R7C4 = 2, clean-up: no 4 in R7C1

26. Naked pair {13} in R9C45, locked for R9 and N8 -> R8C4 = 8, R9C2 = 9, R8C3 = 1

and the rest is naked singles and cage sums
Walkthrough by Caida:
I finally had time to finish this walkthrough. Doing it on the plane didn't work at all - my laptop battery didn't last and my mental math abilities are not as strong as they should be - and I haven't had time to look at it again until today.

I quite liked this puzzle - but kept slowing down looking to use 45 rules and only found application.


Here's my walkthrough (I've gone through it a couple times and made some adjustments to my nomenclature based on my learnings so far - but as always welcome any suggestions!)

Cheers,

Caida



Diagonal Surprise Walkthrough

Prelims:

a. 11(3)n1 = {128/137/146/236/245} (no 9)
b. 6(3)n12 = {123} (no 4..9) (no 1,2,3 in r1c456 – common peers)
c. 21(3)n14 and n2 = {489/579/678} (no 1..3)
d. 20(3)n23 and n6 = {389/479/569/578} (no 1,2)
e. 7(3)n32 = {124} (no 3,5..9) (no 1,2,4 in r3c789 – common peers)
f. 9(2)n36 and n5 = {18/27/36/45} (no 9)
g. 7(2)n47 = {16/25/34} (no 7..9)
h. 19(3)n54 and n89 = {289/379/469/478/568} (no 1)
i. 17(2)n5 = {89} (no 1..7) (8,9 locked for n5)
j. 10(4)n56 = {1234} (no 5..9) (no 1,2,3,4 in r5c6 – common peers)
k. 22(3)n89 = {589/679} (no 1..4) (no 9 in r9c456 – common peers)
l. 10(3)n9 = {127/136/145/235} (no 8,9)

m. cleanup: 9(2)n5; r4c5 no 1,5,6,7
n. cleanup: 9(2)n36: r4c8 no 5,7,8

1. 19(3)n45 no {89} combo available
1a. -> no 2 in 19(3)n45
1b. -> 19(3)45 requires either 8 or 9; only available in r5c3
1c. -> no 3..7 in r5c3
1d. -> {89} locked for r5 in c34
1e. -> no [45] in 9(2)n5 - > this would make n5 of 10(4)n56 equal {123} and would make n5 of 19(3)n45 equal {67}; no possible combination of 19(3) with {67}
1f. -> 5 locked in 19(3)n45 in n5 in r46c4
1g. -> 19(3)n45 = {568} (only possible combination with 5)
1h. -> 6 locked in 19(3)n45 in n5 in r46c4
1i. -> r5c3 = 8
1j. -> r5c4 = 9; r4c5 = 8
1k. -> r5c6 = 7; r6c6 = 2
1l. -> HS r6c6 = 2 (only 2 in 10(4)n56)
1m. cleanup 9(2)n46: r3c9 no 7

2. 2 in 6(3)n12 locked in r1c3 and r2c4
2a. -> no 2 in r2c3 (common peer)

3. 20(3)n6: r46c9 no 3 or 4 as no {789} in r5c8 (combos {389/479} only possibilities for 3 or 4)

4. 17(3)n14: r3c1 and r4c2 no 1 as no 7 or 9 in r5c1

5. 18(3)n78: r9c3 and r8c4 no 1 as no {89} in r9c5
5a. options for 18(3)n78: (order r8c4,r9c35) = [8]{19}/[297]/[396]/[8]{37}/[495]/[7]{56}
5b. -> r9c35 no 2,4

6. 13(3)n3 = {139/157/238/256/346}; ({148/247} combos blocked by 7(3)n23)
6a. -> {124} locked in n3 in 13(3)n3 and 7(3)n23
6b. -> no 1,2,4 anywhere else in n3

7. 14(3)n36 = {158/167/347/356} (no 9)
7a. min. r2c9+r3c8 = 8
7b. -> no 7,8 in r4c7
7c. Hidden Single r4c9 = 8

8. 20(3)n6 = [8][39/57]
8a. -> r5c8 no 4,6; r6c9 no 5,6
8b. 7 locked in n4 in r4c123
8c. 9 locked in n4 in r4c123
8d. cleanup: r4c8 no 1

9. Hidden killer triple on {789} in n3 at r1c7, 13(3)n3 and 14(3)n36
9a. -> r1c7 = {789},
9b. 13(3)n3 = {139/157/238} (no 4,6)
9c. 14(3)n36 = {158/167/347};
9d. -> r4c7 = {14} (no 3,5,6)
9e. -> r3c8 no 5 (8 only available in r3c8)
9f. -> 14(3)n36 combo {347} blocked by 13(3)n3 (no 3,4)
9g. -> r4c7 = 1
9h. single r2c7 = 4

10. Innies and Outies n3: r1c7 + r3c9 – r3c6 = 12
10a. r1c7 + r3c9 = either 13 or 14
10b. r3c9 no 3
10c. cleanup: r4c8 no 6

11. naked pair {34} in r4c68 -> no 3,4 elsewhere in r4

12. 3 in n3 locked in 13(3)n3 = {139/238} (no 5,7)

14. 5 in n3 locked in r23c9 -> no 5 elsewhere in c9

15. naked triple {123} in r2c4 and r3c56 -> no 1,2,3 elsewhere in n2
15a. 3 in n2 locked in 6(3)n12; -> no 3 in r1c3
15b. naked pair {12} locked in r1c38 -> no 1,2 elsewhere in r1
15c. hidden pair {12} locked in r23c8 -> no 1,2 elsewhere c8
15d. 2 in 6(3)n12 locked in r1c3 and r2c4; no 2 in r2c2 (CPE)

16. 10(3)n9 = {136/145/235} (no 7)
16a. -> r9c9 = {12}

17. 14(3)n69; min r5c9+r6c8 = 7
17a. -> r7c9 no 9
17b. -> r7c9 no 6 (r5c9 and r6c8 cannot be {35} blocked by r5c8)
17c. -> r6c8 no 6 (no combo of r57c9 = 8)

18. 11(3)n1 = {137/146/236/245}
18a. -> combo {128} blocked by r1c3 (no 8)
18b. -> r3c3 no 5 (requires 2 in either r1c1 or r2c2)
18c. killer pair {12} in n1 locked for r1c3 and 11(3)n1
18d. 2 locked in n1 in r13c3 -> no 2 elsewhere in c3

19. 20(3)n23 = [497/569/659/758] (combo [587] blocked by 21(3)n2)
19a. no 9 in r1c5, no 8 in r2c6
19b. hidden single in r2; r2c1 = 8

20. 21(3)n14 = 8 + 13(2)n14 = [49/67/76] (no 5)
20a. r3c2 no 9

21. 21(3)n2 = {489/579/678}
21a. 7 locked for n2 in either 21(3)n2 or r3c4
21b. -> r1c5 no 7
21c. cleanup r1c7 no 8 (step 19)
21d. 8 locked in n3 in r3c78 -> no 8 elsewhere in r3
21e. r2c5 no 5 (blocked by r1c7)
21f. 20(3)n23 = [569/659] other combinations blocked by 21(3)n2 and r3c4
21g. -> {56} locked in r1c5 and r2c6 for n2
21h. -> r1c7 = 9
21i. hidden single r2c5 = 9; r3c1 = 9

Now it is all over – just singles and sums


Last edited by Ed on Tue Nov 24, 2009 1:17 am, edited 7 times in total.

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Ed
PostPosted: Tue Jul 15, 2008 8:11 am 
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Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Assassin 76 by Ruud (Nov 07)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:2304:2304:3842:3842:4868:4357:4357:1799:1799:6409:3338:3842:4868:4868:4868:4357:4880:3601:6409:3338:3338:3349:3349:3349:4880:4880:3601:6409:6409:4381:3614:3614:3614:3361:3601:3601:3108:3108:4381:4381:6440:3361:3361:4139:4139:3108:4142:5423:6440:6440:6440:4147:2356:4139:4142:4142:5423:5177:5177:5177:4147:2356:2356:1599:4416:5423:5423:4419:4147:4147:5190:3911:1599:4416:4416:4419:4419:4419:5190:5190:3911:
Solution: 
+-------+-------+-------+
| 7 2 5 | 9 3 4 | 8 6 1 |
| 9 3 1 | 2 8 6 | 5 7 4 |
| 8 4 6 | 5 7 1 | 3 9 2 |
+-------+-------+-------+
| 3 5 9 | 4 2 8 | 6 1 7 |
| 4 6 7 | 1 9 5 | 2 3 8 |
| 2 1 8 | 7 6 3 | 9 4 5 |
+-------+-------+-------+
| 6 9 4 | 8 5 7 | 1 2 3 |
| 5 7 3 | 6 1 2 | 4 8 9 |
| 1 8 2 | 3 4 9 | 7 5 6 |
+-------+-------+-------+
Quote:
cathyw: Getting in first again ... Rating of 1.00 imho
Para: With Cathy's reassurance that it was only a rating 1.00... And it proved to be a quickie. Took me about 40 minutes to solve with keeping the walk-through. A rating of 1.00 sounds about right. Not anything spectacular
Afmob: This one wasn't too difficult..Rating: 1.0 since it was quite straightforward apart from (a) little trick
gary w: about a 1.0.Didn't take too long to do..but about 4 times longer than today's Times "deadly" killer. Ruud's puzzles still set the bench mark
Caida: I think my walkthrough looks different - but think it must be because I over-complicated things..I would be delighted to receive any pointers
azpaull: actually finished on Tuesday - which is very unusual for me. I'll have to give it a 1.0 - to paraphrase Groucho, any Assassin that will allow me to solve it.
Walkthrough by Para with cage overlap:
Hi all

With Cathy's reassurance that it was only a rating 1.00, i thought i'd send in my First V1 walk-through since ages. And it proved to be a quickie. Took me about 40 minutes to solve with keeping the walk-through. A rating of 1.00 sounds about right. Not anything spectacular.

Walk-through Assassin 76

1. R1C12 = {18/27/36/45}: no 9

2. R1C89 = {16/25/34}: no 7,8,9

3. 19(3) at R2C8 = {289/379/469/478/568}: no 1

4. 9(3) at R6C8 = {126/135/234}: no 7,8,9

5. 20(3) at R7C4 and R8C8 = {389/479/569/578}: no 1,2

6. R89C1 = {15/24}: no 3,6,7,8,9

7. R89C9 = {69/78}: no 1,2,3,4,5

7.5 14(4) at R2C9 = {1238/1247/1256/1346/2345}: no 9

8. 45 on N9: 4 innies: R7C789 + R8C7 = 10 = {1234} -> locked for N9

9. 45 on C89: 2 outies: R39C7 = 10 = [28/37/46]: R3C7: no 5,6,7,8,9; R9C7: no 5,9
9a. 5 in N9 locked for C8
9b. Clean up: R1C9: no 2

10. 45 on C89: 4 innies: R2389C8 = 29 = {5789} -> locked for C8

11. 45 on C12: 2 outies: R39C3 = 8 = {17/26/35}: no 4,8,9

12. 45 on R1234: 2 innies: R4C37 = 15 = {69/78}: no 1,2,3,4,5

13. 45 on N2: 2 innies: R1C46 = 13 = {49/58/67}: no 1,2,3

14. 45 on N5: 2 innies: R5C46 = 6 = {15/24}: no 3,6,7,8,9
14a. Cage overlap: R5C67 can't total 6: R4C7: no 7
14b. Clean up: R4C3: no 8

15. 13(3) at R4C7 = [643]/[6]{25}/[823]/[8]{14}/[913]: R5C7: no 6,7,8,9

16. 17(3) at R4C3 = [692/674/791/782/764/971/962/935]: R5C3: no 1,2,4,5

17. 45 on N8: 2 innies: R8C46 = 8 = {17/26/35}: no 4,8,9

18. 45 on R1234: 2 outies: R5C37 = 9 = [81/72/63]
18a. Clean up: R5C4: no 5(step 16); R5C6: no 1

19. 13(3) at R4C7 = [643/652/823/841]: no 9
19a. Clean up: R4C3: no 6

20. 45 on R89: 2 innies: R8C37 = 7 = [34/43/52/61]: R8C3: no 1,2,7,8,9

21. 45 on C789: 3 outies: R158C6 = [821/641/542/425/452]: R1C6: no 7,9; R8C6: no 3,6,7
21a. Translation through 45's N2,5 and 8: R158C4 = [547/826/943/916]: R1C4 = {589}, R8C4 = {367}
21b. Clean up: R1C6: no 6

22. Naked Quad {1234} in R3578C7 -> locked for C7 (Really should have seen this after step 18)

23. 17(3) at R1C6 = [4]{58/67}: R1C6 = 4; R12C7: no 9
23a. R1C4 = 9; R6C7 = 9(hidden)
23b. Clean up: R5C4: no 2; R8C4: no 7(step 21); R8C6: no 1
23c. Naked Pair {25} in R58C6 -> locked for C6

24. 16(4) at r6C7 = 9{14}[2](last combo): R8C6 = 2; R78C7 = {14} -> locked for C7 and N9
24a. R8C4 = 6; R5C46 = [15]

Now it is very basic, so won't clean up properly anymore. Just showing the final combinations that will get you to all singles.

25. R8C37 = [34](last combo from step 20)
25a. R7C7 = 1

26. R45C7 = [62] (last combo within 13(3) at R4C7)
26a. R3C7 = 3; R9C7 = 7; R4C3 = 9; R5C3 = 7; R5C5 = 9(hidden)

27. R89C9 = [96](last combo)
27a. R1C8 = 6(hidden); R1C9 = 1;
27b. R7C8 = 2(hidden); R7C9 = 3; R456C8 = [134]; R456C9 = [785]

28. R67C3 = [84](last combo within 21(4) at R6C3)

29. R12C3 = [51](last combo within 15(3) at R1C3)
29a. R12C7 = [85]; R9C3 = 2; R3C3 = 6

30. R23C2 = [34](last combo within 13(3) at R2C2)

And the rest is hidden and naked singles till the end.

greetings

Para
Walkthrough by Afmob with one little trick:
This one wasn't too difficult but I needed one little trick to crack it open (step 9c).

A76 Walkthrough:

1. N258
a) Innies N2 = 13(2) = {49/58/67}
b) Innies N5 = 6(2) = {15/24}
c) Innies N8 = 8(2) = {17/26/35}

2. N9
a) Killer pairs (79,89) of 15(2) block {389/479} of 20(3)
b) 20(3) = 5{69/78} -> 5 locked
c) Hidden Quad (1234) in R7C789+R8C7 -> no other candidates
d) 9(3): R6C8 <> 1 since R7C89 <= 7
e) 16(4): R6C7 <> 1 since R7C7+R8C67 <= 14

3.C789
a) Outies C9 = 16(5) = {12346} locked for C8
b) Outies C89 = 10(2) = [28/37/46]
c) Outies C789 = 11(3) -> no 9
d) Outies C789 = 11(3): R8C6 <> 7 because R15C6 >= 5
e) 19(3) = {289/379/478}
f) 7(2): R1C9 <> 2

4. C123
a) Outies C12 = 8(2) = {17/26/35}
b) Outies C123 = 16(3): R8C4 <> 1 since R15C4 <= 14
c) 17(3) @ N4: R45C3 <> 1,2 because R5C4 <= 5

5. N2
a) Innies N2 = 13(2): R1C4 <> 4

6. R6789
a) Innies+Outies: 2 = R5C5 - R6C19
-> R5C5 must be at least 5 since R6C19 >= 3 -> R5C5 = (56789)
-> R6C19 = 3/4/5/6/7 -> R6C19 <> 7,8,9
b) 16(3) @ N6 must have 7,8 or 9 and they're only possible @ R5C9 -> R5C9 = (789)

7. R1234
a) Innies = 15(2) = {69/78}
b) 13(3) @ R4 must have 6,7,8 xor 9 and R4C7 = (6789) -> R5C7 <> 6,7,8,9
c) Outies = 15(4) must have 6,7,8 xor 9 - only possible @ R5C3 -> R5C3 = (6789)
d) 17(3) @ N5: R5C4 <> 5 because R45C3 >= 13

8. N258
a) Outies C123 = 16(3): R8C4 <> 2 since R15C4 <= 13
b) Innies N5 = 6(2): R5C6 <> 1
c) Innies N8 = 8(2): R8C6 <> 6
d) 13(3) @ N5 <> 9 because R5C6 <> 1,3,9
e) 13(3) @ N5 <> 7 because R5C78 would be {15/24} -> no combo for Innies N5
f) 16(4): R6C7 <> 5 since R7C7+R8C67 would be <= 9

9. N456 !
a) 12(3): R5C2 <> 9 because R56C1 would be {12} -> blocked by Killer pair (12) of 6(2)
b) Innies R1234 = 15(2): R4C3 <> 6,8
c) ! Outies R1234 = 15(4) contains Innies N5 = 6(2) -> R5C37 = 9(2) = [63/72/81]
d) 5 locked in R46C9 for C9

10. N123
a) 7(2) = {16/34}
b) 5 locked in 17(3) @ C3 = 5{39/48}; R1C6 <> 5
c) 17(3) = {458} since R1C6 = (48); R1C89 <> 4
d) 7(2) = {16} locked for R1+N3
e) 9(2) = {27/45}
f) Innies N2 = 13(2) = [58/94]
g) Killer pair (45) of Innies N2 blocks {45} of 9(2)
h) 9(2) = {27} locked for R1+N1
i) 13(3) @ N1 = {139/148/346}
j) Hidden Single: R6C7 = 9 @ C7, R9C7 = 7 @ C7, R4C7 = 6 @ C7, R1C8 = 6 @ C8 -> R1C9 = 1

11. N9
a) 20(3) = {578} locked, 8 locked for C8
b) 16(4) = {1249}, 4 locked for C7+N9
c) 9(3) = {234} -> R6C8 = 4; {23} locked for C7+N9
d) 16(4) = {1249} -> R8C6 = 2

12. N8
a) Innies = 8(2) = [62] -> R8C4 = 6
b) 20(3) = 7{49/58} -> 7 locked for R7+N8

13. N23
a) 19(3) = {379} -> R3C7 = 3
b) 17(3) = {458} -> R1C6 = 4; {58} locked for N3
c) Innies N2 = 13(2) = [94] -> R1C4 = 9
d) 15(3) = {159} -> R1C3 = 5, R2C3 = 1
e) 19(4) = {2368} locked for N2
f) 13(3) = {157} locked for R3

14. N1
a) 13(3) = {346} -> R2C2 = 3, R3C2 = 4, R3C3 = 6
b) 25(4) = 89{17/35} -> R4C12 = {17/35}; R4C1 <> 5; {89} locked for C1 ^

15. N56
a) Innies N5 = 6(2) = [15] -> R5C6 = 5, R5C4 = 1
b) 13(3) = [652] -> R5C7 = 2
c) 16(3) = [385] -> R5C8 = 3, R5C9 = 8, R6C9 = 5

16. N47
a) 4 locked in 21(4) = 46{29/38} for N7
b) 6(2) = {15} locked for C1+N7
c) 16(3) = 6[19/28] -> R7C1 = 6
d) 12(3) = 2{37/46} -> R6C1 = 2
e) 16(3) = {169} -> R6C2 = 1, R7C2 = 9

17. Rest is singles.

Rating: 1.0 since it was quite straightforward apart from the little trick
Walkthrough by cathy w:
As promised:

Prelims

a) 9(2) N1 = {18/27/36/45}
b) 7(2) N3 = {16/25/34}
c) 9(3) N6/9 = {126/135/234}
d) 20(3) N8 = {389/479/569/578}
e) 6(2) N7 = {15/24}
f) 20(3) N9 = {389/479/569/578}
g) 15(2) N9 = {69/78}


1. Innies N9: r7c789 + r8c7 = 10 = {1234}
a) -> 20(3) = {569/578}

2. Innies N2: r1c46 = 13 = {49/58/67}

3. Innies N5: r5c46 = 6 = {15/24}

4. Innies N8: r8c46 = 8 = {17/26/35}

5. Outies c12: r39c3 = 8 = {17/26/35}

6. Outies c89: r39c7 = 10 = [28/37/46]
a) -> 5 locked r89c8 n/e c8 -> r1c9 <> 2

7. Innies r1234: r4c37 = 15 = {69/78}
a) -> r5c37 = 9 = {18/27/36} ({45} blocked by split 6(2) r5c46)

8. Outies c123: r158c4 = 16 = [457/547/745/817/826/853/916/925/952/943]
a) -> r1c4 <> 6 -> r1c6 <> 7
b) -> r8c4 <> 1 -> r8c6 <> 7

9. Outies c789: r158c6 = 11 -> r1c6 <> 9 -> r1c4 <> 4

10. Innies r89: r8c37 = 7 = [34/43/52/61]

11. Innies r1: r1c357 = 16

12. Outies N1: r1c4 + r4c12 = 17

13. Outies N3: r1c6 + r4c89 = 12 = 4{17/26}/[35], 5{16/34}/[25], 6[15]/{24}, 8{13}
a) -> r4c89 <> 8

14. Outies N7: r6c23 + r8c4 = 15

15. Outies N9: r6c78 + r8c6 = 15
a) Max from r6c8 + r8c6 = 6+6 = 12 -> r6c7 = min 3

16. 9(3) @ r6c8 = {126/234} -> r6c8 <> 1

17. r56c1 of 12(3) can’t be {12} as would conflict with 6(2) r89c1 -> r5c2 <> 9

18. 13(3) @ r4c7 = [652/643/742/751/841/823/913]
a) r5c7 = (123) -> r5c3 = (678)
b) NQ {1234} r3578c7 -> r126c7 <> 1,2,3,4
c) 17(3) @ r1c6 = [458/485/467/476] -> r1c6 = 4 -> r1c4 = 9
d) Clean up: r1c12 <> 5, r12c3 = [15/24/51], r1c89 <> 3, r5c4 <> 2, r8c6 <> 3 -> r8c4 <> 5

19. 9 locked r23c8 n/e c8
a) 20(3) N9 = {578}, 15(2) N9 = {69} n/e c9 -> r1c8 <> 1
b) Clean up: r3c7 <> 4

20. 19(3) N3 = {289/379} -> r23c8 = {789)
a) NQ {5789} r2389c8 -> r4c8 <> 7, r5c8 <> 7,8
Note: could have got this earlier from innies of c89!

21. Conflicting combo: 9(2) r1c12 <> {18} as would force 7(2) r1c89 = [25] then no candidates left in r1c3!

22. Killer pair {26} in r1c12 + r1c8 -> r1c357 <> 2,6
a) -> r12c3 = {15} n/e N1/c3
b) -> r39c3 = {26} only remaining combo n/e c3
c) -> split 7(2) r8c37 = {34} n/e r8
d) -> split 8(2) r8c46 = {26} n/e r8
e) -> r8c9 = 9, r9c9 = 6 -> r9c3 = 2, r3c3 = 6

Straightforward from here with singles and cage combinations.
:D

Andrew has pointed out some things that ought to be clarified but I don't have time to check it through now. Some time soon hopefully.
Brief solution by gary w:
Thought I would post my solution..at least it's brief!


Some prelims..

1.r5c46=6 4/5
2.r39c7=10 <>5 <>{19}
3.r158c6=11 and with r1c6=4 min r8c6<>789
4.r4c37=15
5.r8c37=7 c46=8
6.r5c37=9 (because of 4. and 1. above) <>{45} blocked by 1. above
7.Outies on N9=15

Now look at c7.
Both 5 and 9 can only be at r12 or 6.(9 cannot be at r4 because of a combo conflict with the 17(3) cage N4. viz; r4c7=9 -> r4c3=6 -> r5c6=1 and so r5c4=5 -> conflict in 17(3) cage.)
If 5 is at r6c7 9 is in r12c7 -> r1c6<>4 -> r8c6<>6 (using 3 above)..but then cannot fulfil requirements for 16(4) cage N69..no combo will do.
Therefore r6c7<>5 so 5 is in r12c7 -> r12c7<>9 (would -> r1c6=3 )
Therefore HS in c7 r6c7=9 -> r78c7=4{1/2} Thus 9(3) cage N69={234}
-> r6c8=4 r8c6=2 r8c4=6 so r8c7=4 (not 1..5. above) r7c7=1 r8c3=3.

Some work to do but it's all over now.


Not too much "crunching" this way.

Regards

Gary
Walkthrough by Caida:
Para wrote:
You could always post your walk-through if you want some pointers on how you solved the puzzle. Just to un-complicate things a bit.
I would be delighted to receive any pointers. :D

Here is my walkthrough: (edited from pointers received from Andrew and Para - thanks!!!)

Assassin 76

Prelims

a. 9(2)n1 = {18/27/36/45} (no 9)
b. 7(2) n3 = {16/25/34} (no 7..9)
c. 19(3)n3 = {289/379/469/478/568} (no 1)
d. 14(4)n36 = {1238/1247/1256/1346/2345} (no 9)
e. 9(3)n69 = {126/135/234} (no 7..9)
f. 6(2)n7 = {15/24} (no 3,6..9)
g. 20(3)n8 and n9 = {389/479/569/578} (no 1,2)
h. 15(2)n9 = {69/78} (no 1..5)


1. 20(3)n9 = {569/578} (no 3,4)
Note: combos {389} and {479} blocked by 15(2)n9
1a. -> 5 locked within 20(3)n9 for n9
1b. -> {69} and {78} locked in 20(3)n9 and 15(2)n9 for n9
1c. -> r7c789 and r8c7 (no 5..9)
1d. r6c8 no 1

2. Innies n2: r1c46 = 13(2) = {49/58/67} (no 1..3)

3. Innies n5: r5c46 = 6(2) = {15/24} (no 3,6..9)

4. Innies r1234: r4c37 = 15(2) = {69/78} (no 1..5)

5. r5c37 = 9(2) = {18/27/36} no (4,5,9)
Note: derived from r5c46 = 6(2) (step 3) and r4c37 = 15(2) (step 4)
Note: {45} blocked by h6(2) from step 3

6. 17(3)n45 = [971]/[962]/[935]/{78}[2]/{67}[4]
6a. -> r5c3 no 1,2
6b. cleanup: r5c7 no 7,8; [872] blocked by r5c37

7. 13(3)n56 = [913/841/751/823/742/652/643]
7a. -> r5c7 no 6
7b. cleanup: r5c3 no 3 -> eliminates [935] option for 17(3)n45
7c. -> r5c4 no 5
7d. cleanup: r5c6 no 1 -> eliminates [913] option for 13(3)n56
7e. -> r4c7 no 9
7f. cleanup: r4c3 no 6

missed in original walkthrough (pointed out by Para) [751/742] blocked by r5c46

8. Innies n8: r8c46 = 8(2) = {17/26/35} (no 4,8,9)

9. Innies r89: r8c37 = 7(2) = {16/25/34} (no 7..9)
Note derived using r8c46 from step 8
9a. r8c3 no 1,2

10. Looking at 12(3)n4 combo {129} and 6(2)n7 and h6(2)r5
10a. -> r6c1 no 9
10b: -> r5c2 no 9

11. Outies c12: r39c3 = 8(2) = {17/26/35} (no 4,8,9)

12. Outies c89: r39c7 = 10(2) = {28/37/46} (no 1,5,9)
12a. ->r3c7 no 6,7,8
12b. 5 locked for c8 in r89c8
12c. -> 20(3)n9 from step 1 r89c8 no 6
12d. cleanup: r1c9 no 2

13. 19(3)n3 = [2]{89}/[3]{79}/[4]{69}/[4]{78}
13a. r23c8 no 2,3,4


14. Outies c123: r158c4 = 16(3) = [916/817/925/826/943/547/745]
14a. -> r1c4 no 4,6
14b. -> r8c4 no 1,2
14c. cleanup: r1c6 no 7,9
14d. cleanup: r8c6 no 6,7
Para pointed out -> [817/925] blocked by r158c6

15. 17(3)n23 option {179} not possible
15a. r12c7 no 1

16. 16(4)n689 = [9]{124}/[8]{125}/[8]{134}/[7]{135}/[6]{145}/[7]{234}/[6]{235}
16a. r6c7 no (1..5)
16b. 5 locked in c9 for n6
16c. cleanup: r1c8 no 2

17. 5 in n3 locked in 17(3)n23 in r12c7
17a. 17(3)n23 = {458}
17b. -> r1c6 no 5,6 (5 must be in r12c7)
17c. -> r12c7 no 2,3,6,7,9
17d. 9 locked in n3 in r23c8
17e. HS r6c7 = 9
Para pointed out: r1c89 no 4; r1c89 = {16}

18. 16(4)n689 = [9]{124}
18a. -> r78c7 no 3; r8c6 no 3,5
18b. cleanup: r8c4 no 3,5
18c. cleanup: r8c3 no 4
18d. 4 locked for c7 and n9 in r78c7
18e. r1c6 = 4; r1c4 = 9
18f. {58} locked in c7 and n3 r12c7

19. 19(3)n3 = [3]{79}; {79} locked for c8 and n3
19a. 7(2)n3 = {16}; {16} locked for r1 and n3
19b. {24} locked in n3 in r23c9 for c9 also locked for 14(4)n36

20. 9(2)n1 = {27} locked for r1 and n1

21. 13(3)n56 = [652/751]
21a. -> r5c6 = 5
21b. -> r5c4 = 1
21c. 13(3)n56 = [652]
21d. 17(3)n45 = [971]
21e. r9c7 = 7

22. 15(2)n9 = {69}; locked for c9
22a. 7(2)n3 = [61]

23. 9(3)n69 = [423]
23a. 16(3)n6 = [385]
23b. r4c89 = [17]
23c. HS r5c5 = 9

24. 12(3)n4 = {46}[2]; {46} locked for n4
24a. r8c6 = 2
24b. r8c4 = 6
24c. r8c37 = [34]
24d. 15(2)n9 = [96]
24e. 9(2)n1 = [72]
24f. 6(2)n7 = {15}; locked for c1 and n7
24g. HS r4c2 = 5
24h. r9c3 = 2
24i. r89c2 = [78]

25. 14(3) n5 = {248}; locked for r4 and n5
25a. r4c1 = 3

26. everything now falls into place with cage sums and singles
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Ed
PostPosted: Tue Jul 15, 2008 8:14 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Assassin 76X by mhparker (Nov 07)
Puzzle pic: 1-9 cannot repeat on the diagonals:
Image
Code: Select, Copy & Paste into solver::
3x3:d:k:3072:3072:4098:4098:5124:2821:2821:3591:3591:5897:1546:4098:5124:5124:5124:2821:2832:4625:5897:1546:1546:5141:5141:5141:2832:2832:4625:5897:5897:3869:3358:3358:3358:3873:4625:4625:4132:4132:3869:3869:6440:3873:3873:3883:3883:4132:3886:5167:6440:6440:6440:4915:5428:3883:3886:3886:5167:3129:3129:3129:4915:5428:5428:1599:5184:5167:5167:5955:4915:4915:3910:1095:1599:5184:5184:5955:5955:5955:3910:3910:1095:
Solution: 
+-------+-------+-------+
| 8 4 7 | 3 6 2 | 1 9 5 |
| 5 2 6 | 1 4 9 | 8 3 7 |
| 9 1 3 | 5 8 7 | 2 6 4 |
+-------+-------+-------+
| 6 3 9 | 4 1 8 | 7 5 2 |
| 7 8 4 | 2 9 5 | 3 1 6 |
| 1 5 2 | 7 3 6 | 9 4 8 |
+-------+-------+-------+
| 3 7 1 | 6 2 4 | 5 8 9 |
| 2 6 8 | 9 5 1 | 4 7 3 |
| 4 9 5 | 8 7 3 | 6 2 1 |
+-------+-------+-------+
Quote:
mhparker: may not be the "non plus ultra" as far as advanced techniques are concerned. ... (Est. rating: 1.5)
Para: I think this puzzle is a rating 1.25, 1.5 is a bit high as it doesn't require much finesse
Afmob: Rating: 1.25, nothing too complicated..
Andrew: If one spots the two key moves quickly then it's definitely 1.25.... I didn't! I spent several hours struggling and nibbling. Perhaps Mike's estimate took account of the difficulty in spotting the key moves
Walkthrough by Para:
Hi all

Nice puzzle. Actually did something on the diagonal this time. Although i am not sure that step is really needed, just very clear. I think this puzzle is a rating 1.25, 1.5 is a bit high as it doesn't require much finesse. I think step 18 is the most important step because that single elimination gets things going after step 19 and 20.

Walk-through Assassin 76X

1. R1C12 = {39/48/57}: no 1,2,6

2. 11(3) at R1C6 and R2C8 = {128/137/146/236/245}: no 9

3. R1C89 = {59/68}: no 1,2,3,4,7

4. 20(3) at R3C4 and R8C2 = {389/479/569/578}: no 1,2

5. 21(3) at R6C8 = {489/579/678}: no 1,2,3

6. R89C1 = {15/24}: no 3,6,7,8,9

7. R89C9 = {13} -> locked for C9 and N9

8. 6(3) at R2C2 = {123} -> locked for N1
8a. Naked Triple {123} in R2C2,R3C3 and R9C9 -> locked for D\; 2 locked within R2C2 + R3C3 locked for N1
8b. Clean up: R1C12 = {48/57}: no 9
8c. Killer Pair {58} in R1C12 + R1C89 -> locked for R1

9. 45 on N2: 2 innies: R1C46 = 5 = {14/23}: no 6,7,9
9a. Cage overlap: R1C67 can't equal 5: R2C7: no 6

10. 45 on N5: 2 innies: R5C46 = 7 = {16/25/34}: no 7,8,9

11. 45 on N8: 2 innies: R8C46 = 10 = {19/28/37/46}: no 5

12. 45 on R1234: 2 innies: R4C37 = 16 = {79} -> locked for R4

13. 45 on R1234: 2 outies: R5C37 = 7 = {16/25/34}: no 7,8,9

14. 45 on R89: 2 innies: R8C37 = 12 = [39]/{48/57}: no 1,2,6; R8C3: no 9
14a. 2 in N9 locked for R9
14b. Clean up: R8C1: no 4

15. 45 on C12: 2 outies: R39C3 = 8 = [17/26/35]: R9C3 = {567}
15a. 20(3) at R8C2 = {479/569/578}: {389} blocked by R9C3: no 3
15b. Killer Pair {45} in R89C1 + 20(3) at R8C2 -> locked for N7
15c. Clean up: R8C7: no 7,8

16. 45 on C89: R39C7 = 8 = [17/35]/{26}: no 4,8,9; R3C7: no 5,7

17. 45 on C789: R158C6 = 8 = {1[5]2/134}: no 6,7,8,9; R5C6: no 2; 1 locked for C6
17a. Clean up: R5C4: no 1,5; R8C4: no 1,2,3,4

18. 16(3) at R1C3 = {69}[1]/[781/952/682]/{49}[3]/{67}[3]: {457} blocked by R1C12: R1C4: no 4
18a. Clean up: R1C6: no 1

19. 45 on C123: R158C4 = 14 = [149]/{23}[9]/[167]:[248/347] blocked by R158C6: R8C4: no 6,8
19a. Clean up: R8C6: no 2,4
19b. Naked Pair {13} in R8C69 -> locked for R8
19c. Clean up: R9C1: no 5; R8C7: no 9

20. Killer Triple {789} in R12C3 + R48C3 -> locked for C3
20a. Clean up: R3C3: no 1
20b. 1 in N1 lockd for C2

21. 20(3) at R8C2 = {569/578}: {479} blocked by R9C3: no 4; 5 locked for N7
21a. R89C1 = [24]
21b. Clean up: R1C2: no 8
21c. 1 in N7 locked for R7

22. 2 in R7 locked within 12(3) cage at R7C4 -> 12(3) = {237/246}: no 5,8,9
22a. 5 in R7 locked for N9
22b. R8C37 = 12 = [84]
22c. Clean up: R3C7: no 3; R5C3: no 3

23. 15(3) at R4C3 = [9]{24}/[7]{26}/[753]: R5C3: no 1
23a. Clean up: R5C7: no 6

24. 1 in C3 locked in 20(4) cage at R6C3 -> 20(4) = 8[219/417]: R6C3 = {24}; R7C3 = 1

25. 20(3) at R8C2 = {569}(last combo) -> locked for N7; 9 locked for C2

26. 15(3) at R6C2 = [5]{37}(last combo): R6C2 = 5; R7C12 = {37} -> locked for R7
26a. R9C3 = 5(hidden); R3C3 = 3; R89C9 = [31]; R23C2 = [21];
26b. R8C6 = 1; R8C4 = 9; R89C2 = [69]; R6C3 = 2; R8C8 = 7; R8C5 = 5
26c. R3C7 = 2; R9C78 = [62]
26d. Clean up: R5C4: no 6; R5C7: no 5

27. 15(3) at R4C7 = [951/753]: R5C6 = 5
27a. R5C4 = 2; R1C46 = [32](45 on C123 and C789)

And the rest is naked and hidden singles.

greetings

Para

ps. The new rank is yokozuna(highest rank in professional Sumo-wrestling) accompanied with the nice moderator colour.

pps. i really hoped you would all be solving my Toroidal Killer Sudoku, but i guess/hope that's for another time
Discussion: diagonals can serve a big purpose:
mhparker:
Para wrote:
Actually did something on the diagonal this time.
Whilst creating this puzzle, I made a discovery (probably common knowledge amongst puzzle makers?). As seems to have often been the case recently, Ruud's cage pattern for the A76 turned out to be very complex. In other words, my (admittedly ropey and old) software was struggling to come up with any variants with a unique solution. When it eventually did (typically after 15 - 20 minutes searching), the result was almost invariably either too easy or too boring (or both).

When I decided to try making a Killer-X out of it, something interesting happened. Not only did it take much less time to generate each variant (typically only around 30 seconds), but a high percentage of the generated puzzles suddenly became much harder (and usually much more interesting).

My theory for this observed effect is as follows: If the cage pattern is very complex, the puzzle needs big initial cage constraints (in the form of cages with fixed or very limited combinations, for example) in order to still have a unique solution. These cage constraints serve as obvious "footholds" for the solver when doing the puzzle, often making it relatively straightforward. Because a Killer-X has extra constraints due to the diagonals, it doesn't require so many initial cage constraints as a non-X variant in order to possess a unique solution. Consequently, it can afford to offer fewer footholds, thus often making the puzzle (contrary to expectation) harder. (Note: The A76X was about mid-range in terms of difficulty).

The interesting thing to note here (and the reason why I'm mentioning all this) is that the diagonals can serve a big purpose (in terms of increasing the quality of the puzzle) even if it appears to the solver as though there are no moves making use of the diagonals whatsoever. Even in this case, they can come into play in the endgame in order to provide a unique solution, usually at the stage where (for the solver) the puzzle has long since become trivial. In other words, even if the solver doesn't require the diagonals, the puzzle itself may do!

Para:
mhparker wrote:
Ruud's cage pattern for the A76 turned out to be very complex. In other words, my (admittedly ropey and old) software was struggling to come up with any variants with a unique solution. When it eventually did (typically after 15 - 20 minutes searching), the result was almost invariably either too easy or too boring (or both).
The reason this pattern gives so much problems are the center 3 nonets(258). There are 6 rows in these nonets that have all there cells in one cage. This gives a lot of options for non-unique patterns. Because of this there are a limited set of valid combinations that would give a unique solution of digits for this pattern. Then there is the extra constraint that the cages also have to be able to be uniquely filled. This tends to give either rather easy of extremely difficult puzzles. The brick wall pattern is another example of the uniqueness problem.

When adding the diagonals you can substantially increase the number of unique combinations for the center 3 nonets, thus also increasing the number of unique puzzles and you will have a wider range of difficulty in your puzzles as you have more options to choose from.

mhparker:
Para wrote:
The reason this pattern gives so much problems are the center 3 nonets(258). There are 6 rows in these nonets that have all there cells in one cage. This gives a lot of options for non-unique patterns.
You're right. For example, if I remove the diagonal constraints from the A76X, it not only doesn't have a unique solution any more, but 15 of the cells within the resulting deadly pattern belong to the 18 cells in n258 that you mention.

I also looked at some of the other grids I generated based on this cage pattern. The easiest one had c123 outies = 6(3) = {123} and c789 outies = 24(3) = {789}. Of course, these fixed cage combinations significantly reduce the number of valid arrangements for the digits in n258 and were possibly critical in causing the puzzle to have a unique solution. But they also made the puzzle trivial. That's the point I was trying to make, and which accounts for the "uniqueness problem" you mention where a high proportion of the generated puzzles become (too) easy.
Para wrote:
This tends to give either rather easy of extremely difficult puzzles.
In practice, none of the non-X variants I generated were extremely difficult this time. But (because it took so long to generate each one, by which time the laptop was running very hot) I only generated 9 of these, which means that the results are maybe not statistically significant.

BTW, with the A73 (where I didn't publish anything), the situation was really extreme. Around 60% of the variants I privately generated were extremely difficult (read: practically unsolvable!), around one third were trivial, and only 5 - 10% of the attempts resulted in something in the 1.25 - 1.75 rating range.
Para wrote:
When adding the diagonals you can substantially increase the number of unique combinations for the center 3 nonets, thus also increasing the number of unique puzzles and you will have a wider range of difficulty in your puzzles as you have more options to choose from.
In practice, it appeared that having diagonals not only increased the number available to choose from, but also made the difficulty spread more even. For now it's somewhat of an unconfirmed observation due to not having enough non-X variants available to say definitely that this is the case. Maybe I need another 20 or so grids to see a definite trend. But at an estimated 20 minutes for each puzzle, that exercise would tie me (and my computer!) up for not much less than a whole working day!
Walkthrough by Afmob:
Congratulations Para!

By the way, here's my walkthrough for Mike's A76 variant. I pretty much used the same "breakthrough" move like Para.

A76X Walkthrough:

1. C12
a) 6(3) = {123} locked for N1
b) 12(2) = {48/57}
c) Outies = 8(2) = [17/26/35]
d) 20(3) <> 3 because R9C3 = (567)

2. R1234
a) Killer pair (58) locked in 12(2) + 14(2)
b) Innies = 16(2) = {79} locked for R4

3. N258
a) Innies N2 = 5(2) = {14/23}
b) Innies N5 = 7(2) = {16/25/34}
c) 7,9 locked in 25(4) @ N5 = 79{18/36/45}
d) Innies N8 = 10(2) -> no 5

4. C789
a) 4(2) = {13} locked for C9+N9
b) Outies C89 = 8(2) = [17/26/35/62]
c) Outies C789 = 8(3) = 1{25/34} -> 1 locked for C6
d) Outies C789: R5C6 <> 2 since it's the only place where 5 is possible

5. R6789+D\
a) Naked triple (123) locked in R2C2+R3C3+R9C9 for D\
b) 2 locked in D\ for N1 -> R3C2 <> 2
c) Innies N8 = [64/73/82/91]
d) Innies R89 = 22(4) - Innies N8 = 10(2) -> R8C37 = 12(2) = {39/48/57}; R8C3 <> 9
e) 2 locked in 15(3) @ R9 for R9
f) 6(2): R8C1 <> 4
g) Outies R6789 = 45(9) - 31(5) - Innies N5 = 7(2) -> R5C37 = 7(2) <> 7,8,9
h) Killer pair (45) locked in 6(2) + 20(3) for N7
i) R8C37 = 12(2): R8C7 <> 7,8

6. N258
a) Innies N5 = 7(2): R5C4 <> 1,5
b) 15(3) @ R4C3 <> 1 because 9 only possible @ R4C3 and R5C4 <> 1,5
-> 15(3) = {249/267/357}
c) 15(3) @ R4C3: R5C3 <> 3 because 5 only possible there
d) Clean up: R5C7 <> 4,6 (step 5g) -> 15(3) @ R4C7 = (159/249/357}
e) Killer pair (25) locked in both 15(3) for R5
f) Outies C123 = 14(3): R8C4 <> 6 because R25C4 would be <= 7
g) Innies N8: R8C6 <> 4

7. N258 !
a) ! 16(3) <> {178/457} since it's blocked by Killer pairs (45,78) of 12(2)
b) 16(3) must have 1,2 xor 3 and it's only possible @ R1C4 -> R1C4 = (123)
c) Innies N2 = 5(2): R1C6 <> 1
d) Outies C789 = 8(3): R8C6 <> 2 because R1C6 <> 1,5
e) Innies N8 = 10(2): R8C4 <> 8

8. R789
a) Naked pair (13) locked in R8C69 for R8
b) 6(2): R9C1 <> 5
c) 20(4): R67C3 <> 5,6,7,8,9 because R8C34 >= 15
d) R8C37 = 12(2): R8C7 <> 9
e) 3 locked in R7C123 for R7

9. C123 !
a) ! 7,8,9 locked in 16(3)+R48C3 for C3
b) Outies C12 = 8(2) = [26/35]
c) 1 locked in R23C2 for C2
d) 20(3) <> 4 because R9C3 = (56)
e) Hidden Single: R9C1 = 4 @ N7 -> R8C1 = 2
f) 20(3) = {569} because R8C3 = (78) blocks {578}; {569} locked for N7, 9 locked for C2

10. R789
a) 1 locked in R7C13 for R7
b) 12(3) = {246} locked for R7+N8
c) 5,9 locked in R7C789 for N9
d) R8C7 = 4 -> R8C3 = 8 (step 9d)
e) 15(3) @ N9 = {267} locked for N9
f) 15(3) @ N7 = {357} because R7C12 = {13/17/37} and only {37} leads to a combination for 15(3)
-> R6C2 = 5, {37} locked for R7
g) R7C3 = 1
h) 20(4) = 18[29/47]
i) Hidden Single: R3C3 = 3 @ C3 -> R3C2 = 1, R2C2 = 2, R9C9 = 1, R8C9 = 3, R8C6 = 1
j) Innies N8 = 10(2) = [91] -> R8C4 = 9
k) R8C2 = 6, R9C2 = 9, R9C3 = 5, R8C8 = 7, R8C5 = 5, R6C3 = 2, R3C7 = 2, R9C7 = 6, R9C8 = 2

11. N23
a) 11(3) @ R2C8 = 2[36/54]
b) Killer pair (56) locked in 11(3) @ R2C8 + 14(2) for N3
c) 11(3) @ N2 = 1{28/37} -> 1 locked for C7
d) Innies N2 = 5(2) = {23} locked for R1+N2
e) 16(3) = 3{49/67} -> R1C4 = 3
f) 11(3) = [218] -> R1C6 = 2, R1C7 = 1, R2C7 = 8
g) 14(2) = {59} locked for R1+N3

12. Rest is clean-up and singles.

Rating: 1.25, nothing too complicated
Walkthrough by Andrew:
Mike estimated A76X as 1.5 but both Para and Afmob rated it as 1.25. I can see where both the estimate and the rating come from. If one spots the two key moves quickly then it's definitely 1.25. Maybe both Para and Afmob spotted those two moves quickly. I didn't!

Perhaps Mike's estimate took account of the difficulty in spotting the key moves. Both key moves are based on the 16(3) cage at R1C3; Para's steps 18 and 20, Afmob's steps 7a and 9a.

I spent several hours struggling and nibbling, see my comment after step 19, before I revisited that 16(3) cage and found the {457} elimination. Then because that gave key eliminations in R1C46 I missed the killer triple in C3 so my later stage was a lot longer.

It is, in fact, possible to solve the puzzle using only one of the key eliminations. I did that without spotting the killer triple. Similarly I think it would be possible to solve it using the killer triple, but missing the {457} elimination, since the killer triple is present for all combinations in 16(3) except for {178} which clashes with the killer triple as well as with R1C12.


Here is my walkthrough for A76X, without the killer triple in C3.

This is a Killer-X. I've included all the eliminations on the diagonals because it's so easy to overlook them if you are doing your own eliminations.

Prelims

a) R1C12 = {39/48/57}, no 1,2,6
b) R1C89 = {59/68}
c) R89C1 = {15/24}
d) R89C9 = {13}, locked for C9 and N9
e) 6(3) cage in N1 = {123}, locked for N1, clean-up: no 9 in R1C12
f) R3C456 = {389/479/569/578}, no 1,2
g) 11(3) cage at R1C6 = {128/137/146/236/245}, no 9
h) 11(3) cage at R2C8 = {128/137/146/236/245}, no 9
i) 21(3) cage at R6C8 = {489/579/678}, no 1,2,3
j) 20(3) cage in N7 = {389/479/569/578}, no 1,2

1. Naked triple {123} in R2C2 + R3C3 + R9C9, locked for D\
1a. 2 locked in R2C2 + R3C3 for D\ -> no 2 in R3C2

2. Killer pair 5,8 in R1C12 and R1C89, locked for R1

3. 45 rule on N2 2 innies R1C46 = 5 = {14/23}

4. 45 rule on R1234 2 innies R4C37 = 16 = {79}, locked for R4

5. 45 rule on N5 2 innies R5C46 = 7 = {16/25/34}, no 7,8,9

6. 45 rule on R1234 4 outies R5C3467 = 14, R5C46 = 7 -> R5C37 = 7 = {16/25/34}, no 7,8,9

7. 45 rule on N8 2 innies R8C46 = 10 = {19/28/37/46}, no 5

8. 45 rule on R89 4 innies R8C3467 = 22 -> R8C37 = 12 = [39]/{48/57}, no 1,2,6, no 9 in R8C3

9. 2 in N9 locked in R9C78, locked for R9, clean-up: no 4 in R8C1
9a. 15(3) cage in N9 = 2{49/58/67}

10. 45 rule on C12 2 outies R39C3 = 8 = [17/26/35]

11. 45 rule on C89 2 outies R39C7 = 8 = [17/26/35/62], no 4,8,9, no 5,7 in R3C7

12. 45 rule on C12 4 innies R2389C2 = 18, max R23C2 = 5 -> min R89C2 = 13, no 3

13. 20(3) cage in N7 = {479/569/578}
13a. Killer pair 4,5 in R89C1 and 20(3) cage, locked for N7, clean-up: no 7,8 in R8C7 (step 8)
13b. 3 in N7 locked in R7C123 + R8C3
13c. 45 rule on N7 4 innies R7C123 + R8C3 = 19 = {1369/1378/2368}

14. 45 rule on N3 3 outies R1C6 + R4C89 = 9, max R4C89 = 8, no 8

15. 45 rule on R6789 2 innies R6C19 = 1 outie R5C5
15a. Max R5C5 = 9 -> max R6C19 = 9, no 9, no 8 in R6C1
15b. R6C19 cannot make 4 -> no 4 in R5C5

16. 7,9 in N5 locked in 25(4) cage = 79{18/36/45}, no 2

17. 45 rule on C789 3 outies R158C6 = 8 = 1{25/34}, 1 locked for C6, clean-up: no 1 in R5C4 (step 5), no 1,2,3,4 in R8C4 (step 7)
17a. 5 of {125} must be in R5C6 -> no 2 in R5C6, clean-up: no 5 in R5C4 (step 5)

18. 45 rule on C123 3 outies R158C4 = 14 = {149/167/239/248/347}
18a. 7 of {167} must be in R8C4 -> no 6 in R8C4, clean-up: no 4 in R8C6 (step 7)
18b. R158C4 = [149/167/239/329/428/437] (cannot be [248/347] which don’t give valid permutations for R158C6]

19. 16(3) cage at R1C3 = {169/259/268/349/367} (cannot be {178/358/457} which clash with R1C12; all 3 cells of the 16(3) cage see R1C12)
19a. 3 of {349} must be in R1C4 -> no 4 in R1C4, clean-up: no 1 in R1C6 (step 3)
[This move was actually available after step 3! Initially I saw the {178/358} clashes but missed the {457} clash which is less obvious.]

20. R158C6 (step 17) = 1{25/34}
20a. 1 of {125} must be in R8C6 -> no 2 in R8C6, clean-up: no 8 in R8C4 (step 7)

21. Killer pair 1,3 in R8C69, locked for R8, clean-up: no 9 in R8C7 (step 8), no 5 in R9C1
21a. 3 in R7 locked in R7C123, locked for R7

22. 15(3) cage at R4C3 = {249/267/357} (cannot be {159} because no 1,5,9 in R5C4, cannot be {456} because R4C3 only contains 7,9), no 1, clean-up: no 6 in R5C7 (step 6)
22a. 3 of {357} must be in R5C4 -> no 3 in R5C3, clean-up: no 4 in R5C7 (step 6)
22b. 15(3) cage at R4C7 = {159/249/357}
22c. Taking these cages together R5C3467 = {1256/2345} = 25{16/34}, 2,5 locked for R5

23. Min R8C34 = 15 -> max R67C3 = 5, R6C3 = {1234}, R7C3 = {123}

24. R7C123 + R8C3 (step 13c) = {1378/2368} (cannot be {1369} because R8C3 only contains 7,8), no 9, 8 locked for N7
24a. 20(3) cage (step 13) = {479/569}, 9 locked in R89C2, locked for C2
24b. 7 of {479} must be in R9C3 -> no 7 in R89C2

25. Hidden killer pair 1,2 in R7C123 (step 24) and R7C456 -> R7C456 must contain 1/2
25a. R7C456 = {147/246} (cannot be {129} which contains 1 and 2, cannot be {156} which clashes with R7C123 = {236} because of the hidden killer pair) = 4{17/26}, no 5,8,9, 4 locked for R7 and N8

26. 5,9 in R7 locked in R7C789, locked for N9, clean-up: no 4,8 in 15(3) cage (step 9a) -> R8C7 = 4, R8C3 = 8 (step 8), clean-up: no 3 in R3C7 (step 11)
26a. 15(3) cage in N9 = {267}, locked for N9

27. 21(3) cage at R6C8 = {489/579} (cannot be {678} because 6,7 only in R6C8) = 9{48/57}, no 6
27a. 4,7 only in R6C8 -> R6C8 = {47}
27b. 9 locked in R7C89, locked for R7

28. 9 on D\ locked in R5C5 + R6C6, locked for N5
28a. 9 in C7 locked in R46C7, locked for N6

29. 19(4) cage at R6C7 = {1459/1468/3457} (cannot be {2458/2467} because R8C6 only contains 1,3)
29a. 6,7,9 only in R6C7 -> R6C7 = {679}

30. 8 in N6 locked in 15(3) cage = {168/348} (cannot be {258} because 2,5 only in R6C9), no 2,5,7
30a. 1,3 of {168/348} must be in R5C8 -> R5C8 = {13}
30b. 8 locked in R56C9, locked for C9, clean-up: no 6 in R1C8

31. 2 in C9 locked in R234C9, locked for 18(4) cage -> no 2 in R4C8
31a. 7 in C9 locked in R23C9, locked for N3 and 18(4) cage
31b. 18(4) cage = {2367/2457}, no 1,9
31c. 3 of {2367} must be in R4C8 -> no 6 in R4C8

32. 1 in N6 locked in R5C78, locked for R5, clean-up: no 6 in R5C4 (step 5)

33. R8C6 = 1 (hidden single in C6), R8C4 = 9 (step 7), R89C9 = [31], 1 locked for D\, R89C1 = [24], 4 locked for D/, clean-up: no 8 in R1C2, no 7 in R7C456 (step 25a), no 7 in R9C3 (step 24a)
33a. Naked triple {246} in R7C456, locked for R7 and N8

34. R8C34 = 17 -> R67C3 = 3 = [21], 1 locked for D/, R3C3 = 3, R23C2 = [21]

35. R9C2 = 9 (hidden single in R9)

36. R7C12 = {37} -> R6C2 = 5, R8C2 = 6, locked for D/, R9C3 = 5, R8C8 = 7, locked for D\, R8C5 = 5, R6C8 = 4, R3C7 = 2, locked for D/, R9C78 = [62], clean-up: no 8 in R1C8, no 5 in R7C89 (step 27)
36a. R7C89 = [89], R7C7 = 5, locked for D\, R1C1 = 8, locked for D\, R1C2 = 4, R5C5 = 9, R6C6 = 6, R4C4 = 4, R1C9 = 5, locked for D/, R1C8 = 9, R56C9 = [68], R4C9 = 2, clean-up: no 1 in R1C4 (step 3), no 3 in R5C46 (step 5)

and the rest is naked singles
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Ed
PostPosted: Tue Jul 15, 2008 8:17 am 
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Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Assassin 77 by Ruud (Nov 07)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:2816:2816:5634:5123:5123:4869:4869:4869:4616:2816:5634:5634:5634:5123:5123:4869:4616:4616:3090:7955:7955:7955:3094:5143:5143:5143:2330:3090:4636:4636:7955:3094:3360:3360:5143:2330:2852:4636:4390:7955:3094:3360:6442:5143:3372:2852:2852:4390:4912:4912:4912:6442:3372:3372:1590:1590:4390:3385:3385:3385:6442:3645:3645:4927:4927:4390:3906:2883:1604:6442:4678:4678:4927:2633:2633:3906:2883:1604:846:846:4678:
Solution: 
+-------+-------+-------+
| 2 1 6 | 5 4 3 | 8 7 9 |
| 8 5 4 | 7 2 9 | 1 6 3 |
| 3 9 7 | 8 1 6 | 4 5 2 |
+-------+-------+-------+
| 9 4 8 | 3 6 1 | 5 2 7 |
| 1 6 2 | 4 5 7 | 9 3 8 |
| 7 3 5 | 2 9 8 | 6 4 1 |
+-------+-------+-------+
| 4 2 9 | 1 7 5 | 3 8 6 |
| 5 8 1 | 6 3 2 | 7 9 4 |
| 6 7 3 | 9 8 4 | 2 1 5 |
+-------+-------+-------+
Quote:
Para: This is an odd puzzle. The opening is very easy, after that i think there's very little places to progress . For me it's a rating 1.00
goooders: not sure i agree with paras rating sure the beginning is easy but then it grinds to a halt and becomes horrible is it possible that para is really rather good and cant see the difficulties others may have?
Afmob: I didn't have any problems with this one at all. Rating: 1.0, an easy assassin, so Para's estimated rating should fit
gary w: I sympathise with goooders.I too started off well and then got stuck for quite a while..Took me over 3 hours to complete..so I too would rate this as more than 1.0..(but) I have to agree with you two guys that it really wasn't that hard an assassin. .... it should have come out much quicker for me!
Andrew: I was going to rate A77 at 1.25 since I felt it was a typical Assassin, ... However I missed one important step.... Para also did a reasonable amount of combination/permutation work so IMHO it's arguable that the rating should be an easier 1.25 rather than 1.0. It took me longer (than 3 hours).
Walkthrough by Para:
Hi all

This is an odd puzzle. The opening is very easy, after that i think there's very little places to progress but i think my path probably is the shortest to finish it. For me it's a rating 1.00.

Walk-through Assassin 77

1. 11(3) at R1C1 and R5C1 = {128/137/146/236/245}: no 9

2. R34C1 = {39/48/57}: no 1,2,6

3. R34C9 = {18/27/36/45}: no 9

4. 19(3) at R6C4 and R8C1 = {289/379/469/478/568}: no 1

5. R7C12 and R89C6 = {15/24}: no 3,6,7,8,9

6. R7C89 = {59/68}: no 1,2,3,4,7

7. R89C4 = {69/78}: no 1,2,3,4,5

8. R89C5 = {29/38/47/56}: no 1

9. R9C23 = {19/28/37/46}: no 5

10. R9C78 = {12} -> locked for R9 and N9
10a. Clean up: R8C5: no 9; R8C6: no 4,5; R9C23: no 8,9

11. 45 on N47: 1 outie: R3C1 = 3
11a. R4C1 = 9
11b. 11(3) at R1C1 = {128/146/245}: no 7
11c. 18(3) at R4C2 = {378/468/567}: no 1,2
11c. Clean up: R4C9: no 6

12. 45 on N9: 2 outies: R56C7 = 15 = {69/78}: no 1,2,3,4,5
12a. 45 on N9: 2 innies: R78C7 = 10 = {37/46}: no 5,8,9
12b. 25(4) at R5C7 = {3679/4678} -> 6,7 locked for C7

13. 45 on N7: 2 outies: R56C3 = 7 = {16/25/34}: no 7,8
13a. 45 on N7: 2 innies: R78C3 = 10 = {19/28/37/46}: no 5

14. 45 on C1: 4 outies: R1678C2 = 14 = {1238/1247/1256/1346/2345}: no 9
14a. 9 in N7 locked within R78C3 -> R78C3 = {19} -> locked for C3 and N7
14b. R7C12 = {24}(last combo) -> locked for R7 and N7
14c. R9C23 = {37}(last combo) -> locked for R9 and N7
14d. Clean up: R56C3: no 6; R8C4: no 8; R8C5: no 4,8; R8C7: no 6

15. 45 on R89: 2 innies: R8C37 = 8 = [17]
15a. R7C3 = 9; R7C7 = 3; R89C6 = [24]
15b. R89C4 = {69}(last combo) -> locked for C4 and N8
15c. R89C5 = [38](last combo)
15d. R7C89 = {68}(last combo) -> locked for N9
15e. R56C7 = {69}(last combo) -> locked for C7 and N6

16. 1 in N4 and 7 in C1 locked within 11(3) cage at R5C1 -> 11(3) = {17}[3]; R6C2 = 3; R56C1 = {17} -> locked for C1 and N4
16a. R9C23 = [73]
16b. R56C3 = {25}(last combo) -> locked for C3 and N4

16. 31(5) at R3C2 = {16789/25789/34789/35689/45679}: 9 locked within cage -> R3C2 = 9(only place in cage)

17. 45 on C1234: 3 innies: R167C4 = 8 = {125}/[341]: no 7,8; R1C4: no 4; 1 locked for C4

18. 45 on C6789: 3 innies: R267C6 = 22 = {89}[5]/{69}[7]: no 1,3; R26C6: no 5,7; 9 locked for C6

19. 45 on R6789: 4 outies: R5C1379 = 20 = [1298/1568/7265/7562]: R5C9: no 1,3,4,7

20. 13(3) at R5C9 = [2]{47}/[8]{14}: [5]{17} blocked by R6C1: R5C9: no 5; R6C89: no 2,5,8; 4 locked for R6 and N6
20a. Naked triple {147} in R6C189 -> locked for R6
20b. R6C6 = 8(hidden); R27C6 = [95](step 18); R7C45 = [17]
20c. R16C4 = {25}(last combo from step 17) -> locked for C4
20d. Naked Pair {25} in R6C34 -> locked for R6
20e. Clean up: R3C9: no 5

21. 31(5) at R3C2 = 9{3478}(last combo): no 6; 3 locked within R45C4 for C4 and N5
21a. R1C6 = 3(hidden)

22. 13(3) at R4C6 = {1[5]7}(last combo) -> R4C7 = 5; R45C6 = {17} -> locked for C6 and N5
22a. R3C6 = 6
22b. Naked Pair {34} in R45C4 -> locked for C4, N5 and 31(5) at R3C2
22c. Naked Pair {78} in R3C34 -> locked for R3
22d. Clean up: R3C9: no 4; R4C9: no 1,2,3

23. 20(4) at R1C4 = 9{245}(last combo) -> locked for N2
23a. R3C5 = 1; R34C9 = [27]; R3C78 = [45]; R5C9 = 8;
23b. R7C89 = [86]; R2C9 = 3(hidden); R9C7 = 2(hidden); R9C8 = 1
23d. R6C89 = [41]; R1C9 = 9; R12C8 = [76]; R8C8 = 9; R89C9 = [45]
23d. R89C4 = [69]; R9C1 = 6

24. 11(3) at R1C1 = {128/245}: no 6; 2 locked for N1
24a. R1C3 = 6(hidden)
24b. R2C234 within 22(4) at R1C3 = [547]: [1]{78} blocked by R2C7

And the rest is all naked singles.

greetings

Para
Walkthrough by Afmob:
I didn't have any problems with this one at all. Maybe I immediately saw a direct and short solving path?

A77 Walkthrough:

1. C1234
a) Innies N7 = 10(2) <> 5
b) Outies N7 = 7(2) <> 7,8,9
c) Innies N47 = 9 -> R4C1 = 9
d) 12(2) = [39] -> R3C1 = 3
e) 11(3) @ N1 = {128/146/245} -> no 7
f) Innies C1234 = 8(3) = 1{25/34} -> 1 locked for C4
g) 19(3) @ C4 must have 2,3,4 xor 5 and R6C4 = (2345) -> R6C56 <> 2,3,4,5

2. R789
a) 3(2) = {12} locked for R9+N9
b) 6(2): R8C6 <> 4,5
c) 11(2): R8C5 <> 9
d) 10(2) = {37/46}
e) Innies N9 = 10(2) = {37/46}
f) Outies N9 = 15(2) = {69/78}
g) 25(4) = 67{39/48} -> 6,7 locked for C7
h) Innies R89 = 8(2) = [17/26]
i) Innies N7 = 10(2) = [82/91]
j) Innies N9 = 10(2) = [37/46]

3. N89
a) 7 locked in 13(3) @ R7 for N8 = 7{15/24}
b) 15(2) = {69} locked for C4+N8
c) 11(2) = {38} locked for C5
d) Hidden triple (689) in R7C389 @ R7 -> no other candidates
e) 14(2) = {68} locked for R7+N9
f) 18(3) = {459} locked for N9
g) R7C3 = 9, R7C7 = 3, R8C7 = 7
h) Innies N7 = 10(2) = [91] -> R8C3 = 1
i) 6(2) = {24} locked for R7+N7
j) 10(2) = {37} locked for R9+N7
k) R9C5 = 8, R8C5 = 3, R8C6 = 2 -> R9C6 = 4

4. C6789
a) 25(4) = {3679} -> 6,9 locked for C7+N6
b) Innies C6789 = 22(3) = 9{58/67} -> 9 locked for C6
c) Innies C6789 = 22(3) must have 5 xor 7 and R7C6 = (57) -> R26C6 <> 5,7
d) Outies C9 = 27(4) = 9{378/468/567} -> 9 locked for C8

5. N14
a) Innies N4 = 7(2) = {25/34}
b) 7 locked in 11(3) @ C1 -> 11(3) = {137}, R6C2 = 3, {17} locked for C1+N4
c) 17(4) = {1259} -> {25} locked for C3+N4
d) R9C2 = 7, R9C3 = 3
e) 31(5) = 9{1678/2578/3478/3568/4567} -> R3C2 = 9

6. C456
a) 19(3) = 8{29/47/56} because {469} blocked by R6C7 = (69) -> R6C6 = 8
b) Outies C6789 = 22(3) = [985] -> R2C6 = 9, R7C6 = 5
c) R7C4 = 1, R7C5 = 7
d) 19(3) = 8[29/56]
e) Outies C1234 = 8(3) = {125} because R6C4 = (25) -> {25} locked for C4
f) 31(5) = {34789} -> 3 locked for C4+N5
g) 13(3) = {157} because R45C6 = {16/17/67} -> only {17} leads to a combination for 13(3)
-> R4C7 = 5, {17} locked for C6+N5
h) 20(4) = {2459} locked for N1 because R1C4 = (25); 4 locked for C5
i) 12(3) = 1[29/65] -> R3C5 = 1
j) Naked pair (34) locked in R45C4 for 31(5)
k) Naked pair (78) locked in R3C34 for R3
l) R3C6 = 6, R1C6 = 3

7. N3
a) Hidden Single: R1C9 = 9
b) 3 locked in 18(3) = {369} locked; {36} locked for R2
c) 19(4) = 37{18/45} -> R1C8 = 7
d) 19(4) = {1378} -> {18} locked for C7

8. N1
a) 22(4) <> 2 because {2578} impossible since (25) only possible @ R2C2
b) 2 locked in 11(3) = 2{18/45}
c) Hidden Single: R1C3 = 6 @ R1
d) 22(4) = [6547] because 6{178} blocked by R2C7 = (18)
-> R2C2 = 5, R2C3 = 4, R2C4 = 7

9. Rest is singles.

Rating: 1.0, an easy assassin, so Para's estimated rating should fit
Walkthrough by Andrew:
I finished A77 late Thursday night, well actually about 1am on Friday but felt it was getting too late to post a walkthrough then. I've only just gone through Para's and Afmob's walkthroughs.

I was going to rate A77 at 1.25 since I felt it was a typical Assassin, admittedly with a fairly easy start, but still in the range covered by 1.25. I'll stick with that rating for the way I solved it. However I missed one important step, see my comment after step 3. Don't know how I missed that, it's so obvious! :oops: Spotting that ought to have made my solution a bit quicker.
Para wrote:
Check my walk-through. I think you'll have to agree with the way i solved it, it is a 1.00.
I've just done that. As well as spotting his key move, step 19, Para also did a reasonable amount of combination/permutation work so IMHO it's arguable that the rating should be an easier 1.25 rather than 1.0.

I think there has been a tendency recently to rate puzzles down by comparing them with the hardest ones in a rating range, overlooking that each rating value covers a range of difficulty.
gary w wrote:
Took me over 3 hours to complete..so I too would rate this as more than 1.0.Be interesting to see what others think.
Good point Gary. It took me longer, including time to re-work steps when I spotted steps that ought to have gone in earlier.

Here is my walkthrough for A77.

Prelims

a) R34C1 = {39/48/57}, no 1,2,6
b) R34C9 = {18/27/36/45}, no 9
c) R7C12 = {15/24}
d) R7C89 = {59/68}
e) R89C4 = {69/78}
f) R89C5 = {29/38/47/56}, no 1
g) R89C6 = {15/24}
h) R9C23 = {19/28/37/46}, no 5
i) R9C78 = {12}, locked for R9 and N9, clean-up: no 8,9 in R9C23, no 9 in R8C5, no 4,5 in R8C6
j) 11(3) cage in N1 = {128/137/146/236/245}, no 9
k) 11(3) cage in N4 = {128/137/146/236/245}, no 9
l) R6C456 = {289/379/469/478/568}, no 1
m) 19(3) cage in N7 = {289/379/469/478/568}, no 1
n) 31(5) cage at R3C2 must contain 9

1. 45 rule on N47 1 innie R4C1 = 9, R3C1 = 3, clean-up: no 6 in R4C9
1a. 11(3) cage in N1 = {128/146/245}, no 7

2. 45 rule on R89 2 innies R8C37 = 8 = [17/26]/{35}, no 4,8,9, no 6,7 in R8C3

3. 45 rule on C1234 3 innies R167C4 = 8 = 1{25/34}, 1 locked for C4
[At this stage I ought to have seen 45 rule on C6789 3 innies R267C6 = 22 = 9{58/67}, 9 locked for C6.]

4. 45 rule on N7 2 innies R78C3 = 10 = [73/82/91], clean-up: no 3 in R8C7 (step 2)
4a. R56C3 = 7 = {16/25/34}

5. 45 rule on N9 2 innies R78C7 = 10 = [37/46], clean-up: no 3 in R8C3 (step 2), no 7 in R7C3 (step 4)
5a. R56C7 = 15 = {69/78}
5b. R5678C7 = 67{39/48}, 6,7 locked for C7

6. Naked pair {12} in R8C36, locked for R8, clean-up: no 9 in R9C5

7. 19(3) cage in N7 = {469/568} (cannot be {379} because 3,9 only in R8C2, cannot be {478} which clashes with R9C23) = 6{49/58}, no 3,7, 6 locked for N7, clean-up: no 4 in R9C23
7a. 9 of {489} must be in R8C2 -> no 4 in R8C2

8. Naked pair {37} in R9C23, locked for R9, clean-up: no 8 in R8C4, no 4,8 in R8C5

9. 7 in C1 locked in R56C1 -> 11(3) cage in N4 = {137}, locked for N4, clean-up: no 4,6 in R56C3 (step 4a)
9a. R6C2 = 3, R56C1 = {17}, R9C23 = [73]
9b. Naked pair {17} in R56C1, locked for C1, clean-up: no 5 in R7C2

10. Naked pair {25} in R56C3, locked for C3 and N4 -> R8C3 = 1, R7C3 = 9 (step 4), R8C6 = 2, R9C6 = 4, R8C7 = 7 (step 2), R7C7 = 3 (step 5), clean-up: no 8 in R56C7 (step 5a), no 5 in R7C1, no 5 in R7C89, no 4 in R8C1 (step 7), no 8 in R9C4

11. Naked pair {68} in R7C89, locked for R7 and N9

12. R89C5 = [38] (hidden pair in N8)

13. Naked pair {69} in R56C7, locked for C7 and N6

14. Naked pair {69} in R89C4, locked for C4

15. R3C2 = 9 (only remaining cell for 9 in 31(5) cage)

16. 11(3) cage in N1 (step 1a) = {128/146/245}
16a. 1 in {128/146} must be in R1C2 -> no 6,8 in R1C2
16b. R12C1 = {24} would clash with R7C1 -> no 5 in R1C2

17. R6C456 = {289/478/568} (cannot be {469} which clashes with R6C7) = 8{29/47/56} -> R6C6 = 8
17a. R6C4 = {245} -> no 2,4,5 in R6C5
17b. Hidden killer pair 6,9 in R6C5 and R6C7 -> R6C5 = {69}, clean-up: no 4 in R6C4 (step 17)

18. Naked pair {25} in R6C34, locked for R6

19. 4 in R6 locked in R6C89, locked for N6, clean-up: no 5 in R3C9
19a. 13(3) cage in N6 = 4{18/27}, no 3,5
19b. 2,8 only in R5C9 -> R5C9 = {28}

20. 4 in C7 locked in R123C7, locked for N3, clean-up: no 5 in R4C9

21. 45 rule on C9 4 outies R2678C8 = 27 = {3789/4689/5679} = 9{378/468/567}, no 1,2, 9 locked for C8
21a. 4 of {4689} must be in R6C8 -> no 4 in R8C8
21b. 3 of {3789} must be in R2C8, 7 of {5679} must be in R6C8 -> no 7 in R2C8

22. R8C9 = 4 (hidden single in R8)

23. R6C8 = 4 (hidden single in R6)

24. R167C4 (step 3) = {125} (cannot be {134} because 3,4 only in R1C4), 2,5 locked for C4

25. 31(5) cage at R3C2 = {34789} (only remaining combination), no 6
25a. 3 locked in R45C4, locked for C4 and N5
25b. 8 locked in R3C34, locked for R3, clean-up: no 1 in R4C9

26. 13(3) cage at R4C6 = {157/256} = 5{17/26}, no 8,9
26a. CPE no 5 in R4C5

27. Naked quad {1567} in R3457C6, locked for C6

28. Naked pair {39} in R12C6, locked for N2

29. 45 rule on C789 2 outies R13C6 – 4 = 1 innie R4C7
29a. Max R4C7 = 5 -> max R13C6 = 9 -> R1C6 = 3, R2C6 = 9
29b. -> R3C6 – 1 = R4C7 -> R3C6 = 6, R4C7 = 5, clean-up: no 3 in R4C9

30. Naked pair {17} in R45C6, locked for C6 and N5 -> R7C6 = 5, R7C45 = [17]

31. Naked pair {34} in R45C4, locked for C4, N5 and 31(5) cage

32. 20(4) cage in N2 = {2459} (only remaining combination), no 1, locked for N2 -> R3C5 = 1, clean-up: no 8 in R4C9
32a. R45C5 = 11 = [29/65]

33. Naked pair {78} in R3C34, locked for R3 -> R34C9 = [27], R56C9 = [81], R45C6 = [17], R56C1 = [17], R7C89 = [86], R3C78 = [45], R19C9 = [95], R2C9 = 3, R2C8 = 6, R8C8 = 9, R9C1 = 6, R89C4 = [69]

34. Naked pair {18} in R12C7, locked for C7 and N3 -> R9C78 = [21], R1C8 = 7

35. R1C3 = 6 (hidden single in R1)
35a. 22(4) cage at R1C3 = {4567} (cannot be {1678} because R2C234 = {178} clashes with R2C7) -> R2C234 = [547]
[This step could also be done by UR -> R2C3 = 4 but why would anybody use UR when there’s a direct killer move?]

and the rest is naked singles
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Ed
PostPosted: Tue Jul 15, 2008 8:20 am 
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Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Assassin 77v2 by Ruud (Nov 07)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:4608:4608:4610:3843:3843:6405:6405:6405:3592:4608:4610:4610:4610:3843:3843:6405:3592:3592:2578:4883:4883:4883:4630:4887:4887:4887:3098:2578:3356:3356:4883:4630:5408:5408:4887:3098:4132:3356:5414:4883:4630:5408:2858:4887:4140:4132:4132:5414:4400:4400:4400:2858:4140:4140:2870:2870:5414:3385:3385:3385:2858:4413:4413:3135:3135:5414:6978:1603:5188:2858:4166:4166:3135:6978:6978:6978:1603:5188:5188:5188:4166:
Solution: 
+-------+-------+-------+
| 3 9 5 | 6 4 7 | 8 1 2 |
| 6 4 1 | 8 2 3 | 9 7 5 |
| 8 7 2 | 5 9 1 | 6 3 4 |
+-------+-------+-------+
| 2 3 9 | 1 6 5 | 7 4 8 |
| 7 1 8 | 4 3 9 | 2 5 6 |
| 4 5 6 | 7 8 2 | 3 9 1 |
+-------+-------+-------+
| 5 6 3 | 2 7 4 | 1 8 9 |
| 9 2 4 | 3 1 8 | 5 6 7 |
| 1 8 7 | 9 5 6 | 4 2 3 |
+-------+-------+-------+
Quote:
Ruud: Without the easy starter and a lot more work
Para: i understand the non-symmetrical cage-pattern now, didn't notice the 77 in the first run
Afmob: Rating: It was a bit more difficult than V1 so I estimate rating about 1.25
Andrew: I'm impressed that Para managed to solve this puzzle by deliberately avoiding the 45 rule. However it did mean that he had to work a lot harder ...I agree with Afmob's rating of 1.25.
Walkthrough by Para:
Hi all

Here's a walk-through for A77V2. There was so many combination work in the beginning that i wanted to see if i could avoid the 45-test till the end. And i succeeded. So this walk-through doesn't contain a single 45-test.
At least i understand the non-symmetrical cage-pattern now, didn't notice the 77 in the first run.

Walk-through A77V2.

1. R34C1 = {19/28/37/46}: no 5

2. R34C9 = {39/48/57}: no 1,2,6

3. 21(3) at R4C6 = {489/579/678}: no 1,2,3

4. R7C12 = {29/38/47/56}: no 1

5. 27(4) at R8C4 = {3789/4689/5679}: no 1,2

6. R89C5 = {15/24}: no 3,6,7,8,9

7. 11(4) at R5C7 = {1235} -> locked for C7

8. R7C89 = {89} -> locked for R7 and N9
8a. R7C12 = {47/56}: no 2,3
8b. 13(3) at R7C4 = {247/256}: {157/346} blocked by R7C12: no 1,3; 2 locked for R7 and N8
8c. R89C5 = {15}: no 4 -> locked for C5 and N8
8d. 13(3) at R7C4 = {247} -> locked for R7 and N8
8e. R7C12 = {56} -> locked for R7 and N7

9. 12(3) at R8C1 = {129/147/237} = {1|3..},{7|9..}: {138} blocked by R7C3: no 8
9a. Killer Pair {13} in R7C3 + 12(3) at R8C1 -> locked for N7

10. 16(3) at R8C8 = {367/457} = {3|4..},{4|6..}: no 1,2; 7 locked for N9
10a. Killer Pair {46} in 16(3) at R8C8 + R9C7 -> locked for N9

11. 27(4) at R8C4(R89C4-R9C23) = {39}{78}/{68}{49}/{69}{48}: {38}{79} blocked by 12(3) at R8C1; 27(4) needs either a 3 in N8 or a 4 in R9

12. 20(3) at R8C6: combination analysis
12a. {1289} blocked by R9C7
12b. {69}[41] blocked by R7C7({13}) + 16(3) at R8C8({3|4..})
12c. {1568} blocked by R9C5
12d. {2459} blocked by R89C6
12e. {38}[45] blocked by 27(4) at R8C4(has both a 3 in N8 and a 4 in R9)
12f. 20(4) at R8C6 = {39}[62]/{68}[42]: R9C8 = 2

13. 27(4) at R8C4(R89C4-R9C23) = {39}{78}/{68}{49}: {69}{48} blocked by 20(4) at R8C6: R9C23 = {49/78} = {4|7..},{7|9..}
13a. 12(3) at R8C1 = {129/237}: {147} blocked by R9C23: no 4; 2 locked for N7
13b. Killer Pair {79} in 12(3) at R8C1 + R9C23 -> locked for N7

14. 1 in N9 locked for C7
14a. 2 in C7 locked for N6

15. 2 in N3 locked within 14(3) at R1C9: 14(3) = {239/248/257}={7/8/9..}: no 1,6
15a. R123C7 needs at least 2 of {789} because of C7(only other place is R4C7)
15b. R123C7 can have a maximum of 2 of {789} because of 14(3) at R1C9, so R123C7 contains 2 of {789} -> R4C7 = {789}
15c. Killer Triple {789} in R123C7 + 14(3) at R1C9 -> locked for N3
15d. Clean up: R4C9: no 3,4,5

16. 1 in N3 locked for C8
16a. 19(5) at R3C6 = {12349/12358/12367/12457/13456}: 1 locked in R3C68 -> locked for R3
16b. 19(5) at R3C2: 1 locked within R45C4 -> locked for C4 and N5
16c. Clean up: R4C1: no 9

17. 1 in N6 locked within 16(3) cage at R5C9: 16(3) = {169}: {178} blocked by R4C79: {169} -> locked for N6
17a. Naked Pair {78} in R4C79 -> locked for R4 and N6
17b. 4 in N6 locked for C8 and 19(5) at R3C6
17c. 9 in C7 locked for N3
17d. Clean up: 14(3) at R1C9 = {248/257}: no 3; R3C1: no 2,3; R3C9: no 3

18. Killer Pair {45} in 14(3) at R1C9 + R3C9 -> locked for N3
18a. R9C7 = 4(hidden); R8C3 = 4(hidden)
18b. 16(3) at R8C8 = {367} -> locked for N9
18c. R78C7 = [15]; R89C5 = [15]; R7C3 = 3; R9C1 = 1(hidden)
18d. R8C12 = {29}(last combo) -> locked for R8 and N7
18e. R9C23 = {78} -> locked for R9 and 27(4) at R8C4
18f. R8C6 = 8(hidden); R9C6 = 6; R89C4 = [39]; R9C9 = 3
18g. R56C7 = {23} -> locked for N6
18h. R45C8 = {45} -> locked for C8 and 19(5) at R3C6
18i. Naked Quad {6789} in R123C7 + R2C8 -> locked for N3
18j. Clean up: R3C1: no 9

19. 19(5) at R3C6 = [237]{45}/{1[6]3}{45}: no 8,9; R3C6: no 7

20. 21(3) at R4C6 = {4[8]9/5[7]9}: R45C6 = {49/59}: no 7; 9 locked for C6 and N5

21. 15(3) at R1C4 = {1248/1257/1347/1356/2346}: {1239} blocked by R3C6: no 9
21a. R3C5 = 9(hidden)
21b. 18(3) at R3C5 = 9[27]/{36}: no 4,8; R5C5: no 2

22. 17(3) at R6C4 = {278/368}: {458} blocked by R45C6; {467} blocked by R45C5: no 4,5; 8 locked for R6 and N5
22a. Naked Quint {23678} in R45C5 + R6C456 -> locked for N5
22b. Killer Pair {23} in 17(3) at R6C4 + R6C7 -> locked for R6

23. 4 in R6 locked for N4
23a. 5 in R6 locked for N4
23b. 4 in R6 locked within 16(3) at R5C1: 16(3) = [3]{49}/[7]{45}: no 1,2,6,8; R5C1: no 9; R6C12: no 7

24. 21(4) at R5C3 = [95/86]34: R5C3 = {89}; R6C3 = {56}
24a. 7 in R6 locked within 17(3) at R6C4: 17(3) = {278} -> locked for R6 and N5
24b. R56C7 = [23]; R6C9 = 1(hidden)
24c. R45C5 = {36} -> locked for C5

25. 13(3) at R4C2 = {139/238}: no 6,7; 3 locked for C2 and N4
25a. R5C1 = 7
25b. R6C12 = {45}(last combo within 16(3)) -> locked for N4
25c. R6C3 = 6; R6C8 = 9; R5C9 = 6; R7C89 = [89]; R8C89 = [67]
25d. R4C79 = [78]; R45C5 = [63]; R5C3 = 8; R34C1 = [82]
25e. R3C79 = [64]; R2C8 = 7; R4C2 = 3(hidden); R8C12 = [92]; R9C23 = [87]
25f. R45C6 = {59}(last combo within 21(3)) -> locked for C6 and N5
25g. R45C4 = {14} -> locked within C4

26. 25(4) at R1C6 = {1789} -> R1C68 = [71]
26a. R3C8 = 3; R3C2 = 7(hidden); R3C6 = 1(hidden)
26b. R67C6 = [24]; R2C6 = 3; R1C1 = 3(hidden)

27. 15(4) at R1C4 = {246}3 -> R1C4 = 6; R12C5 = {24} -> locked for C5 and N2
27a. R23C4 = [85]; R3C3 = 2; R12C7 = [89]; R6C45 = [78]; R7C45 = [27]

28. 18(3) at R1C1 = 3[96]: R1C2 = 9; R2C1 = 6

And the rest is naked singles.


greetings

Para
Walkthrough by Afmob:
Seems like Para is the only one up til now who made a walkthrough for V2, so I'd like to join him. I used Innies and Outies to crack this one.

A77 V2 Walkthrough:

1. N9
a) 17(2) = {89} locked for R7+N9
b) 16(3) = 7{36/45} -> 7 locked
c) 11(4) = {1235} locked for C7
d) Killer pair (46) locked in 16(3) + R9C7

2. R789
a) Innies R7 = 4(2) = {13} locked for R7
b) Killer pair (25) of 6(2) blocks {256} of 13(3)
c) 13(3) = {247} locked for R7+N8
d) 11(2) = {56} locked for N7
e) 6(2) = {15} locked for C5+N8
f) Innies R89 = 9(2) = [45/72/81]
g) 12(3) <> 8 because {138} blocked by R7C3 = (13)
h) Killer pair (13) locked in 12(3) + R7C3 for N7
i) 12(3) <> 4 because {147} blocked by Killer pair (47) of 27(4)

3. C6789
a) Outies C9 = 30(4) = {6789} locked for C8
b) 14(3): R12C9 <> 8,9 because R2C8 >= 6
c) Innies C6789 = 9(3) <> 7,8,9
d) Innies C6789 = 9(3) = 2{16/34} because R7C6 = (24) -> 2 locked for C6

4. R9+N9
a) 27(4) = 89{37/46} -> R9C6 <> 8,9
b) Killer pair (36) locked in 27(4) + R9C6 for N8
c) 27(4): R9C4 <> 6 because R9C7 = 4 would block {4689}
d) 20(4) = {1469/2369/2468/3458} because R9C67 = {34/36/46}
e) 20(4): R9C8 <> 3 because there is no combo with {346}
f) 20(4) <> {3458} because it's blocked by Killer pair (34) of 27(4)
-> 6 locked for R9
-> no 5 in 20(4)

5. C6
a) Killer pair (36) locked in Innies C6789 + R9C6

6. N47 !
a) Innies = 17(1+2): R4C1 <> 7,8,9 because R9C23 >= 11
b) Innies = 17(1+2): R4C1 <> 6 because R9C23 would be {47} -> not possible in 27(4)
c) 10(2): R3C1 <> 1,2,3,4
d) Innies N4 = 16(3): R56C3 <> 1,2 because R4C1 <= 4
e) Outies N4 = 15(1+2): R3C1 <> 9 because R78C3 <> 2,5 (6(2) impossible)
f) 10(2): R4C1 <> 1
g) Innies = 17(1+2): R4C1 <> 3 because R9C23 <> 5,6 (14(2) impossible)
h) 10(2): R3C1 <> 7
i) ! Outies N4 = 15(1+2): R8C3 <> 7 because R3C1 = (68) -> R78C3 = 7/9(2) = [18/34]

7. R89
a) Innies = 9(2): R8C7 <> 2
b) Hidden Single: R9C8 = 2 @ N9
c) 1 locked R78C7 for C7

8. C789
a) 2 locked in 14(3) for C9 -> 14(3) = 2{39/48/57}
b) 19(5) = {13456} -> R3C7 = 6
c) R3C1 = 8 -> R4C1 = 2
d) 1 locked in 16(3) @ C9(N6) = 1{69/78}
e) 20(4) = {2468} -> R9C7 = 4, R9C6 = 6, R8C6 = 8
f) 16(3) @ N9 = {367}, 3 locked for C9+N9
g) 12(2),14(3) <> 9, R4C9 <> 4

9. N47
a) Innies = 17(1+2): R9C23 = 15(2) = {78} locked for N7+R9 because R4C1 = 2
b) 12(3) = {129} -> R8C2 = 2, {19} locked for C1+N7
c) R7C3 = 3, R8C3 = 4, R7C7 = 1, R8C7 = 5
d) 27(4) = {3789} -> {39} locked for C4

10. C789
a) Naked triple (789) locked in R12C7+R2C8 for N3
b) Killer pair (45) locked in 14(3) + R3C9 for N3
c) 25(4) = 89{17/35} because R1C8 = (13) -> R1C6 <> 1,4; 8 locked for C7
d) 12(2): R4C9 <> 5
e) 16(3) @ N6 = {169} locked for N6 because R4C9 = (78) blocks {178}
f) 21(3) = {579} -> R4C7 = 7, {59} locked for C6+N5
g) 25(4) = {1789} -> R1C6 = 7, R1C8 = 1
h) 19(5) = {13456} -> R3C6 = 1

11. R123
a) 15(4) = {2346} locked for N2
b) R3C4 = 5, R2C4 = 8
c) 18(4) = 8{...} -> no 9
d) 19(5) = 5{...} -> no 9
e) 19(5) = {12457} because R3C3 = (27)
f) Hidden Single: R1C2 = 9 @ N1
g) R2C8 = 7
h) 1 locked in 18(4) @ N1 -> no 2
i) 18(4) must have 3 xor 4 and it's only possible @ R2C2 -> R2C2 = (34)
j) 18(4) must have 5 xor 6 and R1C3 = (56) -> R2C3 <> 5,6

12. C123
a) Killer pair (56) locked in 18(3) + R7C1 for C1
b) 7 locked in 16(3) @ C1 for N4 = 7{36/45}
c) Killer pair (56) locked in 16(3) + 21(4) for N4

13. C5
a) Hidden Single: R4C5 = 6 @ R4
b) 18(3) = {369} locked for C5 because R3C5 = (39)
c) 17(3) = {278} locked for R6+N5

14. Rest is singles.

Rating: It was a bit more difficult than V1 so I estimate rating about 1.25
Walkthrough by Andrew:
I finished this yesterday but have only just worked through Para's and Afmob's walkthroughs.

We all started pretty much the same way although sometimes finding different reasons for our steps; I think there must be one narrow part of the solving path using the 20(4) and 27(4) cages in R89 to make the first placement. Later innies of N47 seems to be another narrow part although Para must have found a different way that didn't specifically use that. Otherwise there was plenty of scope for different solving paths.

I'm impressed that Para managed to solve this puzzle by deliberately avoiding the 45 rule. However it did mean that he had to work a lot harder after the first placement than those of us who used the 45 rule.

I agree with Afmob's rating of 1.25. Para's route avoiding the 45 rule was probably an easy 1.5.

Here is my walkthrough for A77V2.

Prelims

a) R34C1 = {19/28/37/46}, no 5
b) R34C9 = {39/48/57}, no 1,2,6
c) R7C12 = {29/38/47/56}, no 1
d) R7C89 = {89}, locked for R7 and N9, clean-up: no 2,3 in R7C12
e) R89C5 = {15/24}
f) 21(3) cage at R4C6 = {489/579/678}, no 1,2,3
g) 11(4) cage at R5C7 = {1235}, locked for C7
h) 27(4) cage at R8C4 = 9{378/468/567}, no 1,2, CPE no 9 in R9C6
i) 19(5) cage at R3C2 must contain 1
j) 19(5) cage at R3C6 must contain 1

1. 45 rule on R89 2 innies R8C37 = 9 = [45/63/72/81]

2. 45 rule on R7 2 innies R7C37 = 4 = {13}, locked for R7
2a. 45 rule on R789 4 outies R56C37 = 19, max R56C7 = 8 -> min R56C3 = 11, no 1

3. 2 in R7 locked in R7C456, locked for N8, clean-up: no 4 in R89C5
3a. R7C456 = 2{47/56}

4. Naked pair {15} in R89C5, locked for C5 and N8, clean-up: no 6 in R7C456 (step 3a)

5. Naked triple {247} in R7C456, locked for R7 and N8

6. Naked pair {56} in R7C12, locked for N7, clean-up: no 3 in R8C7 (step 1)

7. 27(4) cage at R8C4 = 89{37/46}, CPE no 8 in R9C6

8. 2 in N7 locked in 12(3) cage = 2{19/37}, no 4,8
8a. Killer pair 1,3 in 12(3) cage and R7C3, locked for N7
8b. 8 in R9 locked in R9C234 -> no 8 in R8C4

9. 16(3) cage in N9 = {367/457} = 7{36/45}, no 1,2, 7 locked for N9
9a. Killer pair 4,6 in 16(3) cage and R9C7, locked for N9

10. 20(4) cage at R8C6 = {1469/2369/2468/3458} (cannot be {1289} because 8,9 only in R8C6, cannot be {1568/2459} because 1,2,5 only in R9C8)
10a. 8,9 only in R8C6 -> R8C6 = {89}
10b. 3 of {2369/3458} must be in R9C6 -> no 3 in R9C8
10c. R45C6 = {89} clashes with R8C6 -> no 4 in R4C7

11. 27(4) cage at R8C4 (step 7) = 89{37/46}
11a. 6 in {4689} must be in R8C4 (R9C24 or R9C34 = [46] clash with R9C7) -> no 6 in R9C4

12. 45 rule on C9 4 outies R2678C8 = 30 = {6789}, locked for C8
12a. Min R2C8 = 6 -> max R12C9 = 8, no 8,9

13. 45 rule on C6789 3 innies R267C6 = 9 = {126/234} (cannot be {135} because R7C6 only contains 2,4) = 2{16/34}, no 5,7,8,9, 2 locked for C6
13a. Killer pair 3,6 in R26C6 and R9C6, locked for C6
13b. Max R6C6 = 6 -> min R6C45 = 11, no 1 in R6C4

14. 25(4) cage at R1C6 = {1789/2689/3589/3679/4579/4678}
14a. 1 of {1789} must be in R1C8 -> no 1 in R1C6

15. 19(5) cage at R3C6 = {12349/12358/12367/12457/13456}
15a. 8 of {12358} must be in R3C7 -> no 8 in R3C6

16. 45 rule on N47 3 innies R4C1 + R9C23 = 17
16a. R9C23 = {4789} = 13, 15 or 16 (cannot be 11 because {47} cannot be in 27(4) cage (step 11), cannot be 12 because no 5 in R4C1) -> R4C1 = {124}, R3C1 = {689}
16b. R9C23 = {49/78/79}, R89C4 = [38/39/68/93] (step 11)
16c. R89C6 cannot be [83] -> 20(4) cage at R8C6 cannot be {3458}, no 5 in R9C8

17. 45 rule on N7 4 innies R78C3 + R9C23 = 22
17a. R9C23 = 13, 15 or 16 (step 16a) -> R78C3 = 6, 7 or 9
17b. R78C3 = [18/34] (cannot total 6), clean-up: no 2 in R8C7 (step 1)
17c. R9C23 = {49/78}, R89C4 = [39/68/93]

18. R9C8 = 2 (hidden single in N9)
18a. 1 in N9 locked in R78C7, locked for C7
18b. 2 in C7 locked in R56C7, locked for N6

19. 45 rule on C1234 3 innies R167C4 = 15 = {249/258/267/348/357/456} (cannot be {159/168} because R7C4 only contains 2,4,7), no 1

20. 19(5) cage at R3C6 (step 15) = {13456} (only remaining combination) -> R3C7 = 6, R9C7 = 4, clean-up: no 4 in R4C1, no 9 in R9C23 (step 17c), no 5 in R89C9 (step 9)
20a. 3 in 19(5) cage locked in R345C8, locked for C8
20b. 20(4) cage at R8C6 (step 10) = {2468} -> R89C6 = [86], clean-up: no 1 in R26C6 (step 13)

21. R8C7 = 5 (hidden single in N9) -> R89C5 = [15], R8C3 = 4
21a. R7C7 = 1 (hidden single in N9), R7C3 = 3, clean-up: no 7 in 12(3) cage (step 8)

22. R9C1 = 1 (hidden single in R9) -> R4C1 = 2, R3C1 = 8, R8C12 = [92], R89C4 = [39], clean-up: no 4 in R4C9

23. R9C9 = 3 (hidden single in R9), clean-up: no 9 in R34C9

24. R78C3 = 7 -> R56C3 = 14 = {59/68}, no 7

25. R3C6 = 1 (hidden single in C6)
25a. R1C8 = 1 (hidden single in C8), R3C8 = 3 (hidden single in N3)
25b. 25(4) cage at R1C6 (step 14) = {1789} (only remaining combination), no 4,5
25c. 8 locked in R12C7, locked for C7 and N3

26. Naked triple {789} in R12C7 and R2C8, locked for N3, clean-up: no 5 in R4C9

27. Naked triple {245} in R123C9, locked for C9

28. 2 in N3 locked in 14(3) cage = {257} (only remaining combination) -> R2C8 = 7, R8C89 = [67], R4C9 = 8, R3C9 = 4, R7C89 = [89], R6C8 = 9, R4C7 = 7, clean-up: no 5 in R5C3 (step 24)

29. R1C6 = 7 (hidden single in C6)

30. Naked triple {234} in R267C6, locked for C6
30a. Naked pair {59}, locked for N5

31. 5 in R6 locked in R6C123, locked for N4

32. 5,7 in R3 locked in R3C234 for 19(5) cage = {12457} (only remaining combination), no 7 in R5C4

33. Naked triple {257} in R3C234, locked for R3 and 19(5) cage -> R3C5 = 9

34. Naked pair {14} in R45C4, locked for C4 and N5

35. Naked pair {23} in R6C67, locked for R6

36. 4 in R6 locked in R6C12, locked for N4
36a. 16(3) cage = {457} (only remaining combination) -> R5C1 = 7
36b. Naked pair {45} in R6C12, locked for R6, clean-up: no 9 in R5C3 (step 24)

37. Naked pair {68} in R56C3, locked for C3 and N4 -> R9C23 = [87]

38. R3C2 = 7 (hidden single in R3)

39. R3C5 = 9 -> R45C5 = 9 = {36}
39a. Naked pair {36} in R45C5, locked for C5 and N5 -> R6C6 = 2, R27C6 = [34], R56C7 = [23]

40. 4 in C5 locked in R12C5, 15(4) cage at R1C4 = {2346} (only remaining combination) -> R1C4 = 6
40a. Naked pair {24} in R12C5, locked for C5 and N2 -> R7C45 = [27], R6C45 = [78], R56C3 = [86], R56C9 = [61], R45C5 = [63], R3C34 = [25], R2C4 = 8, R12C7 = [89]

41. R4C2 = 3 (hidden single in R4), R1C1 = 3 (hidden single in R1)
41a. R1C2 + R2C1 = 15 = [96]

and the rest is naked singles
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Ed
PostPosted: Tue Jul 15, 2008 8:23 am 
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Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Maverick 2 (aka M2) by mhparker (Nov 07)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:4864:4864:4864:4611:4611:3077:3077:6151:6151:4617:4864:4611:4611:2061:4366:4366:4366:6151:4617:2835:2835:5141:2061:1303:4366:4121:6151:4617:4380:5141:5141:2061:1303:8481:4121:6151:4380:4380:8481:8481:8481:8481:8481:3627:3627:6957:1326:8481:2864:4401:3378:3378:3627:4661:6957:1326:5432:2864:4401:3378:2876:2876:4661:6957:5432:5432:5432:4401:5700:5700:4678:4661:6957:6957:2634:2634:5700:5700:4678:4678:4678:
Solution: 
+-------+-------+-------+
| 2 9 7 | 1 6 8 | 4 5 3 |
| 8 1 4 | 7 3 5 | 9 2 6 |
| 3 6 5 | 9 4 2 | 1 7 8 |
+-------+-------+-------+
| 7 4 6 | 5 1 3 | 8 9 2 |
| 5 8 2 | 6 9 4 | 3 1 7 |
| 9 3 1 | 8 2 7 | 5 6 4 |
+-------+-------+-------+
| 6 2 9 | 3 8 1 | 7 4 5 |
| 1 5 3 | 4 7 6 | 2 8 9 |
| 4 7 8 | 2 5 9 | 6 3 1 |
+-------+-------+-------+
Quote:
mhparker, lead-in: This one lives up to its name by ruffling JSudoku's and SudokuSolver's feathers somewhat (in the nicest possible way, of course ;) ). And yet the puzzle is solvable purely by logic. (Est. rating: 1.75)
Afmob: What a difficult killer! It reminded me of the recent A78 killer since the solving path was so long, and I was not able to find a shortcut like in M1. Rating: A tough 1.75. It was more difficult than M1 but the Brick Wall (which is my reference for the hardest puzzle I've solved so far) is still a in a different league
Para: I agree with the 1.75 rating. It was a tough one, with some interesting moves that help settle down the puzzle.
mhparker on A86 thread: there are 2 critical moves .... that are difficult to spot. .. which also had an extremely narrow initial solving path, except the M2 remained difficult..
Andrew (in 2012): I tried this puzzle for the first time this year. I'd found Maverick 1 very difficult, so didn't try Mav 2 when it was posted.
Belated thanks to Mike for a challenging puzzle!
The first key breakthrough step was fairly easy to spot but difficult to analyse and convince myself that it was correct. However if I'd spotted Afmob's step 7a, Para's step 8c, then I wouldn't have needed my interesting step. Later each of us used different ways to reduce R67C4 to {38}; the important final breakthrough.
Rating: 1.75.
2022 forum Revisit here
Walkthrough by Afmob:
What a difficult killer! It reminded me of the recent A78 killer since the solving path was so long, the massive use of Innies+Outies difference and I was not able to find a shortcut like in M1.

M2 Walkthrough:

1. C789
a) 16(2) = {79} locked for C8
b) Innies+Outies N9: 2 = R6C9 - R8C7
-> R8C7 <> 8,9; R6C9 <> 1,2
c) Innies+Outies C89: 11 = R79C7 - R2C8
-> R79C7 <> 1,2; R2C8 <> 8
d) 11(2): R7C7 <> 4

2. C45
a) 8(3) = 1{25/34} -> 1 locked
b) Innies C5 = 20(3) -> no 2
c) 17(3): Killer pairs (35,45) of 8(3) blocks {359/458} -> no 5
d) 20(3): R3C4 <> 4 because R4C8 = (79) blocks {479}

3. R6789
a) Innies = 7(2) <> 7,8,9

4. R1234+C1
a) Innies R1234 = 12(2) <> 1,2,6
b) Innies+Outies C1: R15C1 = R9C2
-> R15C1 <> 9; R9C2 <> 1,2

5. R456
a) 33(7) = 126{3489/3579/4578} -> {126} locked between R5 and N4 -> R5C12 <> 1,2,6
b) 17(3) @ N4 = 5{39/48} -> 5 locked for N4
c) Innies R1234 = 12(2): R4C7 <> 5
d) Innies R6789 = 7(2): R6C8 <> 2

6. C123
a) Innies+Outies C1: R15C1 = R9C2
-> R9C2 <> 3 and R1C1 <> 7,8 because R5C1 >= 3
b) Innies+Outies N1: 3 = R4C1 - R2C3
-> R4C1 <> 1,2,3; R2C3 <> 2,7,8,9

7. R456!
a) ! R4C7 <> 7 since it sees all 7's in R5
b) Innies R1234 = 12(2) = {39/48}
c) 5 locked in 17(3) @ N4 for R5
d) 33(7) = {1234689}
e) Hidden Single: R5C9 = 7 @ R5
f) R4C8 = 9, R3C8 = 7
g) 14(3) = 7{16/25/34}
h) Innies R1234 = 12(2) = {48} locked for R4
i) 20(3) must have 8 or 9 and they're only possible @ R3C4 -> R3C4 = (89)
j) 20(3) = 5{69/78} -> R4C4 = 5

8. R456
a) Naked pair (67) locked in R4C13 for R4+N4
b) 17(3) @ N4 = {458} locked for N4 because R4C2 = (48)
c) Both 5(2): R3C6 <> 1, R7C2 <> 1
d) 4,6 locked in 33(7) between R5 and N6 -> R5C8 <> 4,6
e) 14(3): R6C8 <> 1,3

9. N1
a) Innies+Outies N1: 3 = R4C1 - R2C3, R4C1 = (67)
-> R2C3 = (34)
b) 11(2) <> 4

10. R67
a) 11(2) <> 6
b) 18(3) <> 2

11. C1+R1
a) Innies+Outies C1: R15C1 = R9C2
-> R9C2 <> 4 and R1C1 <> 6 because R5C1 >= 4
b) 12(2): R1C6 <> 5

12. C789
a) Innies+Outies N9: 2 = R6C9 - R8C7
-> R8C7 <> 5,7
b) Outies N3 = 15(2+1): R2C6 <> 1,2 because R1C6+R4C9 <= 12
c) Innies+Outies C9: 4 = R1C8 - R9C9
-> R1C8 = (568); R9C9 = (124)
d) 24(5) <> {12489} because R9C9 = (124)
e) 24(5) <> {23469} because it's blocked by Killer pair (49) of 18(3)
f) 24(5) = 56{139/148/238} -> 5,6 locked for N3
g) 12(2) = {39/48}
h) Outies N3 = 15(2+1): R2C6 <> 7 because R1C6+R4C9 <> 5,6,7

13. N2
a) 7 locked in 18(4) = 7{146/236/245} because R2C3 = (34)
b) 18(4) must have 3 xor 4 and R2C3 = (34) -> R1C45+R2C4 <> 3,4

14. C345 !
a) Innies C5 = 20(3) <> 3 because R1C5 = (567)
b) Hidden Killer pair (23) in 8(3) + 17(3) and none of them can have both -> 17(3) <> 4
c) ! Innies+Outies C1234: -3 = R1C5 - (R5C34+R6C3); R1C5 = (567)
-> R5C34+R6C3 = 8/9/10(3) -> no 8,9
-> R5C4 <> 1,2,3 since R5C34+R6C3 would be 6(3)

15. C1234
a) Hidden Single: R6C1 = 9 @ N4
b) 18(3) = {378/468/567}
c) Innies+Outies C1: R15C1 = R9C2
-> R5C1 <> 8, R1C1 <> 4,5 because R9C2 <= 8
d) 17(3) = {458} -> 8 locked for C2
e) 11(2) @ C4: R7C4 <> 2
f) 11(2) @ N1: R3C3 <> 3
g) Outies N7 = 9(2+1) -> R89C4 <> 8,9
h) 10(2): R9C3 <> 1,2
i) (89) only possible in R367C4 for C4 -> 11(2) @ C4 must have 8 xor 9 -> 11(2) <> 4,7

16. C789
a) Innies+Outies C89: 11 = R79C7 - R2C8; R2C8 = (1234)
-> 7 locked in R79C7 = 12/13/14/15(2) -> no 3,4,9
-> R2C8 <> 3 since 14(2) with 7 is impossible
b) 11(2): R7C8 <> 2,8
c) 9 locked in 18(3) = 9{18/36/45} for C9
d) 24(5) = 568{14/23} -> 8 locked for N3
e) 12(2): R1C6 <> 4
f) 24(5): R123C9 <> 1 because R4C9 <= 3
g) 1 locked in 17(4) @ N3; 17(4) = 1{259/268/349/358}
h) 17(4) <> 6,8 because (568) only possible @ R2C6
i) 18(3): R78C9 <> 8 because R6C9 <> 1,9

17. C345 !
a) 6,7 locked in 18(4) = 67{14/23} -> no 5
b) Killer pair (67) locked in 17(3) + R1C5 for C5
c) ! Innies+Outies C1234: -3 = R1C5 - (R5C34+R6C3); R1C5 = (67)
-> R5C34+R6C3 = 9/10(3) = {126/234/136}
-> All 3 combos force R12C4 <> 6 because either R1C5 = 6 or R5C4 = 6
d) 18(4) = 67{14/23} -> R1C5 = 6; 7 locked for C4
e) Innies C5 = 20(3) = [695] -> R5C5 = 9, R9C5 = 5
f) 8(3) = {134} locked for C5, 4 locked for N2
g) 10(2): R9C3 <> 3

18. C67
a) 5(2) = {23} locked for C6
b) 12(2): R1C7 <> 9
c) 17(4) = {1259} because R1C7 = (34) blocks {1349}
-> R2C6 = 5, {129} locked for N3

19. C789
a) 6 locked in 24(5) for C9
b) 18(3) = 9{18/45}
c) 3 locked in 24(5) @ C9 -> 24(5) = {23568}
d) Hidden Single: R4C5 = 1 @ R4, R1C7 = 4 @ N3 -> R1C6 = 8
e) 24(5) = {23568} -> R1C8 = 5, R1C9 = 3, R4C9 = 2, 8 locked for C9
f) 18(3) = {459} locked for C9

20. R3+N1
a) 1 locked in 19(4) = 19{27/36}, 9 locked for N1
b) 11(2) = [38/56/65]
c) 19(4) = {1279} locked because {1369} blocked by Killer pair (36) of 11(2)
d) Killer pair (68) locked in 11(2) + R3C9 for R3

21. R5+N4
a) Naked pair (46) locked in R5C46 for R5
b) R5C1 = 5, R5C2 = 8, R4C2 = 4, R4C7 = 8, R4C6 = 3 -> R3C6 = 2

22. R9
a) Naked pair (67) locked in R9C27
b) R9C9 = 1
c) 10(2) = [82] -> R9C3 = 8, R9C4 = 2
d) Hidden Single: R9C6 = 9
e) 22(4) = {2569} -> R8C6 = 6, R8C7 = 2
f) 18(4) = 16{38/47} -> R9C7 = 6

23. Rest is singles.

Rating: A tough 1.75. It was more difficult than M1 but the Brick Wall (which is my reference for the hardest puzzle I've solved so far) is still a in a different league. I guess now I would rate M1 with a 1.5
Walkthrough by Para:
Hi all

Just finished this. I agree with the 1.75 rating. It was a tough one, with some interesting moves that help settle down the puzzle. A lot of tough combination work till step 23, which breaks it open completely.

Walk-through Maverick 2

1. R1C67 = {39/48/57}: no 1,2,6

2. 8(3) at R2C5 = {125/134}: no 6,7,8,9; 1 locked for C5

3. R3C23, R67C4 and R7C78 = {29/38/47/56}: no 1

4. 20(3) at R3C4 = {389/479/569/578}: no 1,2

5. R34C6 and R67C2 = {14/23}: no 5,6,7,8,9

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

7. R34C8 = {79} -> locked for C8
7a. Clean up: R7C7: no 2,4

8. 45 on R1234: 2 innies: R4C27 = 12 = {39/48/57}: no 1,2,6
8a. 33(7) at R4C7 = {1234689/1235679/124578}: 1,2,6 locked within cage -> pointing: R5C12: no 1,2,6
8b. 17(3) at R4C2 = {359/458}: no 7; 5 locked for N4
8c. 7 in R5 locked within R5C345679 -> pointing: R4C7: no 7
8d. Clean up: R4C27: no 5

9. 5 in N4 locked for R5
9a. 33(7) at R4C7 = {1234689}: no 7
9b. R5C9 = 7(hidden); R34C8 = [79]
9c. R4C27 = {48} -> locked for R4
9d. 17(3) at R4C2 = {458} -> locked for N4
9e. 4 locked in 33(7) at R4C7: pointing -> R5C8: no 4
9f. 9 in R5 locked for 33(7) at R4C7
9g. 14(3) at R5C8 = 7{16}/[25/34]: no 8; R6C8: no 2,3
9h. Clean up: R3C6: no 1; R7C2: no 1; R3C23: no 4; R1C6: no 5

10. 20(3) at R3C4 = [965/875]: R3C4 = {89}; R4C3 = {67}; R4C4 = 5
10a. Clean up: R67C4: no 6

11. 45 on N1: 1 innie and 1 outie: R2C3 + 3 = R4C1: R4C1 = {67}; R2C3 = {34}
11a. Naked Pair {67} in R4C13 -> locked for R4 and N4

12. 45 on R6789: 2 innies: R6C38 = 7 = [16/25/34]
12a. Clean up: R5C8: no 6

13. 18(3) at R2C1 = {29}[7]/{38}[7]/{48}[6]/{56}[7]/[756]: {39}[6] blocked by step 11: no 1
13a. 1 in N1 locked within 19(4) cage at R1C1 -> 19(4) = {1279/1369/1378/1459/1468/1567}

14. 45 on N3: 3 outies: R12C6 + R4C9 = 15 = [95][1]/[86][1]/{49}[2]/[85][2]/[76][2]/{39}[3]/{48}[3]/[75][3]: R2C6: no 1,2,7

15. 45 on C5: 3 innies: R159C5 = 20 = {389/479/569/578}: no 2

16. 45 on N9: 1 innie and 1 outie: R6C9 = R8C7 + 2: R6C9: no 1,2; R8C7: no 5,7,8,9

17. 45 on C9: 1 innie and 1 outie: R1C8 = R9C9 + 4: R1C8 = {568}; R9C9: {124}

18. 24(5) at R1C8 = [6]{1359}/[6]{1458}/[5]{2368}/[8]{2356}: [8]{1249}/[8]{1456}/[5]{1369}/[5]{1468}/[6]{2349} blocked by step 17: 5,6 locked for N3
18a. Clean up: R1C6: no 7
18b. R12C6 = [95/86/85]/{49/39/48} = {8|9..}
18c. Killer Pair {89} in R12C6 + R3C4 -> locked for N2

19. 7 in N2 locked within 18(4) at R1C4 -> 18(4) = {1467/2367/2457}: {34} in R2C3 -> R1C45 + R2C4: no 3,4; R12C4 = {6|7..}

20. 45 on C1234: 1 outie and 3 innies: R1C5 + 3 = R5C34 + R6C3: Max R5C34 + R6C3 = 10: no 8,9; Min R5C34 + R6C3 = 8: R5C4: no 1,2,3
20a. R6C1 = 9(hidden)
20b. R67C4 = [29]/{38}: {47} blocked by R12C4 + R5C4: no 4,7; R7C4: no 2
20c. Killer Pair {89} in R3C4 + R67C4 -> locked for C4
20d. Clean up: R9C3: no 1,2

21. 18(3) at R6C9 = [8]{19}/[3]{69}/[6]{39}/[4]{59}/[5]{49}/[4]{68}: [8]{46}/[6]{48} blocked by step 16: no 2

22. 45 on C1234: R1C5 + 3 = R56C3 + R5C4: [5]-{13}[4]/[6]-{12}[6]/[6]-{23}[4]/[7]-{13}[6]
22a. 18(4) at R1C4 (R1C5-R12C4-R2C3) = [7]{16}[4]/[6]{17}[4]/[6]{27}[3]/[5]{27}[4]:[7]{26}[3] blocked by step 22: R12C4 = {16/17/27} = {1|7..}

23. 45 on N7: 3 outies: R6C2 + R89C4 = 9 = [1]{26}/[2]{16}/[2]{34}/[3]{24}: [1]{17} blocked by R12C4: no 7; 2 locked within outies: R6C4: no 2
23a. 7 in C4 locked within R12C4 for N2: R12C4 = {17/27}: no 6
23b. Clean up: R9C3: no 3; R7C4: no 9
23c. R67C4 = {38} -> locked for C4
23d. R3C4 = 9; R4C13 = [76]; R2C3 = 4(step 11)

24. 45 on C5: 3 innies: R159C5 = [587]/[5]{69}/[695]: no 3,4; R9C5: no 8; 5 locked for C5
24a. 8(3) at R2C5 = {1[4]3} -> locked for C5; R3C5 = 4
24b. R34C6 = {23} -> locked for C6
24c. R1C67 = [84]; R4C27 = [48]; R7C4 = 3(hidden); R6C4 = 8; R67C2 = [32]
24d. R159C5 = {569} -> locked for C5
24e. R56C3 = {12} -> locked for C3 and 33(7) at R4C7
24f. R1C58 = {56} -> locked for R1
24g. Clean up: R3C2: no 5; R3C3: no 8; R6C8: no 4(step 12); R5C8: no 3; R8C7: no 6(step 12)

25. 45 on N7: 2 outies: R89C4 = 6 = {24} -> locked for C4 and N8
25a. R5C4567 = [6943]; R3C6 = 2(hidden); R4C56 = [13]; R4C9 = 2; R56C8 = [16]; R1C8 = 5

There are loads of singles left but this will get it to all singles.
26. R7C78 = [74](last combo)

And this will leave you all singles.

greetings

Para

ps. This is the first puzzle i have ever seen that SumoCue makes more progress than Sudoku Solver. This is mostly because two properties of SumoCue seems to be missing from Sudoku Solver
Walkthrough by Andrew (in 2012):
I tried this puzzle for the first time this year. I'd found Maverick 1 very difficult, so didn't try Mav 2 when it was posted. Also I might have been put off by comments that I'd given too high a rating for my walkthrough for Mav 1.

Prelims

a) R1C67 = {39/48/57}, no 1,2,3
b) R3C23 = {29/38/47/56}, no 1
c) R34C6 = {14/23}
d) R34C8 = {79}
e) R67C2 = {14/23}
f) R67C4 = {29/38/47/56}, no 1
g) R7C78 = {29/38/47/56}, no 1
h) R9C34 = {19/28/37/46}, no 5
1) 8(3) cage at R2C5 = {125/134}
j) 20(3) cage at R3C4 = {389/479/569/578}, no 1,2

Steps resulting from Prelims
1. 8(3) cage at R2C5 = {125/134}, 1 locked for C5
1a. Naked pair {79} in R34C8, locked for C8, clean-up: no 2,4 in R7C7

2. 17(3) cage at R6C5 = {269/278/368/467} (cannot be {359/458} which clash with 8(3) cage at R2C5), no 5

3. 45 rule on C5 3 innies R159C5 = 20 = {389/479/569/578}, no 2

4. 45 rule on R1234 2 innies R4C27 = 12 = {39/48/57}, no 1,2,6

5. 45 rule on R6789 2 innies R6C38 = 7 = {16/25/34}, no 7,8,9

6. 20(3) cage at R3C4 = {389/569/578} (cannot be {479} because 4{79} clashes with R4C8 and 7{49}/9{47} clash with R4C27 + R4C8, killer ALS block), no 4
6a. 3 of {389} must be in R4C34 (R4C34 cannot be {89} which clashes with R4C278) -> no 3 in R3C4

7. 33(7) cage at R4C7 = {1234689/1235679/1245678}, CPE no 1,2,6 in R5C12

8. 45 rule on N1 1 outie R4C1 = 1 innie R2C3 + 3, no 7,8,9 in R2C3, no 1,2,3 in R4C1

9. 45 rule on N9 2 outies R6C9 = 1 innie R8C7 + 2, no 1,2 in R6C9, no 8,9 in R8C7

10. 13(3) cage at R6C6 = {139/148/157/238/247/256/346}
10a. 9 of {139} must be in R67C6 (R67C6 cannot be {13} which clashes with R34C6) -> no 9 in R6C7

11. 17(3) cage at R4C2 = {359/458}, no 7, 5 locked for N4, clean-up: no 2 in R2C3 (step 8), no 5 in R4C7 (step 4), no 2 in R6C8 (step 5)

12. 20(3) cage at R3C4 (step 6) = {389/569/578}
12a. 5 of {578} must be in R4C4 (R4C34 cannot be {78} which clashes with R4C27 + R4C8, killer ALS block) -> no 7 in R4C4

13. 45 rule on C1 2 innies R15C1 = 1 outie R9C2
13a. Min R15C1 = 4 -> min R9C2 = 4
13b. Max R15C1 = 9, no 7,8,9 in R1C1, no 9 in R5C1

14. 45 rule on C89 2 outies R79C7 = 1 innie R2C8 + 11
14a. Min R79C7 = 12, no 1,2 in R9C7
14b. Max R79C7 = 17 -> max R2C8 = 6

15. 33(7) cage at R4C7 = {1234689/1235679/1245678}, R6C38 (step 5) = {16/25/34}
15a. 14(3) cage at R5C8 = {167/257/347} (cannot be {149/158/239/248/356} which clash with 33(7) cage because R5C89 “see” all of 33(7) cage except for R6C3 and R6C38 are linked as a hidden cage; the three remaining combinations remain valid because of R6C38) , no 8,9 -> R5C9 = 7, R34C8 = [79], clean-up: no 5 in R1C6, no 6 in R2C3 (step 8), no 4 in R3C23, no 3,5 in R4C2, no 3 in R4C7 (both step 4), no 5,7 in R8C7 (step 9)
15b. 2 of {257} must be in R5C8 -> no 5 in R5C8
[Maybe there’s some direct way to prove that R6C38 must equal R6C8 plus one of R5C89? If there is, I didn’t spot it.
After step 11, I’d missed 7 in R5 only in R5C345679, CPE no 7 in R4C7 which Afmob and Para both used. In a way I’m glad that I missed that as then I wouldn’t have found my interesting step 15a. ;-)]

16. Naked pair {48} in R4C27, locked for R4, clean-up: no 1,5 in R2C3 (step 8), no 1 in R3C6

17. 20(3) cage at R3C4 (step 6) = {569/578} (cannot be {389} because 8,9 only in R3C4), no 3
17a. 8,9 only in R3C4 -> R3C4 = {89}
17b. Naked pair {67} in R4C13, locked for R4 and N4 -> R4C4 = 5, clean-up: no 6 in R67C4, no 1 in R6C8 (step 5), no 6 in R5C8 (step 15a)

18. 33(7) cage at R4C7 = {1234689} (only remaining combination), no 5

19. 45 rule on C9 1 outie R1C8 = 1 remaining innie R9C9 + 4, R1C8 = {568}, R9C9 = {124}

20. 17(3) cage at R4C2 (step 11) = {458} (only remaining combination, cannot be {359} because R4C2 only contains 4,8), locked for N4, clean-up: no 3 in R6C8 (step 9), no 4 in R5C8 (step 15a), no 1 in R7C2

21. 18(3) cage at R2C1 = {279/369/378/468/567} (cannot be {189/459} because R4C1 only contains 6,7), no 1

22. 18(3) cage at R6C9 = {189/369/459/468}, no 2

23. 45 rule on N3 3(2+1) remaining outies R12C6 + R4C9 = 15
23a. Max R4C9 = 3 -> min R12C6 = 12, no 1,2 in R2C6

24. R1C8 = R9C9 + 4 (step 19)
24a. 24(5) cage at R1C8 = {13569/14568/23568} (cannot be {12489/23469} which give innie-outie difference clash with R1C8 + R9C9), 5,6 locked for N3, clean-up: no 7 in R1C6

25. R12C6 + R4C9 = 15 (step 23)
25a. R4C9 = {123} -> R12C6 = 12,13,14 cannot be {57/67} because 5,6,7 only in R2C6 -> no 7 in R2C6

26. 7 in N2 only in 18(4) cage at R1C4 = {1467/2367/2457} (cannot be {1278} because R2C3 only contains 3,4), no 8,9
26a. R2C3 = {34} -> no 3,4 in R1C45 + R2C4

27. R159C5 (step 3) = {479/569/578} (cannot be {389} because R1C5 only contains 5,6,7), no 3
27a. 8 of {578} must be in R5C5 -> no 8 in R9C5

28. 17(3) cage at R6C5 (step 2) = {269/278/368} (cannot be {467} which clashes with R159C5), no 4

29. 45 rule on C1234 3 innies R56C3 + R5C4 = 1 outie R1C5 + 3
29a. R1C5 = {567} -> R56C3 + R5C4 = 8,9,10, no 8,9 in R5C34
29b. R56C3 = {123} -> R5C4 = {46} (only way to make total greater than 6)

30. R6C1 = 9 (hidden single in N4), clean-up: no 2 in R23C1 (step 21), no 2 in R7C4

31. R15C1 = R9C2 (step 13)
31a. Min R15C1 = 5 -> min R9C2 = 5
31b. Max R9C2 = 8 -> max R15C1 = 8, no 8 in R5C1
31c. 8 in N4 only in R45C2, locked for C2, clean-up: no 3 in R3C3
31d. 5 in N4 only in R5C12
5 in R5C1 => min R15C1 = 6 or 5 in R5C2 => no 5 in R9C2
-> min R9C2 = 6
31e. R9C2 = {67}, min R5C1 = 4 -> max R1C1 = 3

32. 45 rule on N9 3 innies R78C9 + R8C7 = 16 = {169/259/268/349} (cannot be {358} = {58}3 because 18(3) cage at R6C9 cannot be 5{58})
32a. R7C78 = {38/56}/[74] (cannot be [92] which clashes with R78C9 + R8C7), no 2,9

33. 45 rule on N7 3(1+2) remaining outies R6C2 + R89C4 = 9 -> max R89C4 = 8, no 8,9 in R89C4, clean-up: no 1,2 in R9C3

34. Hidden killer pair 8,9 in R3C4 and R67C4, R3C4 = {89} -> R67C4 must contain one of 8,9 -> R67C4 = [29/38/83], no 4,7

35. 7 in N9 only in R7C78 = [74] or in 18(4) cage at R8C8 -> if 18(4) cage contains 4 it must also contain 7 (locking cages)
35a. 18(4) cage = {1278/1359/1368/1467/2358/2457} (cannot be {1458/2349/3456} which contain 4 but not 7, cannot be {2367} which clashes with R7C78, cannot be {1269} which clashes with R78C9 + R8C7)
35b. R1C8 = R9C9 + 4 (step 19)
35c. 18(4) cage = {1278/1368/1467/2358/2457} (cannot be {1359} which gives innie-outie difference clash with R1C8 + R9C9), no 9
35d. 7 of {1467/2457} must be in R9C7 -> no 4 in R9C7

36. 9 in N9 only in R78C9, locked for C9
36a. R78C9 + R8C7 (step 32) contains 9 = {169/259/349}, no 8

37. 24(5) cage at R1C8 (step 24a) = {14568/23568}, 8 locked for N3, clean-up: no 4 in R1C6

38. 17(4) cage at R2C6 = {1259/1349/2348} (cannot be {1268/1358/2456} because 5,6,8 only in R2C6), no 6

39. 6 in N2 only in 18(4) cage at R1C4 (step 26) = {1467/2367}, no 5

40. R159C5 (step 27) = {479/569/578}
40a. R1C5 = {67} -> no 6,7 in R59C5

41. R12C6 + R4C9 = 15 (step 23)
41a. R4C9 = {123} -> R12C6 = 12,13,14 = {39/48/49/58/59}
41b. 4,5 of {48/58} must be in R2C6 -> no 8 in R2C6

42. 17(4) cage at R2C6 (step 38) = {1259/1349}, 1 locked for N3

43. 13(3) cage at R6C6 = {148/157/238/247/256/346} (cannot be {139} which clashes with R6C23, ALS block), no 9

44. 27(5) cage at R6C1 contains 9 = {12789/13689/14679/23679} (cannot be {14589/23589} because R9C2 only contains 6,7, cannot be {24579/34569} which clash with R5C1), no 5

45. R5C3 + R6C23 = {123} = 6
45a. 45 rule on N14 using R5C3 + R6C23 = 6, 2 remaining innies R24C3 = 10 = [37/46]
45b. Consider permutations for R24C3
R24C3 = [37] => 18(4) cage at R1C4 (step 39) = {2367}, 2 locked for C4 => R67C4 = {38}
or R24C4 = [46] => R3C4 = 9 (step 17) => R67C4 = {38}
-> R67C4 = {38}
[One of these options could be taken as far as a contradiction; I’ve avoided doing this because it’s not necessary.]

46. Naked pair {38} in R67C4, locked for C4 -> R3C4 = 9, R4C3 = 6 (step 17), R2C3 = 4 (step 45a), R4C1 = 7, clean-up: no 3 in R1C7, no 2,5 in R3C2, no 2 in R3C3, no 7 in R9C3, no 4,6 in R9C4

47. 17(4) cage at R2C6 (step 42) = {1259/1349} -> R2C7 = 9, R1C7 = 4, R1C6 = 8, R4C7 = 8, R4C2 = 4, R5C12 = [58], clean-up: no 1 in R6C2, no 6 in R6C9, no 6 in R8C7 (both step 9), no 3 in R7C8

48. Naked pair {23} in R67C2, locked for C2 -> R3C2 = 6, R3C3 = 5, R9C2 = 7, R12C2 = [91], R8C2 = 5, clean-up: no 3 in R9C3

49. Naked pair {38} in R23C1, locked for C1 and N1 -> R1C13 = [27], R1C5 = 6, R1C4 = 1, R9C4 = 2, R9C3 = 8, R2C4 = 7, R1C89 = [53], R9C9 = 1 (step 19), R4C9 = 2, R23C9 = [68], R2C8 = 2, R3C7 = 1, R2C6 = 5 (step 42), R2C5 = 3, R4C5 = 1, R4C6 = 3, R3C6 = 2, R3C5 = 4, R5C5 = 9, R9C5 = 5, clean-up: no 6 in R7C7

50. Naked pair {78} in R78C5, locked for C5 and N8 -> R6C5 = 2, R67C2 = [32], R6C3 = 1, R67C4 = [83], R78C3 = [93], R8C4 = 4 (cage sum), R8C7 = 2, R6C9 = 4 (step 9), R6C8 = 6, R6C67 = [75], R7C6 = 1 (cage sum)

and the rest is naked singles.


I'll rate my walkthrough for Maverick 2 at 1.75 because of step 15a which uses the interaction of a "sees all except" step with a hidden cage. I also used a couple of short forcing chains later.
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Ed
PostPosted: Tue Jul 15, 2008 8:28 am 
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Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Assassin 78 by Ruud (Nov 07)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:6144:6144:4610:4610:4610:5893:5893:5893:2824:3849:6144:1803:4610:2829:2829:5893:2824:2824:3849:3849:1803:3605:3605:2829:2840:2840:6170:3849:1820:1820:3605:5407:5408:5408:6170:6170:6180:1820:4390:5407:5407:5407:5408:3371:6170:6180:6180:4390:4390:5407:4402:3371:3371:4917:6180:3127:3127:5689:4402:4402:2364:4917:4917:2879:2879:5441:5689:5689:4420:2364:4166:4917:2879:5441:5441:5441:4420:4420:4420:4166:4166:
Solution: 
+-------+-------+-------+
| 7 8 2 | 3 5 9 | 1 6 4 |
| 1 9 3 | 8 6 4 | 7 2 5 |
| 5 6 4 | 2 7 1 | 8 3 9 |
+-------+-------+-------+
| 3 4 1 | 5 2 7 | 9 8 6 |
| 8 2 7 | 9 3 6 | 5 4 1 |
| 9 5 6 | 4 1 8 | 2 7 3 |
+-------+-------+-------+
| 2 3 9 | 7 4 5 | 6 1 8 |
| 4 1 8 | 6 9 2 | 3 5 7 |
| 6 7 5 | 1 8 3 | 4 9 2 |
+-------+-------+-------+
Quote:
Ruud, lead-in: This could become a classic. SumoCue (unreleased) gives it the highest rating I've ever seen for a puzzle it can solve. JSudoku chokes. Richard's SudokuSolver is still running while I'm writing this.
mhparker: The puzzle proved to be less difficult than Ruud's comments suggested, but very enjoyable nevertheless. Estimated rating: 1.25
goooders: i agree with mhp's rating
Nasenbaer: Enjoyable - yes, but I needed more than 4 hours to solve it! Maybe I'm a little rusty. ;)
Afmob: I haven't found a fast way to solve it so it took me rather long to solve it
Para: Took me a while to solve.. I think 1.25 is probably a fair rating, but it takes a very odd move to crack it which you normally don't look for
gary w: Given Ruud's comment I approached this one with some trepidation but it turned out to be fairly standard..took me about 2 hours
Andrew: I must admit I was really struggling until I got a hint from Afmob. ....After that it was pretty straightforward
CathyW: I'd been looking at 78 on and off all week and still didn't crack it. (Had to cheat and look at the posted WTs :( )
Walkthrough by mhparker:
Hi folks,

Happy to be able to post the first WT for a change! :-)

The puzzle proved to be less difficult than Ruud's comments suggested, but very enjoyable nevertheless. Estimated rating: 1.25.


Assassin 78 Walkthrough

Prelims:

a) 24(3) at R1C1 = {789}, locked for N1
b) 11(3) at R1C9, R2C5 and R8C1 = {128/137/146/236/245} (no 9)
c) 11(2) at R3C7 = {29/38/47/56} (no 1)
d) 7(3) at R4C2 = {124}, locked for N4
e) 21(3) at R4C6 = {489/579/678} (no 1..3)
f) 12(2) at R7C2 = {39/48/57} (no 1,2,6)
g) 22(3) at R7C4 = {589/679}, 9 locked for N8
h) 9(2) at R7C7 = {18/27/36/45} (no 9)

1. Innie/Outie difference (I/O diff.), N1: R4C1 = R1C3 + 1
1a. -> no 1,3 in R1C3; no 8,9 in R4C1

2. I/O diff., N3: R1C6 = R3C9 (no eliminations yet)

3. I/O diff., N7: R7C1 = R9C4 + 1
3a. -> no 1 in R7C1

4. I/O diff., N9: R9C7 = R6C9 + 1
4a. -> no 1 in R9C7; no 9 in R6C9

5. I/O diff., N1245: R146C6 = R7C1 + 22
5a. -> R7C1 = 2; R146C6 = {789}, locked for C6
5b. -> R9C4 = 1 (step 3)
5c. cleanup: no 7 in R8C7; R3C9 = {789} (step 2)

6. Naked triple (NT) at R1C126 = {789}, locked for R1

7. 14(3) at R3C4, 11(2) at R3C7 and R3C9 form hidden killer triple type 1:1:1 on {789}
7a. -> no 7,8,9 in R4C4; no 5,6 in R3C78

8. 1 in R7 locked in N9 -> not elsewhere in N9
8a. cleanup: no 8 in R7C7

9. Outies, N8: R6C6 + R9C7 = 12(2) = [75/84/93]
9a. -> R9C7 = {345}
9b. cleanup: R6C9 = {234} (step 4)

10. 2 unavailable to 11(3) at R8C1 = {137/146} (no 5,8)

11. Split 20(3) at R8C3+R9C23 = {389/569/578} (no 4)
(Note: {479} blocked by 12(2) (Prelim f) or 11(3) (step 10) - take your pick)

12. Split 22(3) at R5C1+R6C12 = {589/679} (no 3)
12a. 9 locked for N4

13. 9 in C3 locked in N7 -> not elsewhere in N7
13a. cleanup: no 3 in R7C3

14. I/O diff., N4: R6C4 = R4C1 + 1
14a. -> no 2,3,5,9 in R6C4

15. 17(3) at R5C3 = {368/458/467}
15a. 4 only available in R6C4
15b. -> no 7 in R6C4
15c. cleanup: no 6 in R4C1 (step 14); no 5 in R1C3 (step 1)

16. 15(4) at R2C1 = {1257/1347/1356}
(Note: {2346} blocked by R1C3 or 7(2) at R2C3 - take your pick)
16a. 1 locked for N1
16b. cleanup: no 6 in R23C3

17. Hidden single (HS) in C3 at R4C3 = 1
17a. -> R45C2 = {24}, locked for C2
17b. cleanup: no 8 in R7C3

18. Innies C12: R79C2 = 10(2) = {37} (no 5,6,8) (last combo), locked for C2 and N7
18a. cleanup: no 4 in R7C3

19. HS in N1 at R1C1 = 7
19a. cleanup: no 7 in R3C9 (step 2)

20. Hidden pair (HP) in C1 at R56C1 = {89} (no 5,6), locked for N4
20a. -> R6C2 = 5 (split 22(3) cage sum)

21. Naked single (NS) at R4C1 = 3
21a. -> R1C3 = 2 (step 1), R6C4 = 4 (step 14)
21b. cleanup: no 5 in R9C7 (step 4)

22. 7(2) at R2C3 = {34} (last combo, or HP(C2)), locked for N1

23. 6 in N4 locked in C3 -> not elsewhere in C3

24. I/O diff., N2: R1C6 = R4C4 + 4
24a. -> R1C6+R4C4 = [95]
24b. -> R3C9 = 9 (step 2)
24c. cleanup: no 2 in R3C78

25. R12C2 = [89]

26. Naked pair (NP) at R46C6 = {78}, locked for N5

27. Split 16(3) at R1C45+R2C4 = {358/367} (no 1,4) (all other combos unplaceable)
27a. must have 1 of {78}, only available in R2C4
27b. -> R2C4 = {78} (no 3,6)
27c. 3 locked in R1C45 for R1 and N2

28. {14} in R1 locked in N3 -> not elsewhere in N3

29. 11(2) at R3C7 = {38} (last combo), locked for R3 and N3

30. R23C3 = [34]

31. Split 14(3) at R1C78+R2C7 = {167} (no 2,4,5) (all other combos unplaceable)
31a. -> R2C7 = 7; R1C78 = {16}, locked for R1 and N3
31b. cleanup: no 2 in R8C7

32. HS in C7 at R6C7 = 2

33. NS at R6C9 = 3
33a. -> R9C7 = 4 (step 4)
33b. cleanup: no 5 in R78C7

34. R12C4 = [38]
34a. -> R1C5 = 5

35. 22(3) at R7C4 = {679} (no 8) (last combo)
35a. {67} locked for N8

36. Outie, N8 (step 9): R6C6 = 8
36a. -> split 9(2) at R7C56 = [45] (last combo/permutation)

The rest is now singles and cage sums
Walkthrough by Afmob:
I haven't found a fast way to solve it so it took me rather long to solve it. I'm still a bit confused that JSudoku wasn't able to solve it considering it can solve something like the Brick Wall.

Edit: Deleted some steps and correct many typos, thanks Andrew!

A78 Walkthrough:

1. C123
a) 24(3) = {789} locked for N1
b) 7(3) = {124} locked for N4
c) Innies+Outies N1: 1 = R4C1 - R1C3
-> R4C1 <> 8,9; R1C3 <> 1,3
d) Innies+Outies N7: -1 = R9C4 - R7C1
-> R7C1 <> 1, R9C4 <> 9
e) Innies+Outies C123: 3 = R69C4 - R1C3
-> R6C4 <> 9 because R1C3 <= 6

2. R6789
a) 22(3) = 9{58/67} -> 9 locked for N8
b) Innies+Outies N9: -1 = R6C9 - R9C7
-> R9C7 <> 1; R6C9 <> 9
c) Innies+Outies R789: 9 = R6C69 - R7C1
-> R6C69 <> 1 because R7C1 >= 2
d) Innies+Outies R6789: 18 = R5C138 - R6C5
-> R5C8 <> 1; R6C5 <> 7,8,9

3. R1234
a) Innies+Outies R123: -1 = R4C14 - R3C9
-> R3C9 = (56789) since R4C1 >= 3
-> R4C4 <> 6,7,8,9 because R4C1 >= 3
b) Innies+Outies N3: R1C6 = R3C9 = (56789)
c) Innies+Outies R1: 20 = R2C247 - R1C9
-> R1C9 = (1234); R2C47 <> 1,2,3

4. N369
a) Innies+Outies N36: 13 = R14C6 - R6C9
-> R14C6 <> 1,2,3,4,5 because R6C9 >= 2
-> R6C9 = (234)
b) Innies+Outies N9: -1 = R6C9 - R9C7
-> R9C7 = (345)
c) Innies+Outies N3: R1C6 = R3C9 = (6789)

5. N6789
a) Innies+Outies N8: 11 = R6C6+R9C7 - R9C4
-> R6C6 = (789) because R9C7 = (345)
-> R9C4 = (123) because R6C6+R9C7 <= 14
b) Innies+Outies N7: -1 = R9C4 - R7C1
-> R7C1 = (234)
c) ! Innies+Outies N689: 23 = R3C9+R46C6 - R9C4
-> R3C9 <> 6 since R46C6 <= 17
-> R4C6 <> 6 because R3C9 must be 9 like R6C6 -> not possible (step 4c)

6. R1+C6789
a) Innies+Outies N3: R1C6 = R3C9 = (789)
b) Naked triple (789) locked in R146C6 for C6
c) Naked triple (789) locked in R1C126 for R1

7. N258 !
a) 17(4): R9C5 <> 1 because R89C6+R9C7 <= 15
b) 17(3) @ N8: R7C5 <> 1 because R7C6 <> 7,9
c) 7,8,9 locked in 21(5) and R46C6 for N5
d) ! Innies+Outies N25: -2 = R1C3 - R6C4 because of step 6b
-> R1C3 = (24); R6C4 = (46)
e) 17(3) @ N4 = {368/458/467}

8. C123
a) 9 locked in R789C3 for N7
b) 12(2): R7C3 <> 3
c) Innies+Outies N1: 1 = R4C1 - R1C3
-> R4C1 = (35)
d) 15(4) = 36{15/24} -> 6 locked for N1
e) 7(2) <> 1
f) Killer pair (24) locked in 7(2) + R1C3 for C3+N1
g) 2,4 locked in R789C1 for N7
h) R4C3 = 1
i) 12(2) = [39/57/75]
j) Killer pair (59) locked in 12(2) + 21(4) for N7

9. C123
a) 2,4 locked in R789C1 and 11(3) can't have both -> R7C1 = (24)
b) Innies+Outies N7: -1 = R9C4 - R7C1
-> R9C4 = (13)
c) Innies+Outies C12: 3 = R47C3 - R9C2
-> R9C2 = (357) because R47C3 = 1{5/7/9}
d) 1 locked in 11(3) @ N7 -> 11(3) = 1{28/46} because of Killer pair (37) of 11(3)
e) 21(4): R89C3 <> 3 because (89) only possible there and R9C4 <> 5,6,7
f) 3 locked in R79C2 for C2
g) 15(4) = {1356} -> 3 locked for C1
h) 9 locked in 24(4) = 9{258/267/456}

10. C12 !
a) ! Innies+Outies C1: 5 = R368C2 - R1C1
-> R1C1 <> 9 since R368C2 would be 14(3) with 9 locked -> not possible because of 7(3)
b) 24(3) = {789} -> 9 locked for C2
c) ! Innies+Outies C1: 5 = R368C2 - R1C1
-> R1C1 <> 8 since R368C2 would be 13(3) with 8 locked -> not possible because of 7(3)
d) 24(3) = {789} -> R1C1 = 7, {89} locked for C2

11. N5
a) 7 locked in R46C6
b) 21(5) = 1{2369/2459/3458}; {12468} impossible because R6C4 = (46)
c) Killer pair {46} locked in 21(5) + R6C4

12. N3689 !
a) Innies+Outies N3: R1C6 = R3C9 = (89)
b) ! Innies+Outies N689: 23 = R3C9+R46C6 - R9C4
-> R9C4 <> 3 because R46C6 would be {89} -> blocked by R1C6 = (89)
c) R9C4 = 1
d) 21(4) = 1{389/578} because {1569} is blocked by Killer pair (59) of 12(2) @ N7
-> 8 locked for C3+N7

13. C123
a) 11(3) = {146} locked for N7
b) R7C1 = 2
c) 17(3) = {467} -> R6C4 = 4, {67} locked for C3+N7
d) R6C2 = 5, R4C1 = 3
e) 15(4) = {1356} -> 5 locked for N1
f) 7(2) = {34} locked for N1
g) R1C3 = 2

14. N5
a) 21(5) = {12369} locked
b) R4C4 = 5
c) Naked pair (78) locked in R46C6 for C6
d) R1C6 = 9 -> R3C9 = 9 (step 12a)

15. C789
a) 11(2) = {38/47} because {56} blocked by 15(4) = {1356} @ R3
b) 2 locked in 11(3) for R2 -> 11(3) = 2{18/36/45}
c) Innies+Outies N36: 13 = R14C6 - R6C9
-> R6C9 <> 2 because R14C6 >= 16
-> R6C9 = 3 -> R4C6 = 7
d) R6C6 = 8
e) Innies+Outies N9: -1 = R6C9 - R9C7 -> R9C7 = 4
f) R9C1 = 6, R8C2 = 1, R8C1 = 4, R3C2 = 6
g) 13(3) = {148/157/247/256}
h) 9 locked in 21(3) = {579} -> R4C7 = 9, R5C7 = 5
i) 24(4) = 69{18/27} -> 6 locked for N6
j) 13(3) = 4{18/27} -> R5C8 = 4
k) 13(3) = {247} -> {27} locked for R6+N6

16. N23
a) 11(2) = {38} locked for R3+N3
b) 23(4) = {1679} -> R2C7 = 7, {16} locked for R1+N3
c) 18(4) = {2358} -> R1C4 = 3, R2C4 = 8, R1C5 = 5

17. N89
a) 22(3) = {679} locked for N8
b) 17(3) = {458} -> R7C5 = 4, R7C6 = 5
c) R7C3 = 9 -> R7C2 = 3
d) 19(4) = 38{17/26} -> 8 locked for N9
e) 9(2) = [63] -> R7C7 = 6, R8C7 = 3

18. Rest is singles.

By the way, I have never used so much Innies+Outies Difference to solve a Killer.
Outline by gary w:
Hi,

Given Ruud's comment I approached this one with some trepidation but it turned out to be fairly standard..took me about 2 hours.Once i'ld noticed
O-I on nonets 1245 -> r146c6=r7c1+22 and from the IO of N7 r7c1=r9c4+1 thus r7c1=2 and r9c4=1.Also r146c6={789}.
Then all the IO (lots of them in this puzzle!) of N12 mean that r1c3,r4c14,r6c4 are all "tied together" and together with the I N5=24 and r46c6=7/8,7/9,8/9 this enabled a placement of r1c3=2 after which the puzzle came out quite readily.

Of course when I looked at the other guys' wts the moves had pretty much been used by them.
Walkthrough by Andrew:
Congratulations to all who managed to solve Assassin 78. I must admit I was really struggling until I got a hint from Afmob. It was a good hint, just enough to make me think how to use it. Many thanks for that! :) After that it was pretty straightforward with the work I'd already done being helpful.

Really nice walkthrough, Mike! You got to the heart of things very quickly. :D

Here is my walkthrough for Assassin 78, including the hint after step 23.
Many thanks to Para for corrections and feedback.

Prelims

a) R23C3 = {16/25/34}, no 7,8,9
b) R3C78 = {29/38/47/56}, no 1
c) R7C23 = {39/48/56}, no 1,2,6
d) R78C7 = {18/27/36/45}, no 9
e) 24(3) cage in N1 = {789}, locked for N1
f) 11(3) cage in N2 = {128/137/146/236/245}, no 9
g) 11(3) cage in N3 = {128/137/146/236/245}, no 9
h) 7(3) cage in N4 = {124}, locked for N4
i) 21(3) cage at R4C6 = {489/579/678}, no 1,2,3
j) 11(3) cage in N7 = {128/137/146/236/245}, no 9
k) 22(3) cage in N8 = 9{58/67}, 9 locked for N8

1. 45 rule on N1 1 outie R4C1 = 1 innie R1C3 + 1, no 1,3 in R1C3, no 8,9 in R4C1

2. 45 rule on N12 1 innies R1C6 = 2 outies R4C14 + 1
2a. Min R4C14 = 4 -> min R1C6 = 5
2b. Max R1C6 = 9 -> max R4C14 = 8, no 6,7,8,9 in R4C4

3. 45 rule on N9 1 innie R9C7 = 1 outie R6C9 + 1, no 9 in R6C9, no 1 in R9C7

4. 45 rule on N89 2 outies R6C69 = 1 innie R9C4 + 10
4a. Min R9C4 = 1 -> min R6C69 = 11, no 1, no 2 in R6C6, clean-up: no 2 in R9C7 (step 3)
4b. Max R6C69 = 17 -> max R9C4 = 7

5. 45 rule on N7 1 innie R7C1 = 1 outie R9C4 + 1, no 1,9 in R7C1

6. 45 rule on N4 2 outies R6C4 + R7C1 = 1 innie R4C1 + 3
6a. Max R4C1 = 7 -> max R6C4 + R7C1 = 10, no 9 in R6C4
6b. IOU no 3 in R6C4

7. 45 rule on N6 2 outies R3C9 + R4C6 = 1 innie R6C9 + 13
7a. Min R6C9 = 2 -> min R3C9 + R4C6 = 15, no 1,2,3,4,5
7b. Max R3C9 + R4C6 = 18 -> max R6C9 = 5, clean-up: no 7,8,9 in R9C7 (step 3)
7c. Min R6C69 = 11 (step 4a), no 3,4,5 in R6C6

8. 45 rule on N3 1 outie R1C6 = 1 innie R3C9 -> R1C6 = {6789}

9. 45 rule on N8 2 outies R6C6 + R9C7 = 1 innie R9C4 + 11, max R6C6 + R9C7 = 15 -> max R9C4 = 4, clean=up: no 6,7,8 in R7C1 (step 5)

10. 45 rule on C789 2 outies R14C6 = 1 innie R9C7 + 12
10a. Max R14C6 = 17 -> max R9C7 = 5, clean-up: no 5 in R6C9 (step 3)
10b. Max R6C6 + R9C7 = 14 -> max R9C4 = 3 (step 9), clean-up: no 5 in R7C1 (step 5)
10c. Min R6C69 = 11 (step 4a), no 6 in R6C6
Para: "I think you missed the interactions between some 45-tests.
Because you said maximum of R6C6 + R9C7 was maximum 14: [95], but R9C6 = 5 means R14C6 = {89}, so really maximum was 12([75/84/93] if you use 45 on C789) and that gets you the same as in step 24."
Neat! That would have made the solution a lot quicker.

11. 45 rule on C89 2 outies R36C7 = 1 innie R1C8 + 4
11a. IOU no 4 in R6C7

12. 45 rule on N5 4 innies R46C46 = 24 = {1689/2589/2679/3489/3579/3678/4569/4578}
12a. 1 of {1689} must be in R4C4 -> no 1 in R6C4

13. 17(3) cage at R5C3 = {269/278/359/368/458/467}
13a. 2,4 of {278/467} must be in R6C4 -> no 7 in R6C4

14. 45 rule on R1 3 outies R2C247 = 1 innie R1C9 + 20
14a. Min R1C9 = 1 -> min R2C247 = 21, no 1,2,3
14b. Max R2C247 = 24 -> max R1C9 = 4

15. Deleted. It was incorrect and also happened to be unnecessary. When I originally went through my walkthrough before posting it I thought it was probably unnecessary but hadn't seen the flaw which Para pointed out.

16. 45 rule on R89 2 outies R7C47 = 1 innie R8C9 + 6
16a. IOU no 6 in R7C4

17. 45 rule on R12 2 outies R3C36 = 1 innie R2C1 + 4
17a. IOU no 4 in R3C6

18. 45 rule on R6789 3 outies R5C138 = 1 innie R6C5 + 18
18a. Min R6C5 = 1 -> min R5C138 = 19, no 1
18b. Max R5C138 = 24 -> max R6C5 = 6

19. Min R9C7 = 3 -> min R14C6 = 15 (step 10) -> max R67C6 = 15 -> no 1 in R7C5

20. 17(4) cage at R8C6 = {1268/1358/1367/1457/2348/2357/2456}, must contain at least one of 5,6,7,8 in R8C6 + R9C56

21. 17(3) cage at R6C6 = {179/269/278/359/368/458/467}, must contain one of 5,6,7,8 in R7C56
21a. Hidden killer quad 5,6,7,8 in N8 -> 17(4) cage at R8C6 can only contain one of 5,6,7,8 in R8C6 + R9C56 and can also contain 5 in R9C7 = {1358/1457/2348/2357/2456} (cannot be {1268/1367} which contain two of 6,7,8)
21b. 6,7,8 of {1358/1457/2357/2456} must be in R8C6 +R9C56 -> no 5 in R8C6 + R9C56

22. 17(4) cage at R8C6 = {1358/1457/2348/2357/2456}
22a. If {1358} => R9C4 = 2 => no {278} in 17(3) cage at R6C6
22b. If {1457} => 22(3) cage = {589} => no {278} in 17(3) cage at R6C6
22c. If {2348/2357/2456} => no {278} in 17(3) cage at R6C6
22d. -> no {278} in 17(3) cage at R6C6 -> no 8 in R7C56 (8 of {368/458} must be in R6C6)

23. 17(3) cage at R6C6 = {179/269/359/368/458/467}
23a. {179} must be [971] and 7 of {467} must be in R6C6 -> no 7 in R7C6

At this stage I was struggling and Afmob gave me the hint that Mike had used a breakthrough step using 4 combined nonets. I ought to have thought to look for something larger than 2 combined nonets; I have used a L-shaped group of 3 nonets at least once in the past.

24. 45 rule on N3689 3 outies R146C6 = 1 innie R9C4 + 23 -> R146C6 = 24 = {789}, R9C4 = 1, R7C1 = 2 (step 5), clean-up: no 6 in R3C9 (step 8), no 7 in R7C5 (step 23), no 7 in R8C7
24a. Naked triple {789} in R146C6, locked for C6
24b. R5C1 + R6C12 = 22 = 9{58/67}, no 3, 9 locked for N4

25. Naked triple {789} in R1C126, locked for R1

26. 1 in N7 locked in R8C12, locked for R8, clean-up: no 8 in R7C7
26a. 11(3) cage in N7 = 1{37/46}, no 5,8
26b. R8C3 + R9C23 = 20 = {389/569/578} (cannot be {479} which clashes with 11(3) cage), no 4

27. Deleted

28. 45 rule on C123 1 remaining outie R6C4 = 1 innie R1C3 + 2 -> R1C3 = {246}, R6C4 = {468}, clean-up: R4C1 = {357} (step 1)

29. R46C46 (step 12) = {2679/3489/3678/4578}
29a. Two of 7,8,9 must be in R46C6 -> no 8 in R6C4, clean-up: no 6 in R1C3 (step 28), no 7 in R4C1 (step 1)
29b. No combinations with R46C4 = {46} -> no 4 in R4C4
Step 29a inserted and original 29a renumbered.
Thanks Para for sorting out the errors in steps 27 and 28; I’d done my mental arithmetic the wrong way round in step 27 which, when corrected, was superseded by step 28.

30. R1C6 = R4C14 + 1 (step 2)
30a. R4C14 cannot total 6 -> no 7 in R1C6, clean-up: no 7 in R3C9 (step 8)
30b. 7 in R1 locked in R1C12 -> no 7 in R2C2
30c. 7 in C6 locked in R46C6, locked for N5
Para: "You could also have locked the 5 in R4C14 for R4 in this step".

31. 15(4) cage at R2C1 = {1356/2346}, 6 locked for N1, clean-up: no 1 in R23C3

32. Killer pair 2,4 in R1C3 and R23C3, locked for C3 and N1 -> R4C1 = 1, clean-up: no 8 in R7C2

33. Naked pair {24} in R45C2, locked for C2, clean-up: no 8 in R7C3

34. 8 in N7 locked in R8C3 + R9C23 = {389/578}, no 6

35. 6 in N7 locked in 11(3) cage = {146}

36. Grouped X-Wing for 6 in 15(4) cage at R2C1 and 11(3) cage in N7, locked for C12, clean-up: no 7 in 24(4) cage at R5C1 (step 24b)
Para: "That grouped x-wing is doing it the hard way as the 6 in C3 is locked for N4. If there's a workable grouped x-wing in which both cage are completely within one nonet (each) then there is always an easier locked candidates move available".
Agreed. I just happened to spot the grouped X-wing.
36a. Naked triple {589} in R5C1 + R6C12, locked for N4 -> R4C1 = 3, R1C3 = 2 (step 1), R6C4 = 4 (step 28), clean-up: no 5 in R23C3, no 5 in R9C7 (step 3)

37. 17(4) cage at R8C6 (step 22) = {2348} (only remaining combination) -> R9C5 = 8, clean-up: no 5 in 22(3) cage in N8
37a. 2 locked in R89C6, locked for C6

38. Naked triple {679} in 22(3) cage, locked for N8
[I missed 6 locked in R8C45 for R8 here. Fortunately it didn’t make much difference.]

39. 5 in N8 locked in R7C56, locked for R7, clean-up: no 7 in R7C23, no 4 in R8C7
39a. 17(3) cage at R6C6 (step 23) = {359/458}, no 7

40. R4C6 = 7 (hidden single in C6), R45C7 = 14 = {59/68}, no 4

41. Naked pair {34} in R23C3, locked for C3 -> R7C23 = [39], R7C4 = 7, clean-up: no 2,6 in R8C7

42. Naked pair {67} in R56C3, locked for C3 -> R9C23 = [75], R8C3 = 8, clean-up: no 1 in R7C7

43. Naked pair {45} in R7C56, locked for R7 and N8 -> R78C7 = [63], R9C7 = 4, R89C6 = [23], R6C9 = 3 (step 3), R9C1 = 6, R8C12 = [41], clean-up: no 5,7,8 in R3C8, no 8 in R45C7 (step 40)

44. Naked pair {15} in R23C1, locked for C1 and N1 -> R3C2 = 6, clean-up: no 5 in R3C7

45. Naked pair {89} in R12C2, locked for C2 and N1 -> R1C1 = 7, R6C2 = 5

46. R8C9 = 7 (cage sum), R8C8 = 5 (hidden single in R8)

47. R46C46 (step 29) = {4578} (only remaining combination) -> R4C4 = 5, R6C6 = 8, R1C6 = 9, R12C2 = [89], R45C7 = [95], R56C1 = [89], R1C7 = 1, R1C9 = 4, R3C9 = 9 (step 8), R9C89 = [92], clean-up: no 2,7 in R3C7, no 2 in R3C8

and the rest is naked singles
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Ed
PostPosted: Tue Jul 15, 2008 8:29 am 
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Location: Sydney, Australia
Assassin 78V2 by mhparker (Nov 07)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:4096:4096:4354:4354:4354:6149:6149:6149:3080:4873:4096:2827:4354:4109:4109:6149:3080:3080:4873:4873:2827:3349:3349:4109:2328:2328:6682:4873:4636:4636:3349:6431:2336:2336:6682:6682:4132:4636:4134:6431:6431:6431:2336:4139:6682:4132:4132:4134:4134:6431:2610:4139:4139:5685:4132:4151:4151:3897:2610:2610:3388:5685:5685:3903:3903:4417:3897:3897:6468:3388:2374:5685:3903:4417:4417:4417:6468:6468:6468:2374:2374:
Solution: 
+-------+-------+-------+
| 4 5 8 | 1 2 9 | 6 7 3 |
| 1 7 9 | 6 3 8 | 2 5 4 |
| 3 6 2 | 7 4 5 | 8 1 9 |
+-------+-------+-------+
| 9 4 6 | 2 5 3 | 1 8 7 |
| 7 8 3 | 4 6 1 | 5 9 2 |
| 2 1 5 | 8 9 7 | 3 4 6 |
+-------+-------+-------+
| 6 9 7 | 5 1 2 | 4 3 8 |
| 8 2 1 | 3 7 4 | 9 6 5 |
| 5 3 4 | 9 8 6 | 7 2 1 |
+-------+-------+-------+
Quote:
gooders: i suspect the cage pattern could produce something quite nasty
mhparker: (Est. rating: 1.75) It takes a clever move to get the ball in motion, but once it's gained momentum, this puzzle should reward you by staying interesting until near the end
Para: It's a bit of an annoying killer because the end is so tedious. Mostly because it seems a bit useless work when you really did all the fun bits already...Furthermore it is a fun killer, so don't be disheartened or anything
Para: I am going to rate it a 1.5, although i actually want to rate it something like a 1.65 but as this isn't a category it will be a 1.5
gary w: I finally cracked Mike's vicious creation..it didn't give up without a fight..a hard slog right to the end.
Andrew (in 2012): This puzzle had a very narrow solving path, right to the end. Para and I found a few steps in different ways but most of our steps were very similar. The biggest difference was how each of us reduced R8C4579 to one combination.
I agree with Para's rating of Hard 1.5.
Walkthrough by Para:
Hi all

Woke up early and didn't feel like going to sleep again so solved Mike's V2 instead. It's a bit of an annoying killer because the end is so tedious. Mostly because it seems a bit useless work when you really did all the fun bits already. And if it would take 3 or less steps to break it down, it actually took me 7 steps. Furthermore it is a fun killer, so don't be disheartened or anything, would have been nicer without the last 7 steps though.
I am going to rate it a 1.5, although i actually want to rate it something like a 1.65 but as this isn't a category it will be a 1.5. The reason for 1.5 and not 1.75 is that it misses that extra bit that tends to be in my 1.75 walk-throughs. This usually is one creative step, an extra special set of contradictions on a 45-test/cage combinations or just one higher technique like a killer x-wing. I kinda feel it is comparable to A66V1.5 as a walk-through and that is a 1.5. I know i am way of what Sudoku Solver thinks, but i think it is just because there are loads of small steps that Sudoku Solver does that i didn't implement in my walk-through as they are completely unnecessary. But as i said it is really a 1.65 so a high 1.5.

Walk-through Assassin78V2

1. R23C3 = {29/38/47/56}: no 1

2. R3C78 = {18/27/36/45}: no 9

3. 26(4) at R3C9 = {2789/3689/4589/4679/5678}: no 1

4. 9(3) at R4C6 and R8C8 = {126/135/234}: no 7,8,9

5. 10(3) at R6C6 = {127/136/145/235}: no 8,9

6. R78C7 = {49/58/67}: no 1,2,3

7. R7C23 = {79} -> locked for N7 and R7
7a. 7 and 9 in N9 locked within R8C79 + R9C7: pointing -> R8C6: no 7,9
7b. Clean up: R8C7: no 4,6

8. 45 on N1: 1 innie and 1 outie: R1C3 + 1 = R4C1: R1C3: no 9; R4C1: no 1

9. 45 on N2: 1 innie and 2 outies: R1C6 + 1 = R1C3 + R4C4: R4C4: no 1(IOU)

10. 45 on N3: 1 innie and 1 outie: R1C6 = R3C9: R1C6: no 1

11. 45 on N4: 1 innie and 2 outies: R4C1 + 5 = R6C4 + R7C1: R6C4: no 5(IOU)

12. 45 on N6: 1 innie and 2 outies: R6C9 + 6 = R4C6 + R3C9: R4C6: no 6(IOU)
12a. 45 on N6: 3 innies and 1 outie: R45C7 + R6C9 = R3C9 + 3: R3C9: no 2
12b. Clean up: R1C6: no 2(step 10)

13. 45 on N7: 1 innie and 1 outie: R7C1 + 3 = R9C4: R7C1: no 8; R9C4: no 1,2,3

14. 45 on N8: 1 innie and 2 outies: R9C4 + 5 = R6C6 + R9C7: R6C6: no 5(IOU)

15. 45 on N9: 1 innie and 1 outie: R6C9 + 1 = R9C7: R6C9: no 9; R9C7: no 1

16. 45 on R89: 4 innies: R8C4579 = 24
16a. 7 and 9 in R89 locked within R8C4579 -> R8C4579 = {2679/3579}: no 1,4,8
16b. Clean up: R7C7: no 5

17. 45 on R89: 1 innie and 2 outies: R7C47 = R8C9 + 4: R7C4: no 4(IOU)
17a. 45 on R89: 2 innies and 1 outie: R7C4 + 9 = R8C79: Max R8C79 = 16 -> Max R7C4 = 7: R7C4: no 8

18. 15(3) at R7C4 = {159/267/357}: 15(3) needs one of {79} in R8C45
18a. Hidden Killer Pair {79} in R8: R8C45 needs one of {79} and R8C79 needs one of {79}
18b. Hidden Killer Pair {79} in N9: R8C79 needs one of {79} and R9C7 needs one of {79} -> R9C7 = {79}
18c. Clean up: R6C9 = {68}

19. 22(4) at R6C9 = [6]{178/349/358}/[8]{149/167/239/347/356}:[6]{259/457}/[8]{257} blocked by R89C7: R7C89 + R8C9 needs one of {579}
19a. Killer Triple {579} in "R7C89 + R8C9" + R89C7 -> locked for N9
19b. 9(3) at R8C8 = {126/234} = {1|4..},{3|6..}: 2 locked for N9
19c. 22(4) at R6C9 = [6]{178/349/358}/[8]{167/347}: [8]{149/356} blocked by 9(3) at R8C8: 7 only in R8C9 -> R8C9: no 6

20. R8C4579 = {3579}: no 2,6: R8C45 needs one of {79} and {26} only in R8C45 so {2679} blocked: {3579} locked for R8
20a. 15(3) at R7C4 = [1]{59}/[3]{57}/[5]{37}: R7C4: no 2,6; 5 locked for N8
20b. 10(3) at R6C6 = [7]{12}/{136}: no 4; R6C6: no 2; 1 locked within cage -> pointing: R89C6: no 1
20c. Clean up: R7C1: no 2

21. 2 in R7 locked within 10(3) cage at R6C6: 10(3) = [7]{12}: R6C6 = 7; R7C56 = {12} -> locked for R7 and N8
21a. 15(3) at R7C4 = {357} -> locked for N8; 7 locked for R8
21b. R9C7 = 7(hidden); R6C9 = 6(step 15); R9C4 = 9(step 14); R7C1 = 6(step 13)
21c. Clean up: R1C3: no 5; R1C6: no 6; R3C9: no 7; R3C8: no 2

22. Hidden Triple {126} in N9: R8C8 + R9C89 = {126}
22a. 6 in N9 locked for C8
22b. Clean up: R3C7: no 3

23. 15(3) at R8C1 = {28}[5]/{48}[3]: no 1; R8C12 = {28/48}: 8 locked for N7 and R8; R9C1 = {35}

24. 45 on N6: 2 outies: R3C9 + R4C6 = 12 = [93/84]: R3C9 = {89}; R4C6 = {34}
24a. 26(4) at R3C9 = {2789/4589}: no 3; {2|4..},{2|5..} in N6
24b. 9(3) at R4C6 = [3]{15}/[4]{23} = {2|5..} in N6: [3]{24} blocked by 26(4) at R3C9: R45C7: no 4
24c. Killer Pair {25} in R45C7 + (R4C89 + R5C9) -> locked for N6
24d. 16(3) at R5C8 = [7]{18}/{349}: R5C8: no 1,8
24e. Clean up: R1C6 = {89}

25. 45 on N4: 1 innie and 1 outie: R4C1 = R6C4 + 1: R4C1: no 7,8
25a. Clean up: R1C3: no 6,7

26. 45 on N36: 2 outies: R14C6 = [93]: [84] blocked by R89C6
26a. R3C9 = 9(step 10)
26b. R45C7 = {15}(last combo in 9(3)) -> locked for C7 and N6
26c. R78C7 = [49]
26d. 16(3) at R5C8 = {4[3]9}(last combo): R6C7 = 3; R56C8 = {49} -> locked for C8 and N6
26e. Naked Triple {268} in R123C7 -> locked for N3
26f. Clean up: R3C8: no 3; R4C1: no 4; R6C4: no 2; R1C3: no 2,3; R2C3: no 2

27. 45 on N2: 2 outies: R1C3 + R4C4 = 10 = [46/82]: R1C3 = {48}; R4C4 = {26}
27a. Clean up: R4C1: no 2; R6C4: no 1

28. 24(4) at R1C6 = 9{6[1]8/2[5]8/2[7]6}: no 3

29. 13(3) at R3C4 = {38/47/56}[2]/{25/34}[6]: no 1

30. 9 in C1 locked for 19(4) at R2C1: 19(4) = {1279/1369/1459/2359]: no 8

31. 16(4) at R5C1 = 6{127/145/235} = {5|7..} in N4: no 8,9
[This should have come before step 30: Andrew]
31a. 16(3) at R5C3 = [718/628/358]: [754] blocked by 16(4); [394] blocked by R6C8: R5C3 = {367}; R6C3 = {125}; R6C4 = 8
31b. R4C1 = 9; R1C3 = 8; R4C4 = 2(all on 45's); R5C9 = 2(hidden); R9C9 = 1; R8C3 = 1(hidden)
31c. R5C2 = 8(hidden); R8C1 = 8(hidden)
31d. Naked Pair {78} in R4C89 -> locked for R4
31e. Clean up: R23C3: no 3; R5C3: no 7
31f. R5C1 = 7(hidden)

32. R6C12 = {12}(last combo within 16(4)) -> locked for R6 and N4
32a. R56C3 = [35]
32b. Clean up: R23C3: no 6
32c. R4C3 = 6(hidden); R4C2 = 4; R8C2 = 2; R9C123 = [534]; R6C12 = [21]
32d. R89C8 = [62]; R8C6 = 4; R3C3 = 2(hidden); R2C3 = 9; R7C23 = [97];
32e. Clean up: R3C8: no 7

33. 16(3) at R1C1 = [3]{67}/[4]{57}: no 1; 7 locked for N1
33a. 7 in R3 locked within 13(3) at R3C4: 13(3) = 2{47} -> R3C45 = {47} -> locked for R3 and N2

34. 16(3) at R2C5 = {6[2]8}/[3]{58}:[2]{68} blocked by R9C6: no 1; R2C5: no 2,5; R2C6: no 6

35. 24(4) at R1C6 = 9[258]/{2[7]6}: [618] blocked by R3C7: no 1
35a. 1 in R1 locked for N2
35b. 17(4) at R1C3 = 8([126]/[1]{35}): {3[1]5} blocked by R7C4: R1C4 = 1; R1C5: no 6

36. 45 on R12: 3 innies: R2C156 = 12 = [138/165/462/435]: R2C1: no 3; R2C5: no 8
36a. R9C5 = 8(hidden); R9C6 = 6
36b. Naked Pair {15} in R5C67 -> locked for R5
36c. 6 in N2 locked for R2

37. Hidden Pair {28} in R2 -> R2C67 = {28}
37a. R2C156 = [138/462] = {3|4..}

38. 12(3) at R1C9 = [417]/[345]: [714] blocked by R2C1; [4]{35} blocked by R2C45; [534] blocked by R2C156: R1C9: no 5,7; R2C8: no 3,7; R2C9: no 3,5
38a. 5 in N3 locked for C8
38b. 3 in R2 locked for N2
38c. Clean up: R2C4: no 5
38d. 5 in C4 locked for N8

39. 24(4) at R1C6 = 9[672]: 9[258] blocked by R1C5

And the rest is all naked singles.

greetings

Para
2012 walkthrough by Andrew:
Prelims

a) R23C3 = {29/38/47/56}, no 1
b) R3C78 = {18/27/36/45}, no 9
c) R7C23 = {79}
d) R78C7 = {49/58/67}, no 1,2,3
e) 9(3) cage at R4C6 = {126/135/234}, no 7,8,9
f) 10(3) cage at R6C6 = {127/136/145/235}, no 8,9
g) 9(3) cage at R8C8 = {126/135/234}, no 7,8,9
h) 26(4) cage at R3C9 = {2789/3689/4589/4679/5678}, no 1

1. Naked pair {79} in R7C23, locked for R7 and N7, clean-up: no 4,6 in R8C7

2. 45 rule on N1 1 outie R4C1 = 1 innie R1C3 + 1, no 9 in R1C3, no 1 in R4C1

3. 45 rule on N3 1 outie R1C6 = 1 innie R3C9, no 2 in R1C6

4. 45 rule on N7 1 outie R9C4 = 1 innie R7C1 + 3, no 8 in R7C1, no 1,2,3 in R9C4

5. 45 rule on N9 1 innie R9C7 = 1 outie R6C9 + 1, no 9 in R6C9, no 1 in R9C7

6. 45 rule on N2 2 outies R1C3 + R4C4 = 1 innie R1C6 + 1
6a. IOU no 1 in R4C4

7. 45 rule on N4 2 outies R6C4 + R7C1 = 1 innie R4C1 + 5
7a. IOU no 5 in R6C4

8. 45 rule on N6 2 outies R3C9 + R4C6 = 1 innie R6C9 + 6
8a. IOU no 6 in R4C6

9. 45 rule on N8 2 outies R6C6 + R9C7 = 1 innie R9C4 + 5
9a. IOU no 5 in R6C6

10. 45 rule on R12 2 outies R3C36 = 1 innies R2C1 + 6
10a. IOU no 6 in R3C6

11. 45 rule on R89 2 outies R7C47 = 1 innie R8C9 + 4
11a. IOU no 4 in R7C4

12. 45 rule on C12 2 outies R47C3 = 1 innie R9C2 + 10
12a. Max R47C3 = 17 -> no 8 in R9C2
12b. Min R9C2 = 1 -> min R47C3 = 11, no 1 in R4C3

13. 45 rule on C89 2 outies R36C7 = 1 innie R1C8 + 4
13a. IOU no 4 in R6C7

14. 7,9 in R9 only in R9C4567, CPE no 7,9 in R8C6
[Alternatively 7,9 in N9 only in R8C7 + R9C79, CPE no 7,9 in R8C6]

[This was how far I’d got when this puzzle first appeared. I’d found step 14 but not how to continue after using it. With hindsight step 14 was available after step 2.]

15. R9C7 = 1 outie R6C9 + 1 (step 5)
15a. 45 rule on N9 4 innies R7C89 + R8C9 + R9C7 = 23 = {1589/1679/2489/2678/3479/3578} (cannot be {2579/3569/4568} which clash with R78C7)
15b. 1 of {1589/1679} must be in R7C89 (R7C89 cannot be {58} because 22(4) cage at R6C9 cannot be 8{58}1 or, if preferred, {58} clashes with R6C9 + R9C7 = [89], 1,6 of {1679} must be in R7C89), no 1 in R8C9
15c. 7,9 of {2489/2678} must be in R8C9 (because 22(4) cage at R6C9 cannot be 8{248}/6{268}) -> no 2 in R8C9
15d. 9 of {2489} must be in R8C9 (step 15c), 3,4 of {3489} must be in R7C89 -> no 4 in R8C9
15e. 1,6 of {1679} must be in R7C89, 7 of {2678} must be in R8C9 (step 15c) -> no 6 in R8C9

[Now for the step which I hadn’t spotted as the continuation from step 14. Step 16b results from the hard work in step 15.]
16. 7,9 in R8 only in R8C4579
16a. 45 rule on R89 4 innies R8C4579 = 24 = {2679/3579} (only combinations which contain both of 7,9), no 1,4,8, clean-up: no 5 in R7C7
16b. R8C4579 = {3579} (only remaining combination because 15(3) cage at R7C4 cannot contain both of 2,6 since no 7 in R7C4), locked for R8

17. R8C45 are both odd -> R7C4 must be odd = {135}
17a. 15(3) cage at R7C4 = {159/357}, 5 locked for N8, clean-up: no 2 in R7C1 (step 4)

18. Hidden killer pair 7,9 in 15(3) cage at R7C4 and R9C456 for N8, 15(3) cage contains one of 7,9 -> R9C456 must contain one of 7,9
18a. Hidden killer pair 7,9 in R9C456 and R9C7 for R9, R9C456 contains one of 7,9 -> R9C7 = {79} -> R6C9 = {68} (step 5)

19. 10(3) cage at R6C6 = {127/136}, no 4, CPE no 1 in R89C6

20. R9C7 = 1 outie R6C9 + 1 (step 5)
20a. R7C89 + R8C9 + R9C7 {step 15a) = {1679/3479/3578} (cannot be {1589} which clashes with R6C9 + R9C7 = [89], cannot be {2489/2678} because 2,4,6,8 only in R7C89), no 2
20b. 2 in N9 only in 9(3) cage at R8C8 = {126/234}, no 5

21. R6C6 + R9C7 = R9C4 + 5 (step 9)
21a. R6C6 + R9C7 cannot be [17/19] because no 3,5 in R9C4 -> no 1 in R6C6

22. 10(3) cage at R6C6 (step 19) = {127/136}, 1 locked for R7 and N8, clean-up: no 4 in R9C4 (step 4)

23. 15(3) cage at R7C4 (step 17a) = {357} (only remaining combination), locked for N8, 7 also locked for R8, clean-up: no 4 in R7C1 (step 4), no 6 in R7C7

24. R9C7 = 7 (hidden single in N9), R6C9 = 6 (step 5), clean-up: no 6 in R1C6 (step 3), no 2 in R3C8

25. 9(3) cage at R8C8 = {126} (hidden triple in N9), 6 locked for C8, clean-up: no 3 in R3C7

26. R7C56 = {12} (hidden pair in R7), locked for N8, R6C6 = 7 (cage sum), clean-up: no 7 in R3C9 (step 3)
26a. R6C6 + R9C7 = R9C4 + 5 (step 9), R6C6 + R9C7 = [77] = 14 -> R9C4 = 9, R7C1 = 6 (step 4)

27. 17(4) cage at R8C3 contains 9 = {1259/1349}, no 8, 1 locked for N7

28. 15(3) cage at R8C1 = {258/348}
28a. 3,5 only in R9C1 -> R9C1 = {35}
28b. 8 in R9 only in R9C56, locked for N8

29. 45 rule on N36 2 outies R14C6 = 12 = {39} (only remaining combination, cannot be {48} which clashes with R89C6, ALS block) -> R1C6 = 9, R4C6 = 3, R3C9 = 9 (step 3), clean-up: no 2 in R2C3

30. R8C7 = 9 (hidden single in N9), R7C7 = 4, clean-up: no 5 in R3C8

31. 9(3) cage at R4C6 = {135} (only remaining combination), 1,5 locked for C7 and N6, clean-up: no 4,8 in R3C8

32. 16(4) cage at R5C1 contains 6 = {1267/1456/2356}, no 8,9

33. 45 rule on N5 2 remaining innies R46C4 = 10 = [28/64/82]
33a. 45 rule on N4 1 innie R4C1 = 1 remaining outie R6C4 + 1 -> R4C1 = {59}, R6C4 = {48}, clean-up: no 8 in R4C4
33b. R4C1 = R1C3 + 1 (step 2), R4C1 = {59} -> R1C3 = {48}

34. 26(4) cage at R3C9 = {2789} (only remaining combination), 2,7,8 locked for N6 -> R6C7 = 3, R56C8 = {49}, locked for C8
34a. Naked triple {268} in R123C7, locked for N3

35. 24(4) cage at R1C6 contains 9 = {1689/2589/2679} (cannot be {3579} because 3,5,7 only in R1C8), no 3

36. 13(3) cage at R3C4 = {238/247/256/346} (cannot be {148/157} because R4C4 only contains 2,6), no 1

37. 16(3) cage at R5C3 = {178/268/358/457} (cannot be {169/259/367} because R6C4 only contains 4,8, cannot be {349} which clashes with R6C8), no 9
[I didn’t spot that 16(3) cage = {457} clashes with 16(4) cage at R5C1, placing R6C4 immediately.]
37a. R6C4 = {48} -> no 4,8 in R56C3
37b. 6,7 of {178/267} must be in R5C3 -> no 1,2 in R5C3
37c. 5 of {358/457} must be in R6C3 -> no 5 in R5C3

38. 8 in N4 only in 18(3) cage at R4C2 = {189/468} (cannot be {378} = {78}3 which clashes with R4C89, ALS block), no 2,3,5,7
38a. 7 in R4 only in R4C89, locked for N6

39. R47C3 = R9C2 + 10 (step 12)
39a. Max R9C2 = 5 -> max R47C3 = 15, no 9 in R4C3
39b. R4C3 = {468} is even, R7C3 = {79} is odd -> R9C2 must be odd = {135}

40. 9 in C1 only in 19(4) cage at R2C1 = {1279/1369/1459/2359}, no 8

41. 18(3) cage at R4C2 (step 38) = {468} (only remaining combination, cannot be {189} because R4C1 + 18(3) cage = 5{189} clashes with 16(4) cage at R5C1), locked for N4, clean-up: no 2 in R6C3 (step 37)

42. Naked triple {125} in R6C123, locked for R6 and N4 -> R4C1 = 9, R1C3 = 8 (step 2), clean-up: no 3 in R23C3
42a. R6C4 + R7C1 = R4C1 + 5 (step 7), R4C1 = 9, R7C1 = 6 -> R6C4 = 8, R4C4 = 2 (step 33)

43. R5C29 = [82] (hidden pair in R5), R9C9 = 1
43a. R8C3 = 1 (hidden single in N7), R6C3 = 5, R6C12 = {12}, R5C1 = 7 (cage sum), R5C3 = 3, clean-up: no 6 in R23C3
43b. R4C3 = 6 (hidden single in C3), R4C2 = 4, R8C2 = 2, R89C8 = [62], R8C6 = 4, R8C1 = 8, R9C1 = 5 (cage sum), R9C23 = [34], R6C12 = [21], clean-up: no 7 in R23C3

44. R23C3 = [92], clean-up: no 7 in R3C8
44a. 19(4) cage at R2C1 (step 40) = {1369/1459}, no 7, 1 locked for N1

45. 7 in R3 only in 13(3) cage at R3C4 (step 36) = {247} (only remaining combination), 4,7 locked for R3 and N2
45a. Naked pair {13} in R3C18, locked for R3

46. 8 in N2 only in 16(3) cage at R2C5 = {268/358}, no 1
46a. 3 of {358} must be in R2C5 -> no 5 in R2C5
46b. 2 of {268} must be in R2C6 (R23C6 cannot be [68] which clashes with R9C6) -> no 2 in R2C5, no 6 in R2C6
46c. 3,6 in R2C5 -> R2C5 = {36}
46d. 8 in N2 only in R23C6, locked for C6 -> R9C56 = [86]
46e. Naked pair {15} in R5C67, locked for R5
46f. R2C67 = {28} (hidden pair in R2)

47. 17(4) cage at R1C3 = {1268/1358}
47a. 2 of {1268} must be in R1C5, 1 of {1358} must be in R12C4 (R12C4 cannot be {35} which clashes with R7C4) -> no 1,6 in R1C5
47b. 6 of {1268} must be in R2C4 (R1C45 cannot be [62] which clashes with R1C8), no 6 in R1C4
47c. 6 in N2 only in R2C45, locked for R2

48. 2 in N3 only in 24(4) cage at R1C6 (step 35) = {2589/2679}, no 1
48a. R1C4 = 1 (hidden single in R1)

49. 45 rule on R12 3 remaining innies R2C156 = 12 = {138/246}
49a. 3 of {138} must be in R2C5 -> no 3 in R2C1

50. 12(3) cage at R1C9 = {147/345}
50a. 7 of {147} must be in R2C89 (R2C89 cannot be {14} which clashes with R2C1), no 7 in R1C9
50b. 5 of {345} must be in R2C89 (R2C89 cannot be {34} which clashes with R2C156), no 5 in R1C9

51. Naked pair {34} in R1C9, locked for R1, clean-up: no 5 in R2C4 (step 47)
51a. Naked pair {36} in R2C45, locked for R2
51b. 5 in C4 only in R78C4, locked for N8

52. 24(4) cage at R1C6 (step 48) = {2679} (only remaining combination, cannot be {2589} which clashes with R1C5) -> R1C78 = [67], R2C7 = 2, R3C7 = 8, R3C8 = 1, R23C6 = [85], R2C5 = 3 (cage sum)

and the rest is naked singles.

I'll rate my walkthrough at Hard 1.5.
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Ed
PostPosted: Tue Jul 15, 2008 8:32 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Assassin 79 by Ruud (Nov 07)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:3328:1537:1537:1537:6404:6404:6406:6406:6406:3328:3338:3339:3339:3339:6404:6404:2064:6406:3602:3338:3604:3604:3094:3094:2064:2064:4634:3602:3602:3602:8222:8222:3094:4897:4897:4634:5156:4645:1574:1574:8222:1577:1577:4897:4634:5156:4645:4645:1840:8222:8222:4403:4403:4403:5156:3127:3127:1840:1840:3899:3899:1853:4403:4159:3127:7489:7489:4419:4419:4419:1853:2119:4159:4159:4159:7489:7489:3917:3917:3917:2119:
Solution: 
+-------+-------+-------+
| 4 2 1 | 3 9 5 | 7 6 8 |
| 9 6 5 | 7 1 8 | 3 2 4 |
| 3 7 8 | 6 4 2 | 1 5 9 |
+-------+-------+-------+
| 1 8 2 | 9 5 6 | 4 7 3 |
| 7 9 4 | 2 3 1 | 5 8 6 |
| 5 3 6 | 4 8 7 | 9 1 2 |
+-------+-------+-------+
| 8 4 7 | 1 2 9 | 6 3 5 |
| 2 1 9 | 5 6 3 | 8 4 7 |
| 6 5 3 | 8 7 4 | 2 9 1 |
+-------+-------+-------+
Quote:
Afmob: made mistakes somewhere and had to start over again twice..Rating: 1.0
gary w: no severe combo crunching needed
Andrew: My solution seems to have taken a bit longer than some of the others. I missed a few things and was slow to spot others ..I'll rate it as a moderate to harder 1.0
azpaull: I enjoyed this - as I do any Assassin that I can finish! Because it took less combo-crunching, I'll put this at a fun 0.75! (Keep mixin' 'em up, Ruud!)
Walkthrough by sublue with no miracle guesses:
I get to be first, with no miracle guesses this time!
Thanks to Afmob and Andrew for correcting typos!
Prelims:
a) N1: Two 13(2) no 1,2,3
b) N12: 6(3) no 4,5,6,7,8,9
c) N12: 14(2) no 1,2,3,4,7
d) N14: 14(4) no 9
e) N3: 8(3) no 6,7,8,9
f) N47: 20(3) no 1,2
g) N5: 32(5) no 1
h) N45 and N56: 6(2) no 3,6,7,8,9
i) N58: 7(3) no 3,5,6,7,8,9
j) N6: 19(3) no 1
k) N78: 29(4) no 1,2,3,4,6
l) N89: 15(2) no 1,2,3,4,5
m) N9: 7(2) no 7,8,9
n) N9: 8(2) no 4,8,9

Solving:
1) R1C234 6(3) = {123} locked for R1

2) N3: 8(3) 1 locked for N3.

3) R5: locked quad {1245} in the two 6(2) for R5.

4) R12: 2 innies R2C28 = 8 -> R2C2 = {567}, R2C8 = {123}
a) R3C2 = {678}

5) R89: 2 innies R8C28 = 5 -> R8C28 = {1234}
a) R7C8 = {3456}

6) N5: 4 innies R45C6 + R56C4 = 13.
a) R4C6 = {36} -> r3c56 NO 3,6,9
b) 1,4 locked into R5C46 and R6C4 for N5

7) N78: 29(4) {5789} locked
a) R8C56 no 5,7,8,9

8) C1: 4 innies: R3489C1 = 12 -> R3489C1 no 7,8,9

9) N3: 2 innies: R2C7+ R3C9 = 12 - > R2C7 and R3C9 no 2,6

10) N7: 2 innies R7C1 + R8C3 = 17 -> R7C1 and R8C3 = {89} locked for N7
a) Cleanup: R7C6 no 7 -> R7C7 no 8 because of the 29(4). R9C6 no 5,7.

11) R789: 2 innies and 1 outie R7C19 = R6C4 + 9 -> R7C9 = {12345}

12) 9 locked in N4 R56C2 n/e.

13) N47: 2 innies and 1 outie: R58C3 = R3C1 +10 -> R5C3 no 1 -> R5C4 no 5, R3C1 no 5,6

14) R567C4 = {124} triple locked for C4
a) Cleanup: R1C4 = 3
b) R1C23 no 3 -> {12} locked for N1

15) N1: 3 innies R23C3 + R3C1 = 16 -> R2C3 no 6,9

16) N12: 13(3) R2C3 no 8, R2C5 no 5,6,7,8,9

17) N89: 17(3) r8C7 = {789} R8C56 no 1,2. 6 locked into R8C56 for N8, R8. R8C7 no 9
a) Cleanup: R9C9 no 2, R7C7 no 9.

18) N8: Quad {5789} at R7C6 and R8C4 and R9C45 -> no 8,9 at R9C6

19) N89: 15(3) R9C78 no 1. 9 locked into R9C78 -> R9C78 no 3,6,7,8

20) N9: R8C7 = 8 since n/e.
a) Cleanup: R8C3 = 9
b) R7C1 = 8
c) R3C4 no 5
d) R12C1 no 5
e) R7C6 = 9
f) R56C1 = [75]
g) R12C1 = {49} locked for C1
h) R5C34 = {24} locked for R5
i) Remainder of puzzle continues to be cleanup, simple sums, hidden and naked singles.
Walkthrough by Afmob:
This one was special since it led to my shortest walkthrough I've written so far. Normally I need some hours to solve Ruud's Assassins but this time it took me about 40 minutes, but more like 2 hours :lol: since I've made mistakes somewhere and had to start over again twice.

Edit: Made a mistake in the beginning which led to a quicker solution. Thanks to Andrew, I corrected it. So after rewriting my walkthrough I still managed to make it my shortest one so far, but it's a bit longer than my first path.

Let's see how demanding the RP version is.

A79 Walkthrough:

1. R789
a) Innies R89 = 5(2) = {14/23}
b) 29(4) = {5789} locked between R8+N8 -> R8C56 <> 5,7,8,9
c) 17(3): R8C7 = (789) because R8C56 <= 10
d) 6 locked in 17(3) = 6{29/38/47} for R8+N8 because (789) only possible @ R8C7
e) 7(2): R7C8 <> 1,2
f) 8(2): R9C9 <> 2
g) Innies N7 = 17(2) = {89} locked for N7
h) 29(4) = {5789} -> 5,7 locked for N8
i) Naked pair (89) locked in R7C16 for R7

2. R789 !
a) ! 15(3) must have 8 xor 9 because it's only possible there and @ R8C7 for N3
-> R8C7 = (89)
b) 17(3) = 6{29/38}
c) Killer pair (23) of 17(3) blocks {23} of Innies R89 = 5(2)
d) Innies R89 = 5(2) = {14} locked for R8
e) 7(2) = [34/61]
f) 8(2): R9C9 <> 7
g) Innies N9 = 30(5) = 89{157/247/256}, {34689} blocked by Killer pair (36) of 7(2)
h) Innies N9 must have 6 xor 7 and R7C7 = (67) -> R7C9+R9C78 <> 6,7

3. R123
a) Innies N3 = 12(2) <> 1,2,6
b) 6 locked in 25(4) @ N3 = 6{289/379/478}
c) Innies R12 = 8(2) = [53/62/71]
d) 13(2): R3C2 <> 4,5,9

4. N4
a) Outies N4 = 13(2+1): R3C1+R5C4 <> 5,6,7,8,9 because R7C1 >= 8
b) 6(2) @ N4: R5C3 <> 1

5. C1234
a) Naked triple (124) locked in R567C4 for C4
b) 6(3) = {123} -> R1C4 = 3, {12} locked for N1+R1
c) Outies N4 = 13(2+1): R5C4 <> 4 because R37C1 >= 11
d) 6(2) = [42/51]
e) 9 locked in R56C2 for N4
f) 18(3) = 9{18/27/36} because {459} blocked by R5C3 = (45)

6. N36
a) Outies N6 = 15(2+1): R3C9 <> 3,4,5 because R5C6+R7C9 <= 10 and {55}+5 impossible
b) Innies N3 = 12(2) = [39/48/57]

7. R456 !
a) ! Innies+Outies R123: -6 = R4C6 - R3C19
-> R4C6 <> 1,2,3 because R3C19 >= 10
b) 3 locked in 32(5) = {35789} locked for N5
c) Hidden Single: R4C6 = 6 @ N5, R8C5 = 6 @ N8
d) 12(3) = 6{15/24}

8. R123 !
a) ! Killer pair (45) locked in 12(3)+8(3) for R3
b) 14(2) = {68} locked for R3
c) R3C2 = 7 -> R2C2 = 6, R3C3 = 8
d) 13(2) = {49} locked for C1+N1
e) Innies N3 = 12(2) = [39] -> R3C9 = 9, R2C7 = 3
f) 25(4) @ N2 = {3589}, {589} locked for N2

9. N45
a) 20(3) = {578} -> R7C1 = 8, {57} locked for C1+N4
b) R5C3 = 4 -> R5C4 = 2
c) R5C6 = 1 -> R5C7 = 5

10. N69
a) Outies N6 = 15(2+1) -> R7C9 = 5
b) R7C6 = 9 -> R7C7 = 6
c) 8(2) = {17} -> R9C9 = 1, R8C9 = 7
d) 18(3) = {369} -> R4C9 = 3, R5C9 = 6

11. Rest is singles.

Rating: 1.0
Neat start solution by gary w:
A nice one..no severe combo crunching needed.And a neat start possible...


1.O-I N1245 -> R2C7+R7C1=R5C6+R6C4+6 and r7c1=8/9
2.I N5 =13/4 and this,together with constraints from the two 6(2) cages means that r5c6+r6c4=6 max (other combos impossible)
3.r2c7+8/9=12 max thus r2c7=3/4 (innies N3=12/2) r3c9=8/9
4.O-I N123 r3c19=r4c6+6
5.O-I N12 r3c1+6=r2c7+r4c6
6.Now only options for r4c6=3/6
6a if 3 -> r2c7=4 r3c1=1 and r3c9=8
6b now cannot complete 14(2) cage N12 and 8(3) cage N3
7.Thus r4c6=6
8.Thus r2c7=r3c1 (5. above) and also =r1c4
8a thus all these must=3 and r3c9=9
9. I r12 r2c28=8 -> 13(2) cage r23c2={67}
9a thus r3c4=6 r3c3=8 r8c3=9 r1c7=8

Mop up now


Regards

Gary
Walkthrough by Andrew:
My solution seems to have taken a bit longer than some of the others. I missed a few things and was slow to spot others that I ought to have seen earlier, in particular I ought to have seen step 23, my breakthrough move, earlier.

I'll rate it as a moderate to harder 1.0.

Here is my A79 walkthrough.

Prelims

a) R12C1 = {49/58/67}, no 1,2,3
b) R23C2 = {49/58/67}, no 1,2,3
c) R3C34 = {59/68}
d) R5C34 = {15/24}
e) R5C67 = {15/24}
f) R7C67 = {69/78}
g) R78C8 = {16/25/34}, no 7,8,9
h) R89C9 = {17/26/35}, no 4,8,9
i) R1C234 = {123}, locked for R1
j) 8(3) cage in N3 = 1{25/34}, 1 locked for N3
k) 19(3) cage in N6 = {289/379/469/478/568}, no 1
l) R567C1 = {389/479/569/578}, no 1,2
m) 7(3) cage at R6C4 = {124}, CPE no 1 in R89C4
n) 14(4) cage at R3C1 = {1238/1247/1256/1346/2345}, no 9
o) 29(4) cage at R8C3 = {5789}, CPE no 5,7,8,9 in R8C56
p) 32(5) cage in N5 = {26789/35789/45689}, no 1, 8,9 locked for N5

1. Naked quad {1245} in R5C3467, locked for R5

2. 45 rule on R12 2 innies R2C28 = 8 = [53/62/71], clean-up: no 4,5,9 in R3C2

3. 45 rule on R89 2 innies R8C28 = 5 = {14/23}, clean-up: no 1,2 in R7C8

4. 45 rule on N7 2 innies R7C1 + R8C3 = 17 = {89}, locked for N7
4a. 5,7 of 29(5) cage locked in R8C4 + R9C45, locked for N8, clean-up: no 8 in R7C7

5. Killer pair 8,9 in R7C1 and R7C67, locked for R7

6. 45 rule on N3 2 innies R2C7 + R3C9 = 12 = {39/48/57}, no 2,6

7. R8C567 = {269/368/467} (cannot be {179/278/359/458} because 5,7,8,9 only in R8C7), no 1, 6 locked for R8C567, clean-up: no 2 in R9C9
7a. 7,8,9 only in R8C567 -> R8C7 = {789}
7b. 6 locked in R8C56, locked for N8, clean-up: no 9 in R7C7
7c. Killer pair 8,9 in R8C4 + R9C45 and R7C6, locked for N8

8. 45 rule on C1234 3 outies R279C5 = 1 innie R4C4 + 1
8a. Min R279C5 = 8 -> min R4C4 = 7
8b. Max R4C4 = 9 -> max R279C5 = 10 -> max R27C5 = 5, R2C5 = {1234}
8c. Min R27C5 = 3 -> max R9C5 = 7

9. 3 in C4 locked in R12C4, locked for N2
9a. 6 in C4 locked in R23C4, locked for N2

10. R279C5 = R4C4 + 1 (step 8)
10a. R279C5 = {125/127/145}, 1 locked in R27C5 for C5
10b. R279C5 = 8 or 10 -> no 8 in R4C4

11. 45 rule on C1 4 innie R3489C1 = 12 = 12{36/45}, no 7,8,9

12. R567C1 = {389/479/578} (cannot be {569} which clashes with R12C1), no 6
12a. 4,5 of {479/578} must be in R6C1 -> no 7 in R6C1

13. 45 rule on R789 2 innies R7C19 = 1 outie R6C4 + 9
13a. Max R6C4 = 4 -> max R7C19 = 13, max R7C9 = 5

14. 45 rule on R89 3 outies R7C238 = 14 = {257/347/356} (cannot be {167} which clashes with R7C7), no 1

15. Hidden killer quad 5,7,8,9 in R8C19, R8C34 and R8C7 -> R8C19 must contain 5/7
15a. 5 in R8 locked in R8C149
15b. 45 rule on R9 4 outies R8C1349 = 23 = {1589/2579/3578}, no 4

16. Hidden killer pair 8,9 in R8C7 and R9C78 for N9, R9C78 must contain 8/9 (cannot contain both) -> R8C7 = {89}, clean-up: no 4 in R8C56 (step 7)
16a. R9C678 = {159/168/249/258/348} (cannot be {267/357/456} which don’t contain 8,9), no 7
16b. 1 of {159/168} must be in R9C6 -> no 1 in R9C78

17. Naked pair {89} in R8C37, locked for R8
17a. Naked pair {57} in R8C4 + R9C5, locked for N8

18. 4 in R8 locked in R8C28 = {14}, locked for R8, clean-up: no 4,5 in R7C8, no 7 in R9C9

19. R7C238 (step 14) = {347/356} (cannot be {257} because R7C8 only contains 3,6) = 3{47/56}, no 2, 3 locked for R7

20. 45 rule on N5 4 innies R4C4 + R5C46 + R6C4 = 13 = {1246/1345} (cannot be {1237} because 3,7 only in R4C4) = 14{26/35}, no 7, 4 locked for N5
20a. 3,6 only in R4C4 -> R4C4 = {36}

21. 12(3) cage at R3C5 = {138/156/237/246/345} (cannot be {129/147} because R4C4 only contains 3,6), no 9
21a. 1 of {138} must be in R3C6 -> no 8 in R3C6

22. 25(4) cage at R1C5 = {1789/3589/4579}, no 2

23. 45 rule on N4 2 outies R37C1 = 1 innie R5C3 + 7
23a. Min R37C1 = 9 -> min R5C3 = 2, clean-up: no 5 in R5C4
23b. Max R5C3 = 5 -> max R37C1 = 12, max R3C1 = 4

24. Naked triple {124} in R567C4, locked for C4 -> R1C4 = 3
24a. Naked triple {12} in R1C23, locked for N1

25. Min R2C45 = 6 -> max R2C3 = 7

26. 3 in N1 locked in R2C3 + R3C1
26a. 45 rule on N1 3 remaining innies R2C3 + R3C13 = 16 = {349/358/367}
26b. 8 of {358} must be in R3C3 -> no 5 in R3C3, clean-up: no 9 in R3C4
26c. 7 of {367} must be in R2C3 -> no 6 in R2C3

27. 45 rule on N6 2 outies R37C9 = 1 innie R5C7 + 9
27a. Min R37C9 = 10 -> no 3,4,5 in R3C9 (R37C9 cannot be [55]), clean-up: no 7,8,9 in R2C7

28. 25(4) cage at R1C5 (step 22) = {3589/4579} (cannot be {1789} because only 3,4,5 in R2C7), no 1, 9 locked for N2, CPE no 5 in R2C4

29. R2C345 = {148/157/238/247/256/346}
29a. 7 of {157/247} must be in R2C4 -> no 7 in R2C3, clean-up: no 6 in R3C3 (step 26a), no 8 in R3C4

30. Killer pair 8,9 in R38C3, locked for C3

31. Hidden killer pair 1,2 in R2C5 and R3C56 for N2, R3C56 must contain 1/2 (cannot contain both) -> R2C5 = {12}

32. 45 rule on C123 6 innies R1C2 + R12358C3 = 29, R1C23 = 3, R38C3 = 17 -> R25C3 = 9 = {45}, locked for C3, clean-up: no 4 in R5C4

33. R3C1 = 3 (hidden single in N1)

34. R567C1 (step 12) = {479/578} -> R5C1 = 7, clean-up: no 6 in R12C1
34a. 4,5 only in R6C1 -> R6C1 = {45}

35. Killer pair 4,5 in R12C1 and R6C1, locked for C1 -> R8C1 = 2, clean-up: no 9 in R8C7 (step 7), no 6 in R9C9

36. R8C7 = 8 (naked single), R8C3 = 9, R9C4 = 8, R7C6 = 9, R7C7 = 6, R78C8 = [34], R7C1 = 8, R6C1 = 5, R5C34 = [42], R4C6 = 6, R5C6 = 1 (both step 20), R5C7 = 5, R6C4 = 4, R7C12 = [12], R7C9 = 5, R7C23 = [47], R8C2 = 1, R8C56 = [63], R9C6 = 4, R89C9 = [71], R8C4 = 5, R9C5 = 7, R3C34 = [86], R2C345 = [571], R1C23 = [21], R23C2 = [67], R4C123 = [182], R9C123 = [653], R4C4 = 9, R3C9 = 9, R2C8 = 2, R9C78 = [29], R2C6 = 8, R1C6 = 5, R3C56 = [42], R1C5 = 9, R12C1 = [49], R3C78 = [15], R1C7 = 7, R6C36 = [67], R4C8 = 7

37. R5C2 = 9 (hidden single in R5)

and the rest is naked singles and cage sums
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Ed
PostPosted: Tue Jul 15, 2008 8:36 am 
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Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Assassin 79 RP by Ruud (Dec 07)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:7424:2561:2561:2561:4868:4868:4614:4614:4614:7424:7424:4619:4619:4619:4868:4868:4112:4614:2578:7424:2068:2068:3350:3350:4112:4112:4890:2578:2578:2578:5918:5918:3350:4129:4129:4890:3876:5925:2854:2854:5918:2345:2345:4129:4890:3876:5925:5925:2864:5918:5918:4659:4659:4659:3876:5431:5431:2864:2864:2107:2107:4157:4659:3647:5431:5185:5185:5699:5699:5699:4157:4157:3647:3647:3647:5185:5185:4685:4685:4685:4157:
Solution: 
+-------+-------+-------+
| 8 3 6 | 1 2 9 | 4 7 5 |
| 9 7 4 | 8 6 5 | 3 1 2 |
| 2 5 1 | 7 3 4 | 9 6 8 |
+-------+-------+-------+
| 4 1 3 | 5 8 6 | 2 9 7 |
| 7 8 2 | 9 1 3 | 6 5 4 |
| 5 6 9 | 4 7 2 | 1 8 3 |
+-------+-------+-------+
| 3 9 8 | 2 5 1 | 7 4 6 |
| 6 4 7 | 3 9 8 | 5 2 1 |
| 1 2 5 | 6 4 7 | 8 3 9 |
+-------+-------+-------+
Quote:
Ruud, lead-in: It is not unsolvable. That's all I want to add...
Para: (RP) is Rejected Pattern. Ruud intended to make an assassin with this pattern but couldn't get the difficulty spot on with this pattern so he changed it a little:
Para: This RP doesn't match up with the 60RP or even 60RP-lite. It is fun to solve
Afmob: But if you find the right moves it doesn't take too long to solve. Estimated rating: 1.5, it had some tricky moves but compared to M2 it's a easier gary w: my solving path was quite short it was difficult to see and the puzzle took me a while to solve. Like Afmob, based on other killers I'd rate it approx. 1.5
Andrew: I found the main challenge was to spot some moves, rather than actual difficulty of the moves. A79RP was easier than Maverick 1 and rate A79RP at 1.5
Walkthrough by Para:
Hi all

This RP doesn't match up with the 60RP or even 60RP-lite. It is fun to solve. The opening is very friendly, but needed some nice moves towards the end.

Walk-through A79-RP

1. 10(3) at R1C2 = {127/136/145/235}: no 8,9

2. R3C34 and R7C67 = {17/26/35}: no 4,8,9

3. 19(3) at R3C9 = {289/379/469/478/568}: no 1

4. R5C34 = {29/38/47/56}: no 1

5. R5C67 = {18/27/36/45}: no 9

6. 11(3) at R6C4 = {128/137/146/236/245}: no 9

7. 21(3) at R7C2 = {489/579/678}: no 1,2,3

8. 14(4) at R8C1 = {1238/1247/1256/1346/2345}: no 9

9. 22(3) at R8C5 = {589/679}: no 1,2,3,4; 9 locked for R8

10. 29(4) at R1C1 = {5789} -> locked for N1
10a. Clean up: R3C4: no 1,3

11. 10(4) at R3C1 = {1234}: pointing -> R56C1: no 1,2,3,4

12. 23(3) at R5C2 = {689} -> locked for N4
12a. 15(3) at R5C1 = {57}[3]: R7C1 = 3; R56C1 = {57} -> locked for C1 and N4
12b. R12C1 = {89} -> locked for C1 and N1
12c. R23C2 = {57} -> locked for C2
12d. 6 in C1 locked for N7
12e. Clean up: R5C4: no 2,3,4,5,6

13. 45 on N7: 1 innie: R8C3 = 7
13a. 21(3) at R7C2 = {489}(last combo) -> locked for N7; 9 locked for R7
13b. R9C3 = 5(hidden)
13c. 22(3) at R8C5 = {589}(last combo) -> locked for R8
13d. R8C2 = 4
13e. R7C23 = {89} -> locked for R7
13f. R567C2 = {689} -> locked for C2
13g. Clean up: R7C67: no 5

14. 45 on R89: 1 outie: R7C8 = 4

15. 1 in N4 locked for R4 and 10(4) at R3C1
15a. 3 in 10(4) at R3C1 -> locked for R4 and N4
15b. Clean up: R5C4: no 6
15c. R5C67 = {18/36/45}: {27} blocked by R5C34: no 2,7

16. 45 on R789: 1 innie and 1 outie: R6C4 + 2 = R7C9: R6C4 = {345}; R7C9 = {567}
16a. 11(3) at R6C4 = [3]{17/26}/[4]{25}: [4]{16} blocked by R7C67: R6C4: no 5
16b. Clean up: R7C9: no 7

17. 45 on R12: 1 innie and 1 outie: R2C8 + 4 = R3C2: R2C8 = {13}
17a. 16(3) at R2C8 = [1]{69/78}/[3]{49/58/67}: R3C78: no 1,2,3

18. 45 on N689: 3 outies: R3C9 + R5C6 + R6C4 = 15: Max R3C9 + R6C4 = 12 -> Min R5C6 = 3: no 1; Min R5C6 + R6C4 = 7 -> Max R3C9 = 8: no 9; Max R5C6 + R6C4 = 12 -> Min R3C9 = 3: no 2
18a. Clean up: R5C7: no 8

19. 13(3) at R3C5 = {13}[9]/{148/157/238/247/256/346}: R3C56: no 9

20. 9 in R3 locked for N3
20a. 9 in R3 locked within 16(3) at R2C8 -> 16(3) = [1]{69}/[3]{49}: no 5,7,8; R3C78 = [49]/{69} = {4|6..}
20b. R3C34 = [17/35]: {26} blocked by R3C1 + R3C78: no 2,6
20c. R3C24 = {57} -> locked for R3

21. 18(3) at R2C3 = {279/369/378/459/468}={8|9..}: {189} blocked by R2C1; {567} blocked by R2C2: no 1
21a. Killer Pair {89} in R2C1 + 18(3) at R2C3 -> locked for R2

22. 45 on N3: 2 innies: R2C7 + R3C9 = 11 = [38/56/74]: R2C7 = {357}; R3C9: no 3

23. 45 on C123: 3 outies and 1 innie: R135C4 + 13 = R2C3 = R135C4 = 15/16/17/19 = [159/357/259/457/179/359/379]: R1C4 = {1234}
23a. 10(3) at R1C2 = {1[6]3}(last combo) -> locked for R1; R1C3 = 6
23b. Naked Pair {13} in R1C2 + R3C3 -> locked for N1
23c. Naked Pair {24} in R25C3 -> locked for C3

24. Hidden Killer Pair {13} in R3C3 + R3C56: R3C56 needs one of {13}
24a. Killer Pair {13} in R1C4 + R3C56 -> locked for N2
24b. 13(3) at R3C5 = {148/238/346}: no 5,7,9

25. 18(4) at R1C7 = {1278/2358/2457}:{1368/1458/1467/2367/3456} blocked by 16(3) at R2C8: no 6
25a. 6 in N3 locked for R3
25b. 18(3) at R2C3 = [2]{79}/[4]{59}/[4]{68}: R2C45 = {59/68/79}= {5|6|7..}: no 2,4

26. Hidden Killer Triple {567} in R3C4 + R2C45 + (R1C56 + R2C6): R1C56 + R2C6 needs one of {567}
26a. 19(4) at R1C5 = {259}[3]/{268}[3]/{246}[7]: {248}[5]/{457}[3] blocked: R1C56 + R2C6 = {259/268/246}: no 7; 2 locked for N2; R2C7: no 5
26b. Clean up: R3C9: no 6

27. 6 in R3 locked within 16(3) at R2C8 -> 16(3) = [1]{69}; R2C8 = 1
27a. R3C2 = 5(step 17); R3C34 = [17]; R1C24 = [31]; R2C27 = [73]; R5C34 = [29]; R4C123 = [413]
27b. R3C1 = 2; R2C3 = 4; R9C2 = 2; R3C9 = 8(step 22)

28. 13(3) at R3C5 = {34}[6]: R4C6 = 6; R3C56 = {34} -> locked for N2
28a. 19(4) at R1C5 = 3{259}(last combo): {259} -> locked for N2; 9 locked for R1
28b. R12C1 = [89]
28c. Clean up: R7C7: no 2

29. 19(3) at R3C9 = 8[74]: 8[56] blocked by R7C9: R45C9 = [74]
29a. R1C7 = 4(hidden); R1C8 = 7(hidden)
29b. Naked Pair {25} in R12C9 -> locked for C9
29c. R7C9 = 6; R6C4 = 4(step 16); R8C8 = 2(hidden); R6C2 = 6(hidden)
29d. R5C2 = 8; R6C3 = 9; R7C23 = [98]; R9C9 = 9(hidden); R8C9 = 1

And the rest is naked and hidden singles.

greetings

Para
Walkthrough by Afmob:
This one started quite promising with some early placements but after that there were only little eliminations you could do. But if you find the right moves it doesn't take too long to solve.

A79 RP Walkthrough:

1. C123
a) 29(4) = {5789} locked for N1
b) 23(3) = {689} locked for N4
c) 10(4) = {1234} locked between C1 and N4 -> R56C1 <> 1,2,3,4
d) 15(3) = {357} -> R7C1 = 3, {57} locked for C1+N4
e) Innies N7 = 10(2) = [37] -> R8C3 = 7
f) 21(3) = {489} locked for N7
g) 10(4) = {1234} -> 3 locked for R4+N4
h) 29(4) = {5789} -> R23C2 = {57} locked for C2
i) 14(4) = {1256} -> R9C3 = 5
j) 8(2): R3C4 <> 1,3
k) 11(2) = [29/47]

2. R789
a) 22(3) = {589} locked for R8
b) Innies+Outies R89: R8C2 = R7C8 = 4
c) 21(3) = {489} -> 8,9 locked for R7
d) 8(2) = {17/26}
e) 11(3): R6C4 <> 5 because R7C45 <> 4
f) Innies+Outies R789: -2 = R6C4 - R7C9
-> R7C9 = (56), R6C4 = (34)
g) 16(4) = 4{129/138/237}
h) 16(4) must have 7,8 xor 9 and it's only possible @ R9C9 -> R9C9 = (789)

3. R45
a) 1 locked in 10(4) for R4; R3C1 <> 1
b) Killer pair (27) of 11(2) blocks {27} of 9(2)
c) 19(3) <> 5 because {568} blocked by R7C9 = (56)

4. R123
a) Innies+Outies R12: 4 = R3C2 - R2C8
-> R2C8 = (13)
b) 16(3): R3C78 <> 1,2,3 because R2C8 <= 3
c) Innies N3 = 11(2) -> R2C7 <> 1,6
d) 10(3): R1C4 <> 2,4 because R1C23 <> 5,7
e) 13(3): R3C56 <> 9 because R4C6 <> 1,3
f) 9 locked in R3C789 for N3
g) Innies N3 = 11(2): R3C9 <> 2

5. N36
a) Innies+Outies: -3 = R7C9 - R25C7; R7C9 = (56)
-> R5C7 <> 8 because R2C9 >= 2
b) 9(2): R5C6 <> 1

6. C123
a) Hidden pair (89) in R67C3 for C3 -> R6C3 <> 6
b) 6 locked in R56C2 for C2
c) 18(3) <> 1 because {189} blocked by R2C1 = (89)
d) 18(3): R2C45 <> 2 because R2C3 <= 6

7. N3689 !
a) ! Outies N689 = 15(2+1): R3C9 <> 9 because R5C6+R6C4 >= 7
b) 9 locked in 16(3) @ N3 = 9{16/34}
c) Innies N3 = 11(2) <> 2
d) 2 locked in 18(4) @ N3 = 2{178/358/367/457}
e) 18(4) @ N3 <> 6 because {2367} blocked by Killer pair (36) of 16(3) @ N3

8. R123
a) 6 locked in R3C789 for R3
b) 8(2) <> 2
c) Naked pair (57) locked in R3C24 for R3
d) 10(3): R1C4 <> 6 because R3C3 = (13) blocks {136}
e) Innies N3 = 11(2): R2C7 <> 4

9. N1234 !
a) Outies N124 = 18(2+1): R2C7 <> 8 since R5C4+R4C6 can't be 10(2) because R4C6 <> 1,3
b) Innies N3: R3C9 <> 3
c) 19(3) <> 3 because R3C9 = (468)
d) ! Innies+Outies N14: 13 = R135C4 - R2C3
-> R1C4 <> 5,7 because R135C4 would be 21 but R2C3 <= 6
e) 10(3) = {136} -> R1C3 = 6; {13} locked for R1
f) Naked pair (13) locked in R1C2+R3C3 for N1
g) 18(3) = {279/459/468} because R2C3 = (24) -> R2C45 <> 3,4
h) 1,3 locked in R2C789 for R2

10. N23 !
a) 1,3 only possible @ R1C4 + 13(3) for N2 -> 13(3) must have 1 xor 3
-> 13(3) = {148/238/346}, {157} impossible because R3C56 <> 5,7
b) ! 19(4): R2C7 <> 5 because R1C56+R2C6 <> 3 and R1C56+R2C6 = {248}
would leave no combo for 13(3)
c) Killer pair (37) locked in 18(4)+R2C7 for N3
d) 16(3) = {169} -> R2C8 = 1, {69} locked for N3

11. R123
a) Outies R12 = 20(3) = {569} -> R3C2 = 5
b) R2C2 = 7, R3C4 = 7 -> R3C3 = 1
c) 18(3) = 4{59/68} -> R2C3 = 4
d) R2C7 = 3
e) 18(4) = {2457} locked for N3
f) R3C9 = 8, R5C3 = 2, R5C4 = 9
g) 19(3) = {478}, {47} locked for C9+N6

12. N89
a) 16(4) = {1249} -> R9C9 = 9, R8C8 = 2, R8C9 = 1
b) 18(3) = 8{37/46} -> 8 locked for R9
c) 20(4) = {3467}, {346} locked for N8
d) 18(3) = {378} -> R9C8 = 3
e) Hidden Single: R8C4 = 3 @ N8
f) 11(3) = {245}, R6C4 = 4, {25} locked for R7+N8
g) Hidden Single: R6C9 = 3 @ C9
h) 18(4) = {1368} -> R7C9 = 6, R6C8 = 8, R6C7 = 1

13. Rest is singles.

Estimated rating: 1.5, it had some tricky moves but compared to M2 it's easier.
Walkthrough by Andrew:
As Para has said, this differs from A79 by having Tetris pieces in N1 and N9 which became two 2-cell cages in A79. The Tetris piece in N1 very quickly becomes two 2-cell cages; however the same doesn't happen in N9 making it harder than A79.

I finished this puzzle last week but have only just gone through Para's and Afmob's walkthroughs. They both used outies from N689 which I remember looking at but probably too early and never returned to them later. As a result my solution path was rather different.

I found the main challenge was to spot some moves, rather than actual difficulty of the moves.

Afmob rated this puzzle at 1.5, saying that it was easier than Maverick 2. I haven't yet tried that puzzle so I'll say that A79RP was easier than Maverick 1 and rate A79RP at 1.5.

Here is my walkthrough for A79RP

Prelims

a) R3C34 = {17/26/35}, no 4,8,9
b) R5C34 = {29/38/47/56}, no 1
c) R5C67 = {18/27/36/45}, no 9
d) R7C67 = {17/26/35}, no 4,8,9
e) R1C234 = {127/136/145/235}, no 8,9
f) R345C9 = {289/379/469/478/568}, no 1
g) 23(3) cage in N4 = {689}, locked for N4, clean-up: no 2,3,5 in R5C4
h) 11(3) cage at R6C4 = {128/137/146/236/245}, no 9
i) 21(3) cage in N7 = {489/579/678}, no 1,2,3
j) R8C567 = 9{58/67}, 9 locked for R8
k) 29(4) cage in N1 = {5789}, locked for N1, clean-up: no 1,3 in R3C4
l) 10(4) cage at R3C1 = {1234}, CPE no 1,2,3,4 in R56C1
m) 14(4) cage in N7 = {1238/1247/1256/1346/2345}, no 9

1. Naked pair {57} in R56C1, locked for C1 and N4, R7C1 = 3, clean-up: no 4,6 in R5C4, no 5 in R7C67
1a. Naked pair {89} in R12C1, locked for C1 and N1
1b. Naked pair {57} in R23C2, locked for C2

2. 1 in N4 locked in R4C123, locked for R4 and 10(4) cage -> no 1 in R3C1
2a. 6 in C1 locked in R89C1, locked for N7
2b. 3 in 10(4) cage locked in R4C23, locked for R4 and N4, clean-up: no 8 in R5C4
2c. R5C67 = {18/36/45} (cannot be {27} which clashes with R5C34)

3. 14(4) cage in N7 = {1256} (only remaining combination with 6 in R89C1) -> R9C3 = 5, 1,2 locked for N7
3a. 4 in C1 locked in R34C1, locked for 10(4) cage -> no 4 in R4C23

4. 21(3) cage in N7 = {489}, (only remaining combination), locked for N7 -> R8C3 = 7
4a. 9 in N7 locked in R7C23, locked for R7

5. R8C567 = {589} (only remaining combination), locked for R8 -> R8C2 = 4
5a. Naked pair {89} in R7C23, locked for R7

6. 45 rule on R89 1 remaining outie R7C8 = 4
6a. 16(4) cage at R7C8 = {1249/1348/2347}, no 6
6b. 7,8,9 only in R9C9 -> R9C9 = {789}

7. 45 rule on R12 1 outie R3C2 = 1 innie R2C8 + 4, R2C8 = {13}
7a. Max R2C8 = 3 -> min R3C78 = 13, no 1,2,3

8. Hidden pair {89} in R67C3, no 6
8a. 6 in N4 locked in R56C2, locked for C2

9. 45 rule on N3 2 innies R2C7 + R3C9 = 11 = {29/38/47/56}, no 1

10. 45 rule on N89 1 remaining innie R7C9 = 1 outie R6C4 + 2, R7C9 = {567}, R6C4 = {345}

11. 45 rule on N89 3 innies R7C459 = 13 = {157/256}
11a. {157} must be {17}5 (cannot be {15}7 which would make 11(3) cage 5{15})
11c. {256} = {25}6/{26}5
11d. -> no 7 in R7C9, no 5 in R6C4 (step 10)

12. 45 rule on R123 2 innies R3C19 = 1 outie R4C6 + 4, no 1,3 in R4C6 -> no 3 in R3C9, clean-up: no 8 in R2C7 (step 9)

13. R1C234 = {127/136/145/235}
13a. 5,7 of {127/235} must be in R1C4 -> no 2 in R1C4
13b. 5 of {145} must be in R1C4 -> no 4 in R1C4

14. R2C345 = {279/369/378/459/468} (cannot be {189} which clashes with R2C1, cannot be {567} which clashes with R2C2), no 1
14a. 2 of {279} must be in R2C3 -> no 2 in R2C45

15. Killer pair 8,9 in R2C1 and R2C345, locked for R2, clean-up: no 2 in R3C9 (step 9)

16. 45 rule on N5 4 innies R45C6 + R56C4 = 22 = {1489/2389/3469/3478/4567} (cannot be {1579/1678/2569/2578} because R6C4 only contains 3,4, cannot be {2479} because 2,7,9 only in R4C6 + R5C4, cannot be {3568} because R5C4 only contains 7,9)
16a. 7,9 must be in R5C4 -> no 7,9 in R4C6
16b. 23(5) cage in N5 must contain 2/4, 6/8 and 7/9

17. R3C19 = R4C6 + 4 (step 12), no 7,9 in R4C6 -> no 9 in R3C9, clean-up: no 2 in R2C7 (step 9)

18. 45 rule on R1 3 outies R2C679 = 1 innie R1C1 + 2
18a. R1C1 = {89} -> R2C679 = {127/145/146/235/236/245} (cannot be {136/137} which clash with R2C8)
18b. 7 of {127} must be in R2C7 -> no 7 in R2C69

19. 45 rule on N36 2 innies R25C7 = 1 outie R7C9 + 3, max R7C9 = 6 -> max R25C7 = 9, no 8 in R5C7, clean-up: no 1 in R5C6

20. 1 in N5 locked in 23(5) cage = {12389/12569/12578/14567} (cannot be {12479} which clashes with R5C4, cannot be {13469/13478} which clash with R6C4, cannot be {13568} because must contain 7/9)

21. 18(4) cage at R6C7 = {1269/1359/1368/1458/1467/2358/2367/2457} (cannot be {1278/2349} because R7C9 only contains 5,6, cannot be {3456} which clashes with R6C4)
21a. R7C9 = {56} -> no 5,6 in R6C789
21b. R7C9 = R6C4 + 2 (step 10) -> 18(4) cage cannot contain {35} or {46} eliminating {1359/1467}
21c. -> 18(4) cage = {1269/1368/1458/2358/2367/2457}
21d. Hidden killer quad 1,2,3,4 in R6C4, R6C56 and R6C789 for R6 -> R6C56 must contain one of 1,2,3,4

22. 13(3) cage at R3C5 = {148/157/238/247/256/346} (cannot be {139} because no 1,3,9 in R4C6), no 9

23. 9 in R3 locked in R3C78, locked for N3
23a. 16(3) cage in N3 = 1{69}/[349], no 5,7,8
23b. If [349] -> R3C1 = 2
23c. R3C34 cannot be {26} (steps 23a and 23b) = [17/35]
23d. Naked pair {57} in R3C24, locked for R3, clean-up: no 4,6 in R2C7 (step 9)

24. Hidden killer pair 1,3 in R3C3 and R3C56 for R3 -> R3C56 must contain 1/3
24a. 13(3) cage at R3C5 (step 22) = {148/238/346} (cannot be {256} because no 1,3), no 5

25. R345C9 = {289/469/478} (cannot be {379} because R3C9 only contains 4,6,8, cannot be {568} which clashes with R7C9), no 3,5
25a. If {478} -> R9C9 = 9
25b. -> no 9 in R6C9

26. 45 rule on N6 2 outies R37C9 = 1 innie R5C7 + 8
26a. R37C9 cannot total 12 -> no 4 in R5C7, clean-up: no 5 in R5C6

27. 5 in N5 locked in 23(5) cage (step 20) = {12569/12578/14567}, no 3

28. Hidden killer triple 7,8,9 in 16(3) cage, R45C9 and R6C789 for N6 -> each must contain one of 7,8,9
28a. 8 of {289/478} in R345C9 must be in R3C9 -> no 8 in R45C9
28b. 16(3) cage = {169/259/268/358/367/457} (cannot be {178} which contains 7,8, cannot be {349} which clashes with R45C9)

29. 2 in N3 locked in 18(4) cage = {1278/2358/2457} (cannot be {2367} which clashes with 16(3) cage), no 6
29a. 6 in N3 locked in R3C789, locked for R3

30. R2C2 = {57}, R2C7 = {357} -> R2C345 cannot contain more than one of 3,5,7
30a. R2C345 (step 14) = {279/369/459/468} (cannot be {378} which contains 3 and 7)

31. 7 in N3 in R1C789 or R2C7, CPE no 7 in R1C56
31a. If 7 in R2C7 => R2C679 = {127} => R1C1 = 8 (step 18a) clashes with 18(4) cage (step 29)
31b. -> no 7 in R2C7, clean-up: no 4 in R3C9 (step 9)
31c. 18(4) cage in N3 (step 29) = {1278/2457}, no 3, 7 locked for R1
31d. 3 in N3 locked in R2C78, locked for R2

32. R345C9 (step 25) = {289/469/478}
32a. 6 of {469} must be in R3C9 -> no 6 in R45C9

33. R2C345 (step 30a) = {279/459/468}
33a. Hidden killer pair 2,4 in R2C345 and R2C679 for R2 -> R2C679 must contain one of 2,4
33b. R2C679 (step 18a) = {145/235/236} (cannot be {146} because R2C7 only contains 3,5, cannot be {245} which contains 2 and 4)

34. R25C7 = R7C9 + 3 (step 19), min R7C9 = 5 -> min R25C7 = 8, no 1 in R5C7, clean-up: no 8 in R5C6
[I missed R25C7 = {35/36}, 3 locked in R25C7 for C7. Didn’t make much difference, R2C7 was fixed in step 36b.]

35. R45C6 + R56C4 (step 16) = {3469/3478} (cannot be {2389} because 2,8 only in R4C6), no 2, 4 locked for N5

36. 19(4) cage at R1C5 = {1369/1459/2359/2368/2458} (cannot be {1468} because R2C7 only contains 3,5)
36a. Killer pair 8,9 in R1C1 and R1C56, locked for R1, clean-up: no 1 in 18(4) cage in N3 (step 31c)
36b. 18(4) cage in N3 = {2457}, locked for N3 -> R2C78 = [31], clean-up: no 6 in R5C6

37. R3C9 = 8 (hidden single in N3), R45C9 = {29/47} (step 32)
37a. Killer pair 7,9 in R45C9 and R9C9, locked for C9

38. R7C9 = 6 (hidden single in C9), R6C4 = 4 (step 10), R5C67 = [36], R3C78 = [96], clean-up: no 2 in R7C67
38a. Naked pair {17} in R7C67, locked for R7
38b. Naked pair {25} in R7C45, locked for N8
38c. Naked pair {89) in R8C56, locked for R8 and N8 -> R8C7 = 5

39. 20(4) cage at R8C3 = {3467} (only remaining combination) -> R9C5 = 4
39a. Naked pair {36) in R89C4, locked for C4 and N8
39a. Naked pair {17} in R79C6, locked for C6

40. R1C4 = 1 (hidden single in C4), R1C23 = [36], R3C34 = [17], R23C2 = [75], R5C34 = [29], R2C3 = 4, R3C1 = 2, R3C56 = [34], R4C6 = 6 (step 24a), R4C123 = [413], R9C2 = 2, R5C2 = 8, R6C23 = [69], R7C23 = [98], clean-up: no 2,9 in R4C9, no 7 in R5C9 (both step 37) -> R45C9 = [74], R9C9 = 9, R5C8 = 5, R56C1 = [75], R5C5 = 1

41. Naked pair {25} in R12C9, locked for C9 and N3 -> R1C78 = [47]

42. Naked pair {25} in R2C69, locked for R2 -> R2C4 = 8, R12C1 = [89], R2C5 = 6

43. R8C8 = 2 (hidden single in R8), R4C8 = 9 (hidden single in C8)

44. R8C9 = 1 (cage sum)

and the rest is naked singles
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