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PostPosted: Sat Jul 19, 2008 9:51 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1043
Location: Sydney, Australia
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|
|----------------------+----------------------+----------------------|
|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 1.25 1.50|uA.96 E1.00 0.95| |
|YAK94 H1.25 1.25|uA.96v2 1.75 2.30| |
|====================================================================|
page #4
Old scores 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|
|----------------------+----------------------+----------------------|
|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
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|
|-----------------------------+-----------------------------+-----------------------------|
|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


There was no Assassin 92


unofficial Assassin 93 (UA93) by mhparker (Mar 08)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:2560:4353:3330:6659:6659:1797:1797:4615:4615:2560:4353:3330:3330:6659:6659:1797:6928:4615:6418:4353:6418:3605:1302:1302:6928:6928:4378:6418:6418:6418:3605:5407:5407:6928:4378:4378:5412:3109:3109:3605:5407:5161:1066:1066:4378:5412:5412:5423:5407:5407:5161:7987:7987:7987:5412:5423:5423:1337:1337:5161:7987:3901:7987:3647:5423:4929:6210:6210:3140:3140:3901:1863:3647:3647:4929:4929:6210:6210:3140:3901:1863:
Solution:
+-------+-------+-------+
| 9 8 3 | 4 6 1 | 2 7 5 |
| 1 5 2 | 8 7 9 | 4 3 6 |
| 6 4 7 | 5 2 3 | 8 9 1 |
+-------+-------+-------+
| 2 9 1 | 3 5 4 | 7 6 8 |
| 4 7 5 | 6 9 8 | 3 1 2 |
| 3 6 8 | 2 1 7 | 5 4 9 |
+-------+-------+-------+
| 8 3 9 | 1 4 5 | 6 2 7 |
| 5 1 6 | 7 3 2 | 9 8 4 |
| 7 2 4 | 9 8 6 | 1 5 3 |
+-------+-------+-------+
Quote:
Caida: I did some heavy combo crunching in order to break this puzzle - I'm sure there must be a more elegant solution
Afmob: relaxing Killer. After all those 1.25 and 1.5+ Killers it was really fun to tackle an "Assassin" without spending all your brain power on it :lol: . Rating: 1.0. I didn't mark any key moves but I think using Innie-Outie-Difference you can avoid combo crunching and solve it without any problems
Andrew: The solution really flowed well with my only real work being to put steps in the right order to simplify my solving path. I agree with Afmob's rating of 1.0
gary w: I've actually enjoyed NOT doing an assassin for a couple of weeks. Now I feel a bit fresher and looking forward to future challenges whereas all those 1.25+ brutes were beginning to wear me down!!
mhparker: I was beginning to get concerned that the Assassins were generally becoming too difficult ... In particular, we weren't getting any 1.0-rated puzzles any more.... Indeed, I was even starting to consider producing "Lite" variants instead of V2s at times!
Walkthrough by Caida:
Below is my walkthrough for UA93.

I did some heavy combo crunching in order to break this puzzle - I'm sure there must be a more elegant solution - but I haven't found it yet.

I'm definitely looking forward to seeing other walkthroughs.

Thanks for this puzzle Mike!
I was glad to have it as I have been struggling with Maverick #4 (and may soon have to just take a peek at the posted walkthroughs).

Cheers,

Caida

Edited to correct a small typo - thanks Afmob!
Edited to correct some more typos - thanks Andrew!

UA93 Walkthrough:

Preliminaries:

a. 10(2)n1 = {19/28/37/46} (no 5)
b. 7(3)n23 = {124} (no 3,5..9)
b1. -> r1c89 no 1,2,4 (CPE)
c. 5(2)n2 and n8 = {14/23} (no 5..9)
d. 4(2)n6 = {13} -> locked for n6 and r5
e. 12(2)n4 = {48/57} (no 2,6,9) (1,3 already eliminated by prelim d)
f. 7(2)n9 = {16/25/34} (no 7..9)
g. 19(3)n78 = {289/379/469/478/568} (no 1)
h. 26(4)n2 = {2789/3689/4589/4679/5678} (no 1)
i. 20(3)n58 = {389/479/569/578} (no 1,2)
j. 27(4)n36 = {3789/4689/5679} (no 1,2)


1. Outies c123: r29c4 = 17(2) = {89} (no 1..7)
1a. -> 8,9 locked for c4
1b. -> 13(3)n12 = {14/23}[8]/{13}[9]
1c. -> r12c3 no 5..9

2. 2 locked in n2 in 5(2) and r1c6
2a. -> no 2 elsewhere in n2

3. 26(4)n2 = {4679/5678} no 3
Note: other combos blocked by r2c4
3a. -> 6,7 locked for n2 in 26(4)n2
3b. -> 3 in n2 locked in r3 -> no 3 elsewhere in r3

4. 24(4)n8 = {2679/3579/3678/4569/4578}
Note: other combos blocked by r9c4
4a. -> killer pair {89} locked in n8 in 24(4)n8 and r9c4 -> no 8,9 elsewhere in n8

5. Outies c789: r18c6 = 3(2) = {12} (no 3..9)
5a. -> 1,2 locked for c6
5b. -> r3c5 no 3,4
5c. -> pair {12} locked in n2 in r1c6 and r3c5 -> no 1,2 elsewhere in n2
5d. -> 4 in 7(3)n23 locked in r12c7 -> no 4 elsewhere in c7 and n3

6. 14(3)n25 = [347/374/356/365/437/527/572/536] (no 1)

7. Outies n47: r3c13+r9c4 = 22(2+1) = {59/68}[8]/{49/58/67}[9]
7a. -> r3c13 no 1,2

8. Outies n36: r1c6+r7c79 = 14(1+2) = [1]{49/58/67}/[2]{39/48/57}
8a. -> r7c79 no 1,2

9. Innies n8: r78c6+r9c4 = 16(3) = [718/619/628/529]
9a. -> r7c6 no 3,4
9b. -> r6c6 no 3

10. Innie and Outie r12: r3c2 – r2c8 = 1
10a. -> r3c1 no 1,2,5
10b. -> r2c8 no 9

11. Innie and Outie r89: r7c8 – r8c2 = 1
11a. -> r7c8 no 1
11b. -> r8c2 no 9

12. Outies and Innie n3: r1c6+r4c7 – r3c9 = 7
12a. -> min r3c9 = 1 -> min r1c6+r4c7 = 8 (r4c7 no 5)
12b. -> max r1c6+r4c7 = 11 -> max r3c9 = 4 (r3c9 no 5..9)
12c. -> max r3c9 = 2 -> max r1c6+r4c7 = 9 (r4c7 no 9)
12d. -> triple {124} locked in n3 in r12c7+r3c9 -> no 1,2 elsewhere in n3
12e. 9 in 27(4)n36 locked in r3c78 -> no 9 elsewhere in n3 and r3
12f. 18(3)n3 = {378/567} -> 7 locked for n3
12g. r2c8 and r3c2 no 8 (step 10)
12h. 27(4)n36 = {3789/5679} -> r4c7 = 7
12i. 7 in r3 locked in n1 -> no 7 elsewhere in n1
12j. -> r12c1 no 3

13. pair {12} in n8 locked in 5(2)n8 and r8c6 -> no 1,2 elsewhere in n8

14. Outies n6: r3c9+r7c79 = 14(1+2)
14a. -> r7c9 no 6 (no combo possible)

15. 17(3)n1 = {19}[7]/{58}[4]/{467} (no 3)
Note: combo {29}[6] blocked by 10(2)n1 and combo {38}[6] blocked by 13(3)n12 (10(2)n1 would be {19} and r12c3 would be {24} -> no combo for 13(3)n12 possible) and combo {28}[7} blocked by 13(3)n12 (10(2)n1 = {19} (only place for 9) and r12c3 would be {34} -> no combo possible for 13(3)n12)
15a. -> 3 in n1 locked in r12c3 -> no 3 elsewhere in c3
15b. -> r12c3 no 4
15c. if 17(3)n1 = {179} then 10(2) = {46}; (combo {28} blocked by 13(3)n12) and if 17(2)n1 = {458/467} then 10(2)n1 = {19} (need to use the 9)
15d. -> 4 in n1 is locked in 17(3) or 10(2) -> no 4 elsewhere in n1
15e. 10(2) = {19/46} (no 2,8)
15f. -> r3c13 = {58/67} = 13(2)
15g. -> r9c4 = 9(step 7)
15h. -> r2c4 = 8
15i. -> r12c3 = {23} -> locked for c3 and n1

16. Innies n2: r1c6+r3c4 = 6(2) = [15/24] (no 3)
16a. single: r3c6 = 3
16b. -> r3c5 = 2

I got lazy - but it is all combos and cage sums to the end now
Walkthrough by Afmob with no !!s:
Thanks Mike for providing a relaxing Killer. After all those 1.25 and 1.5+ Killers it was really fun to tackle an "Assassin" without spending all your brain power on it :lol:.

And it's also good to see that other members post their wts as well.

Edit: Fixed some typos and optimized endgame. Thanks Andrew! His hint helped me to make this my shortest wt so far (2nd best: A79).

UA93 Walkthrough:

1. C789
a) Outies = 3(2) = {12} locked for C6
b) 4(2) = {13} locked for R5+N6
c) 7(3) = {124} locked between R1+N3 -> R1C89 <> 1,2,4; 4 locked for C7+N3

2. C123
a) Outies = 17(2) = {89} locked for C4
b) 12(2) <> 9
c) 13(3): R12C3 <> 5,6,7,8,9 because R2C4 = (89)

3. C456
a) 26(4) = 67{49/58} <> 2,3 because R2C4 = (89) blocks 89{27/36/45} -> 6,7 locked for N2
b) 5(2): R3C5 <> 3,4
c) Naked pair (12) locked in R1C6+R3C5 for N2
d) 3 locked in R3C456 for R3
e) Outies N5 = 10(1+1) = [37/46/55]

4. N3
a) Innies+Outies: 7 = R1C6+R4C7 - R3C9 -> R3C9 = (12) because R1C6+R4C7 <= 11
b) Naked triple (124) locked in R12C7 + R3C9
c) Innies+Outies: 7 = R1C6+R4C7 - R3C9 -> R4C7 <> 5,9 because R1C6 and R3C9 = (12)
d) 27(4) = 79{38/56} -> 9 locked
e) 18(3) = 7{38/56} -> 7 locked
f) 27(4) = 79{38/56} -> R4C7 = 7

5. R123
a) 7 locked in R3C123 for N1
b) 10(2) <> 3
c) Naked pair (12) locked in R3C59 for R3
d) Innies+Outies R12: 1 = R3C2 - R2C8 -> R3C2 <> 5,8; R2C8 <> 9
e) 27(4) = 79{38/56} -> 9 locked for R3
f) Innies+Outies R12: 1 = R3C2 - R2C8 -> R2C8 <> 8
g) Outies R12 = 21(3): R3C2 <> 6 because 7 only possible there
h) 17(3) <> 3 because R3C2 = (47)
i) 3 locked in 13(3) = 3{19/28} for C3
j) Innies+Outies R12: 1 = R3C2 - R2C8 -> R2C8 <> 5
k) 27(4) must have 3 xor 6 and R2C8 = (36) -> R3C78 <> 6

6. N12
a) 6 locked in R3C13 for N1 + 25(5)
b) 10(2) <> 4
c) 17(3) must have 4 xor 7 and R3C2 = (47) -> R12C2 <> 4
d) 4 locked in R3C123 for R3
e) 5(2) = [23] -> R3C5 = 2, R3C6 = 3
f) R3C4 = 5 -> 14(3) = 5{27/36}
g) 26(4) = {4679} locked for N2
h) 13(3) = {238} -> R2C4 = 8; 2 locked for C3+N1
i) 7(3) = {124} -> R1C6 = 1; 2 locked for C7
j) 10(2) = {19} -> R1C1 = 9, R2C1 = 1

7. R789
a) 19(3) = {469} -> R9C4 = 9, {46} locked for C3+N7
b) 12(3) = {129} -> R8C6 = 2, R8C7 = 9, R9C7 = 1
c) 14(3) = {257} locked for N7, 2 locked for R9
d) 5(2) = {14} locked for R7+N8

8. N145
a) 17(3) = {458} -> R1C2 = 8, R2C2 = 5, R3C2 = 4
b) 12(2) = {57} -> R5C2 = 7, R5C3 = 5
c) 14(3) = {356} -> R4C4 = 3, R5C4 = 6
d) 25(5) = {12679} -> R3C1 = 6, R3C3 = 7, R4C1 = 2, {19} locked for R4+N4

9. Rest is singles.

Rating: 1.0. I didn't mark any key moves but I think using Innie-Outie-Difference you can avoid combo crunching and solve it without any problems
Walkthrough by Andrew: shortest for a long time:
Thanks for a fun puzzle Mike. :D The solution really flowed well with my only real work being to put steps in the right order to simplify my solving path.

Caida, Afmob and I also solved it by similar routes so there appears to be a fairly well defined although not narrow or difficult solving path. Having said that I think there were enough differences for me to also post my walkthrough.

I agree with Afmob's rating of 1.0.

Here is my walkthrough, which is my shortest one for a long time.

Prelims

a) R1C12 = {19/28/37/46}, no 5
b) R3C56 = {14/23}
c) R5C23 = {39/48/57}, no 1,2,6
d) R5C78 = {13}, locked for R5 and N6, clean-up: no 9 in R5C23
e) R7C45 = {14/23}
f) R89C9 = {16/25/34}, no 7,8,9
g) 7(3) cage at R1C6 = {124}, CPE no 1,2,4 in R1C89
h) R567C6 = {389/479/569/578}, no 1,2
i) 19(3) cage at R8C3 = {289/379/469/478/568}, no 1
j) 26(4) cage in N2 = {2789/3689/4589/4679/5678}, no 1
k) 27(4) cage at R2C8 = {3789/4689/5679}, no 1,2

1. 45 rule on R12 1 outie R3C2 = 1 innie R2C8 + 1, no 1,2,3 in R3C2, no 9 in R2C8

2. 45 rule on R89 1 outie R7C8 = 1 innie R8C2 + 1, no 1 in R7C8, no 9 in R8C2

3. 45 rule on N3 2 outies R1C6 + R4C7 = 1 innie R3C9 + 7, max R1C6 + R4C7 = 13 -> max R3C9 = 6

4. 45 rule on C123 2 outies R29C4 = 17 = {89}, locked for C4
4a. 13(3) cage at R1C3 = {139/148/238} (only combinations with 8 or 9) -> R12C3 = {1234}

5. 45 rule on C789 2 outies R18C6 = 3 = {12}, locked for C6, clean-up: no 3,4 in R3C5
5a. Max R1C6 + R4C7 = 11 -> max R3C9 = 4 (step 3)
5b. Min R1C6 + R4C7 = 8 (step 3) -> no 4,5 in R4C7

6. 4 of 7(3) cage locked in R12C7, locked for C7 and N3, clean-up: no 5 in R3C2 (step 1)

7. Naked pair {12} in R1C6 and R3C5, locked for N2
7a. Killer pair 1,2 in R7C45 and R8C6, locked for N8

7. 26(4) cage in N2 = {4679/5678} (cannot be {3689/4589} which clash with R2C4), no 3, 6,7 locked for N2
7a. 3 in N2 locked in R3C46, locked for R3

8. Naked triple {124} in R12C7 + R3C9, locked for N3
8a. Naked pair {12} in R3C59, locked for R3

9. Max R3C9 = 2 -> max R1C6 + R4C7 = 9 (step 3), no 9 in R4C7

10. 27(4) cage at R2C8 = {3789/5679}, 9 locked in R3C78, locked for R3 and N3, clean-up: no 8 in R2C8 (step 1)

11. 18(3) cage in N3 = {378/567}, 7 locked for N3, clean-up: no 8 in R3C2 (step 1)

12. 27(4) cage at R2C8 = {3789/5679} -> R4C7 = 7

13. R345C4 = {257/347/356} (cannot be {167} because R3C4 only contains 3,4,5), no 1
13a. 7 of {257/347} must be in R5C4 -> no 2,4 in R5C4

14. 45 rule on N1 2 innies R3C13 = 1 outie R2C4 + 5, R2C4 = {89} -> R3C13 = 13,14 = {58/67/68}, no 4

15. 7 in R3 locked in R3C123, locked for N1, clean-up: no 3 in R12C1

16. R123C2 = {179/458/467} (cannot be {269} which clashes with R12C1, cannot be {278/368} which clash with R3C13, cannot be {359} because no 3,5,9 in R3C2), no 2,3
16a. 7 of {467} must be in R3C2 -> no 6 in R3C2, clean-up: no 5 in R2C8 (step 1)

17. 3 in N1 locked in R12C3, locked for C3
17a. 13(3) cage at R1C3 (step 4a) = {139/238}, no 4

18. 27(4) cage at R2C8 = {3789/5679}
18a. 6 of {5679} -> no 6 in R3C78

19. 6 in R3 locked in R3C13, locked for N1 and 25(5) cage, clean-up: no 4 in R12C1

20. 4 in N1 locked in R123C2, locked for C2, clean-up: no 8 in R5C3
20a. R123C2 (step 16) = {458} (only remaining combination) -> R3C2 = 4, R3C56 = [23], R3C4 = 5, R3C9 = 1, R18C6 = [12], clean-up: no 9 in R2C1, no 3 in R7C45, no 6 in R89C9, no 5 in R9C9
20b. 2 in N3 locked in R12C7, locked for C7
20c. Naked pair {58} in R12C2, locked for C2 and N1 -> R5C23 = [75], R5C4 = 6, R4C4 = 3 (step 13), clean-up: no 2 in R12C1
20d. R12C1 = [91]

21. Naked pair {47} in R18C4, locked for C4 -> R7C45 = [14], R6C4 = 2, R18C4 = [47], R12C7 = [24], R12C3 = [32], R2C4 = 8 (step 17a), R9C4 = 9, R12C2 = [85]
21a. 45 rule on N8 1 remaining innie R7C6 = 5

22. 27(4) cage at R2C8 (step 18) = {3789} (only remaining combination) -> R2C8 = 3, R5C78 = [31]

23. R8C6 = 2 -> R12C7 = 10 = [91], R3C78 = [89], R67C7 = [56]
23a. 45 rule on N9 1 remaining innie R7C9 = 7, R12C9 = [56], R1C8 = 7, R1C5 = 6, clean-up: no 2 in R9C9

24. Naked pair {38} in R89C5, locked for C5 and N8 -> R9C6 = 6, R5C5 = 9, R2C56 = [79], R46C5 = [51]

25. R9C4 = 9 -> R89C3 = 10 = [64]

and the rest is naked singles and a cage sum


Last edited by Ed on Sun Dec 28, 2008 7:32 pm, edited 2 times in total.

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PostPosted: Sat Jul 19, 2008 9:53 am 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1043
Location: Sydney, Australia
deleted double post


Last edited by Ed on Sat Jul 19, 2008 10:24 am, edited 1 time in total.

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PostPosted: Sat Jul 19, 2008 9:55 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1043
Location: Sydney, Australia
unofficial Assassin 94 by mhparker (Mar 08)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:3840:3840:2818:2818:1796:2053:2053:3079:3079:4105:3840:5643:5643:1796:5134:5134:3079:5393:4105:5643:5643:5141:5141:5141:5134:5134:5393:4105:5643:6941:6941:2335:8480:8480:5134:5393:4900:4900:4900:6941:2335:8480:1578:1578:1578:4397:6958:6941:6941:2335:8480:8480:6452:2613:4397:6958:6958:3897:3897:3897:6452:6452:2613:4397:2880:6958:6958:3907:6452:6452:4678:2613:2880:2880:1866:1866:3907:3661:3661:4678:4678:
Solution:
+-------+-------+-------+
| 5 6 3 | 8 4 1 | 7 2 9 |
| 8 4 9 | 7 3 2 | 5 1 6 |
| 7 2 1 | 6 5 9 | 3 4 8 |
+-------+-------+-------+
| 1 3 5 | 4 2 8 | 9 6 7 |
| 4 8 7 | 9 6 5 | 2 3 1 |
| 2 9 6 | 3 1 7 | 4 8 5 |
+-------+-------+-------+
| 6 5 8 | 2 9 4 | 1 7 3 |
| 9 7 4 | 1 8 3 | 6 5 2 |
| 3 1 2 | 5 7 6 | 8 9 4 |
+-------+-------+-------+
Quote:
mhparker, lead-in: Est. rating: 1.5
Caida: I can't remember off-hand how the ratings go - but this didn't "feel" too difficult. I think it's about a 1 (maybe 1.25)
Afmob: It'll be interesting to see if other users can solve it without resorting to the one difficult move..Rating: 1.25. This is a one-trick pony and I think this one move Caida and I used is too difficult/advanced for a 1.0 Killer
Andrew: Wow, this was a tough one! It stretched my brain power to the limit...If I had to rate this puzzle, then it's a 1.25 just on the moves but if difficuly in finding the key breakthrough is taken into account then IMHO it's a 1.5
Walkthrough by Caida:
Thanks for the puzzle!

It was just what I needed to help me procrastinate :-)

Below is my walkthrough. I can't remember off-hand how the ratings go - but this didn't "feel" too difficult. I think it's about a 1 (maybe 1.25).

Cheers,

Caida

Unofficial Assassin 94 Walkthrough
Preliminaries:

a. 11(2)n12 = {29/38/47/56} (no 1)
b. 7(2)n2 and n78 = {16/25/34} (no 7..9)
c. 20(3)n2 = {389/479/569/578} (no 1,2)
d. 8(2)n23 = {17/26/35} (no 4,8,9)
e. 21(3)n36 = {489/579/678} (no 1..3)
f. 19(3)n4 = {289/379/469/478/568} (no 1)
g. 9(3)n5 = {126/135/234} (no 7..9)
h. 33(5)n56 = {36789/45789} (no 1,2)
i. 6(3)n6 = {123} (no 4..9)
i1. -> 1,2,3 locked for n6 and r5 -> no 1,2,3 elsewhere in n6 and r5
j. 10(3)n69 = {127/136/145/235} (no 8,9)
j1. -> r78c9 no 6,7
k. 11(3)n7 = {128/137/146/236/245} (no 9)
l. 15(2)n8 = {69/78} (no 1..5)
m. 14(2)n89 = {59/68} (no 1..4,7)



1. 9(3)n5:
1a. -> r46c5 = {12/13/23} (no 4,5,6)

2. Innies c5: r37c5 = 14(2) = {59} -> locked for c5
Note: combo {68} blocked by 15(2)n8
2a. -> 15(2)n8 = {78} -> locked for n8 and c5
2b. -> r9c7 no 6
2c. -> r12c5 no 2
2d. -> 2 in c5 locked in n5 -> no 2 elsewhere in n5

3. 15(3)n8 = [159/195/591/951/294/492/456/654] (no 3)
3a. -> 9 in n8 is locked in 15(3)n8 and r9c6 -> no 9 elsewhere in n8

4. 19(3)n4 = {478/568} -> no 9
4a. -> 8 locked for n4 and r5
4b. -> killer pair {46} in r5 in 19(3)n4 and r5c5 -> no 4,6 elsewhere in r5

5. Outies r1: r2c258 = 8(3) = {125/134} (no 6..9)
5a. -> 1 locked for r2
5b. -> r1c5 no 1

6. Outies r9: r8c258 = 20(3) = [389/479/578/587/785/875]
6a. -> r8c2 no 1,2,6
6b. -> r8c8 no 1,2,3,4,6

7. Innies c1234: r37c4 = 8(2) = [35/62/71]
7a. -> r3c4 no 4,5,8,9
7b. -> r7c4 no 4,6,9

8. 20(3)n2 = [398/794/659/695/758]
8a. -> r3c6 no 3,6,7

9. 15(3)n8 = [159/195/591/294]
9a. -> r7c6 no 2,6

10. Innies c6789: r37c6 = 13(2) = [49/85/94]
10a. -> r3c6 no 5
10b. -> r7c6 no 1
10c. -> r7c4 no 5 (step 9)
10d. -> r3c4 no 3 (step 7)

11. Innies r5: r5c456 = 20(3) = {479/569}
11a. -> 9 locked for r5 and n5 -> no 9 elsewhere in r5 or n5
Note: I could have just said that 9 in r5 was locked in n5 -> no 9 elsewhere in n5 (but I liked finding the h20(3) – and I wind up using this later on)

12. 11(3)n7: r9c12 no 8

13. r5c4 no 7 -> here’s how:
13a. -> if r5c4 = 7 -> r5c456 = [749](step 11) -> r3c4 = 6 -> 20(3)n2 = [659] this puts a 9 in both r35c4

14. 15(3)n8 does not equal [195] -> here’s how:
14a. -> if 15(3)n8 = [195] -> 20(3)n2 = [758] (steps 2,7,10) -> 14(2)n89 = [68](r9c6 must be 6 as {59} are used in 15(3)n8) -> this eliminates all 8s from 33(5)n56 -> no combo possible for 33(5)
14b. -> 15(3)n8 does not equal [159] -> here’s how:
14c. -. If 15(3)n8 = [159] -> 20(3)n2 = [794] (steps 2,7,10) -> r1c6 = 1 -> this eliminates all possible combos for 7(2)n2
14d. -> 15(3)n8 = [294]
14e. -> 20(3)n2 = [659] (step 2,7,10)
14f. -> 7(2)n2 = {34} -> locked for n2 and c5
14g. single: r5c5 = 6
14h. -> r5c456 = [965] (step 11)
14i. single: r9c6 = 6
14j. r9c7 = 8
14k. r89c5 = [87]
14l. hidden single: r1c6 = 1
14m. r1c7 = 7
14n. 11(2)n12 = [38]

15. 7(2)n78 = [25]
15a. 11(3)n7 = [7]{13}
15b. 18(3)n9 = [5]{49}
15c. pair {56} locked in r46c3 for c3 and n4
15d. single: r7c3 = 8
15e. hidden single: r3c3 = 1, r2c8 = 1
15f. -> r2c2 = 4 (step 5)

singles and cage sums to the end
Walkthrough by Afmob:
Thanks Mike for providing another interesting Killer. It'll be interesting to see if other users can solve it without resorting to the one difficult move.

But this one move was quite interesting because:
Quote:
Step 5a) 8,9 is locked in 33(5) = 789{36/45} + Innies C6789 = 13(2) = {49/58} + R9C7 = (89) for C67

The interesting thing is a 8/9 in Innies C6789 forces a 8/9 for R46C7 @ 33(5).
So the Innies do not only effect C6 but also C7 and thereby 14(2) @ R9.
But this also means that the Killer pairs of 14(2) are not only effective for R9 but for C6 too (because 8,9 only possible @ R9C7).

Step 5b) Therefore the Killer pair (58) of 14(2) blocks {58} of Innies in C6.


UA Walkthrough 94:

1. C5
a) Innies = 14(2) = {59} locked since (68) is a Killer pair of 15(2)
b) 7(2) = {16/34}
c) 15(2) = {78} locked for N8
d) 15(3) = {159/249/456} <> 3
e) 9(3) = 2{16/34} -> 2 locked for N5

2. R5+C46
a) 6(3) = {123} locked for R5+N6
b) Innies C6789 = 13(2) = [49/76/85/94]
c) 19(3) = 8{47/56} because R5C5 = (46) blocks {469} -> 8 locked for R5+N4
d) 9 locked in Innies R5 = 20(3) = 9{47/56} -> 9 locked for N5; R5C46 <> 4,6
e) 9(3) must have 4 xor 6 and R5C5 = (46) -> R46C5 <> 4,6
f) Innies C1234 = 8(2) = [35/62/71]
g) 20(3): R3C9 <> 7 because 4,8 only possible there
h) Innies C6789 = 13(2): R7C6 <> 6
i) 15(3) = 9{15/24} -> 9 locked for R7+N8; R7C4 <> 5
j) Innies C1234 = 8(2) = [62/17]

3. R1
a) Outies R1 = 8(3) = 1{25/34} -> 1 locked for R2
b) 7(2): R1C5 <> 1

4. R789
a) Outies R9 = 20(3) = {389/479/578} because R8C5 = (78)
b) Outies R9 = 20(3): R8C8 <> 3,4 because 9 only possible there
c) 10(3): R78C9 <> 6,7 because R6C9 >= 4
d) 9 locked in R8C13 for R8
e) 14(2) = [59/68]
f) Outies R9 = {578} locked for R8
g) 11(3): R9C12 <> 5,6,7,8 because R8C2 = (578)

5. C67 !
a) 8,9 locked in Innies C6789 + 33(5) + R9C7 for C67
b) ! Innies C6789 <> [58] since it's a Killer pair of 14(2):
If Innies = [58] then 33(5) must have 8 @ R46C7 (step 5a)
c) Innies C6789 = {49} locked for C6
d) 33(5) = 789{36/45} -> 9 locked for C7
e) 14(2) = [68] -> R9C6 = 6, R9C7 = 8

6. R789
a) Killer pair (23) locked in 11(3) + 7(2) for R9
b) 18(3) = {459} -> R8C8 = 5, {49} locked for R9+N9
c) 15(2) = [87] -> R8C5 = 8, R9C5 = 7
d) 11(3) = {137} -> R8C2 = 7, {13} locked for R9+N7

7. C6789
a) 21(3) = 7{59/68} because R9C9 = (49) blocks {489} -> 7 locked for C9
b) 10(3) = 3{16/25} because 4,5 only possible @ R6C9 -> 3 locked for C9+N9
c) 4 locked in Innies C9 = 4{19/28}; R1C9 <> 1,2
d) 20(3) = 9{47/56} -> 9 locked for R3+N2
e) 12(3): R12C8 <> 8,9 because R1C9 >= 4
f) 9 locked in R12C9 for C9
g) 18(3) = {459} -> R9C9 = 4, R9C8 = 9
h) 25(5) = {13678} -> R6C8 = 8, R8C6 = 3
i) 2 locked in 10(3) @ N9 = {235} -> R6C9 = 5, R7C9 = 3, R8C9 = 2
j) Hidden Single: R1C6 = 1 @ C6 -> R1C7 = 7

8. N23
a) 7(2) = {34} locked for C5+N2
b) 20(3) = {569} -> R3C4 = 6, R3C5 = 5, R3C6 = 9
c) 11(2) = [38/92]
d) R3C9 = 8, R1C9 = 9
e) 12(3) = {129} -> R1C8 = 2, R2C8 = 1
f) 20(5) = {23456} -> R2C6 = 2, R2C7 = 5, R4C8 = 6, {34} locked for R3
g) R1C3 = 3, R1C4 = 8, R2C4 = 7

9. N17
a) 15(3) = {456} locked
b) Hidden Single: R3C1 = 7 @ N1
c) 16(3) = [871] -> R2C1 = 8, R4C1 = 1
d) 22(5) = {12379} -> R2C3 = 9, R4C2 = 3
e) 17(3) = {269} locked for C1

10. Rest is singles.

Rating: 1.25. This is a one-trick pony and I think this one move Caida and I used is too difficult/advanced for a 1.0 Killer
Walkthrough by Andrew:
Mike wrote:
An attractive but deadly cage pattern that should require a tad more brain power than last week's puzzle, although nothing an experienced Assassin forum member shouldn't be able to handle...

Wow, this was a tough one! It stretched my brain power to the limit.

The start was easy, then I ground to a halt and went off to solve YAK94 and then uA95 before I came back and found the key contradiction move. Afmob presents it (steps 5a and 5b) as a clash/block but I felt it is really a short contradiction move (my step 25a). Maybe be source of my difficulty is that the killer pair (my step 23e) mask the fact that they are also used as part of a contradiction move. Very clever Mike!

Between solving YAK94 and uA95 I had another look at this from the start and found a couple of interesting combined cages, particularly the one in step 14; the other one in step 16 didn't really lead anywhere but I've kept it in for completeness.

There are so many possible sets of 4 outies but I only found a couple of them were useful; the one on N3 was the better of the two while the one on R123 gave me a hidden single later.

If I had to rate this puzzle, then it's a 1.25 just on the moves but if difficuly in finding the key breakthrough is taken into account then IMHO it's a 1.5. Clearly Caida, Afmob and Ed (off-forum) thought otherwise since they found breakthrough combination moves much more easily.

Here is my walkthrough

Prelims

a) R1C34 = {29/38/47/56}, no 1
b) R12C5 = {16/25/34}, no 7,8,9
c) R1C67 = {17/26/35}, no 4,8,9
d) R89C5 = {{69/78}
e) R9C34 = {16/25/34}, no 7,8,9
f) R9C67 = {59/68}
g) R3C456 = {389/479/569/578}, no1,2
h) R234C9 = {489/579/678}, no 1,2,3
i) R456C5 = {126/135/234}
j) R5C123 = {289/379/469/478/568}, no 1
k) R5C789 = {123}, locked for R5 and N6
l) R678C9 = {127/136/145/235}, no 8,9
m) 11(3) cage in N7 = {128/137/146/236/245}, no 9
n) 33(5) cage at R4C6 = {36789/45789}, no 1,2

1. R456C5 = {126/135/234}
1a. R5C5 = {456} -> no 4,5,6 in R46C5

2. R678C9 = {127/136/145/235}
2a. 6,7 of {127/136} must be in R6C9 -> no 6,7 in R78C9

3. 45 rule on R1 3 outies R2C258 = 8 = 1{25/34}, 1 locked for R2, clean-up: no 1 in R1C5

4. 45 rule on R9 3 outies R8C258 = 20 = {389/479/569/578}, no 1,2

5. 45 rule on C1234 2 innies R37C4 = 8 = {35}/[62/71]

6. 45 rule on C6789 2 innies R37C6 = 13 = {49/58/67}, no 1,2,3

7. 45 rule on C5 2 innies R37C5 = 14 = {59} (cannot be {68} which clashes with R89C5), locked for C5, clean-up : no 2 in R12C5, no 6 in R89C5

8. Naked pair {78} in R89C5, locked for N8, clean-up: no 5,6 in R3C6 (step 6), no 6 in R9C7
8a. 2 in C5 locked in R46C5, locked for N5

9. R8C258 (step 4) = {389/479/578} (cannot be {569} because R8C5 only contains 7,8), no 6
9a. 9 of {389/479} must be in R8C8 -> no 3,4 in R8C8

10. R3C456 = {389/479/569/578}
10a. 4,8 of {479/578} must be in R3C6 -> no 7 in R3C6, clean-up: no 6 in R7C6 (step 6)
10b. 6 of {569} must be in R3C4, 5 of {578} must be in R3C5 -> no 5 in R3C4, clean-up: no 3 in R7C4 (step 5)

11. R7C456 = {159/249}, 9 locked for R7 and N8, clean-up: no 5 in R9C7
11a. 1,2 only in R7C4 -> R7C4 = {12}, clean-up: no 3 in R3C4 (step 5)

12. 9 in R9 locked in R9C789, locked for N9
12a. R8C258 (step 9) = {578} (only remaining combination), locked for R8

13. 11(3) cage in N7 = {128/137/245} (cannot be {146/236} because R8C2 only contains 5,7,8), no 6
13a. R8C2 = {578} -> no 5,7,8 in R9C12

14. Combined cage 11(3) in N7 + R9C34 = 18(1+4) = 5{1246}/7{1235}/8{1234} (cannot be 5{1346} which isn’t consistent with 11(3) cage), 1,2 locked for R9

15. 18(3) cage in N9 = {378/459/468/567} (cannot be {369} because R8C8 only contains 5,7,8)
15a. 5 of {459} must be in R8C8, 5 of {567} must be in R8C8 (cannot be 7{56} which clashes with R9C6) -> no 5 in R9C89

16. Combined cage 18(3) in N9 + R9C67 = 32(1+4) and must contain 9 (step 12) = 5{4689/5679}/7{3589}/8{3579/3678} (cannot be 8{4569} which clashes with 5{1246} in combined cage 11(3) in N7 + R9C34, other combinations for R9C6789 aren’t consistent with 18(3) cage)
16a. -> 18(3) cage in N9 = {378/459/567} (cannot be {468} which doesn’t fit in combined cage)

17. 45 rule on R5 3 innies R5C456 = 20 = {479/569} (cannot be {578} because R5C5 only contains 4,6), no 8, 9 locked for R5 and N5
17a. R5C5 = {46} -> no 4,6 in R5C46
17b. 8 in R5 locked in R5C123, locked for N4

18. 45 rule on C1 3 innies R159C1 = 12 = {138/147/156/237/246/345} (cannot be {129} because no 1,2,9 in R5C1), no 9
18a. 8 of {138} must be in R5C1 -> no 8 in R1C1

19. 45 rule in C9 3 innies R159C9 = 14 = {149/167/239/248/257/356} (cannot be {158/347} which clash with R234C9)
19a. 1 of {149/167} must be in R5C9 -> no 1 in R1C9

20. 45 rule on R123 4 outies R4C1289 = 17, min R4C89 = 9 -> max R4C12 = 8, no 9

21. 45 rule on N3 4 outies R12C6 + R4C89 = 16, min R4C89 = 9 -> max R12C6 = 7, no 7,8,9, no 6 in R1C6, clean-up: no 1,2 in R1C7

22. 7 in C6 locked in R456C6, locked for N5 and 33(5) cage -> no 7 in R46C7

23. R3C456 (step 10) = {479/569/578}
23a. Hidden killer pair 8,9 in R12C4 and R3C456 for N2 -> R12C4 must contain one of 8,9
23b. Hidden killer pair 8,9 in R12C4 and R456C4 for C4 -> R456C4 must contain one of 8,9
23c. Hidden killer pair 8,9 in R456C4 and R456C6 for N5 -> R456C6 must contain one of 8,9
23d. Hidden killer pair 8,9 in R456C6 and R46C7 for 33(5) cage -> R46C7 must contain one of 8,9
23e. Killer pair 8,9 in R46C7 and R9C7, locked for C7
[A slightly shorter version starts with hidden killer pair 8,9 in R37C6 and R456C6.]

24. 33(5) cage at R4C6 = {36789/45789}
24a. 7 in C6 locked in R456C6 (step 22)
24b. R456C6 must contain one of 8,9 (step 23c) -> only one of 3,4,5,6 is in R456C6
24c. 3 of {36789} must be in R46C6 -> no 6 in R46C6

25. R456C6 and R46C7 must each contain one of 8,9 (steps 23c and 23d)
25a. If R46C7 contains 8 => R9C67 = [59], R5C6 = 9, R37C6 = [85] clashes with R9C6
25b. -> no 8 in R46C7, 9 locked in R46C7, locked for C7, N6 and 33(5) cage -> R9C7 = 8, R9C6 = 6, R89C5 = [87], clean-up: no 1 in R9C34

26. 9 in C6 locked in R37C6 (step 6) = {49}, locked for C6
26a. 8 in C6 locked in R46C6, locked for N5
26b. R5C4 = 9 (hidden single in N5), clean-up: no 2 in R1C3
26c. R4C7 = 9 (hidden single in R4)
26d. 9 in N2 locked in R3C56, locked for R3

27. R234C9 = {489/579/678}
27a. 9 of {489/579} must be in R2C9 -> no 4,5 in R2C9

28. 1 in R9 locked in R9C12, locked for N7
28a. 11(3) cage in N7 (step 13) = {137} (only remaining combination) -> R8C2 = 7, R9C12 = {13}, locked for R9 and N7, R8C8 = 5, clean-up: no 4 in R9C34
28b. Naked pair {49} in R9C89, locked for N9

29. Naked triple {123} in R578C9, locked for C9
29a. R678C9 = {127/136/235} (cannot be {145} because 4,5 only in R6C9), no 4

30. Killer pair 2,5 in R7C456 and R9C4, locked for N8
30a. 2 in N8 locked in R79C4, locked for C4, clean-up: no 9 in R1C3

31. 6,7 in N9 locked in R7C78 + R8C7, locked for 25(5) cage -> no 6,7 in R6C8
31a. 25(5) cage at R6C8 = {13678} (only remaining combination), no 2,4 -> R6C8 = 8
31b. R4C6 = 8 (hidden single in R4)

32. 2 in N9 locked in R78C9, locked for C9
32a. R678C9 (step 29a) = {127/235}, no 6

33. 12(3) cage in N3 = {129/138/147/237/246}
33a. 9 of {129} must be in R1C9 -> no 9 in R1C8

34. R9C8 = 9 (hidden single in C8), R9C9 = 4

35. R234C9 = {579/678}, 7 locked for C9 -> R6C9 = 5
35a. R234C9 = {678}, locked for C9 -> R1C9 = 9, R12C8 (step 33) = {12}, locked for C8 and N3 -> R5C8 = 3, R5C79 = [21]

36. Naked pair {23} in R78C9, locked for N9 -> R8C6 = 3 (step 31a), R56C6 = [57], R12C6 = [12], R1C7 = 7, R12C8 = [21], R6C7 = 4 (step 24), R78C9 = [32], clean-up: no 4 in R1C34, no 6 in R1C5

37. Naked pair {16} in R78C7, locked for C7 and N9 -> R7C8 = 7, R4C89 = [67], R3C8 = 4, R3C6 = 9, R3C5 = 5, R3C4 = 6 (step 23), R23C7 = [53], R23C9 = [68], R7C56 = [94], R78C4 = [21], R46C4 = [43], R12C4 = [87], R1C3 = 3, R12C5 = [43], R2C2 = 4, R5C5 = 6, R78C7 = [16], R9C34 = [25], R3C23 = [21], R3C1 = 7, R46C3 [56], R7C3 = 8, R2C13 = [89], R8C13 = [94], R5C123 = [487], R4C2 = 3, R9C12 = [31], R6C2 = 9

38. R8C1 = 9 -> R67C1 = 8 = [26]

and the rest is naked singles


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PostPosted: Sat Jul 19, 2008 10:02 am 
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Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1043
Location: Sydney, Australia
Yet Another killer (YaK) #94 by Jean-Christophe (Mar 08)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:4609:4098:4098:5891:5891:5380:5380:3845:3845:4609:4098:5891:5891:5380:5380:3845:3845:5126:4609:3335:2056:2569:2569:5642:1803:1803:5126:4609:3335:2056:2569:2572:5642:5642:8205:5126:4622:4622:4622:4622:2572:8205:8205:8205:8205:4623:4622:3088:3088:2572:4369:1042:3091:3604:4623:3349:3349:3088:4369:4369:1042:3091:3604:4623:4886:4886:5911:5911:5656:5656:4633:3604:4886:4886:5911:5911:5656:5656:4633:4633:3604:
Solution:
+-------+-------+-------+
| 1 2 8 | 9 4 5 | 6 3 7 |
| 5 6 3 | 7 8 2 | 4 1 9 |
| 4 9 7 | 3 1 6 | 5 2 8 |
+-------+-------+-------+
| 8 4 1 | 6 2 9 | 7 5 3 |
| 3 7 2 | 1 5 8 | 9 6 4 |
| 9 5 6 | 4 3 7 | 1 8 2 |
+-------+-------+-------+
| 7 8 5 | 2 9 1 | 3 4 6 |
| 2 3 9 | 5 6 4 | 8 7 1 |
| 6 1 4 | 8 7 3 | 2 9 5 |
+-------+-------+-------+
Quote:
Afmob: I thought this one was a monster since SS rated it 2.02 and JSudoku used XY-Chains and Turbot Fishes to crack it. But I managed to crack it in (with) two moves... there is nothing complicated about this and even those moves are easy to see I think. Rating: 1.25
mhparker: I agree, although probably a high 1.25
Andrew: Although I used the same key moves as the others, I missed one early move....Missing that early step didn't seem to make the solution path any harder so I'll also rate this puzzle 1.25
sudokuEd: Even knowing there was an easy way to solve this one, it took me many hours to find the key. Felt more like the SSscore to me - but then starting again to get straight to the unlocker: how easy :D
Walkthrough by Afmob:
I thought this one was a monster since SS rated it 2.02 and JSudoku used XY-Chains and Turbot Fishes to crack it. But I managed to crack it in a fairly early state. So apart from the two moves (step 5a, 5e) there is nothing complicated about this and even those moves are easy to see I think.

Though I must say that it was stubborn in the endgame.

YAK 94 Walkthrough:

1. R6789
a) Innies R89 = 8(2+1) <> 7,8,9; R8C1 <> 6
b) 18(3) @ C1: R67C1 <> 1,2,3 because R8C1 <= 5
c) 4(2) = {13} locked for C7
d) 1 locked in R6C79 for R6
e) Innies = 8(2) = {26/35}
f) Innies+Outies N7: 5 = R6C1 - R9C3 -> R6C1 <> 4,5; R9C3 = (1234)

2. R1234
a) 7(2): R3C8 <> 4,6
b) Innies = 7(2) <> 7,8,9; R4C5 <> 6
c) Innies N3 = 23(3) = {689} locked for N3
d) 7(2) <> 1
e) 20(3) = 9{38/56} because R23C9 = (689) -> R4C9 = (35), 9 locked for C9+N3

3. C6789
a) Innies C9 = 11(2) <> 1,2; R5C9 <> 3,5
b) Outies = 24(3) = {789} locked for C5
c) 15(4) = 17{25/34} -> 1 locked for C8
d) 21(4) must have two of (12345) and they are only possible @ R12C6 -> R12C6 <> 6,7,8,9

4. C1234
a) Innies C1 = 9(2) <> 9
b) 23(4) @ N7: R89C4 <> 1,2,3 because R8C5+R9C3 <= 10

5. C456 !
a) Killer triple (789) locked in R79C5 + 23(4) for N8
-> 23(4) @ N8 can only have one of (789)
b) 23(4) @ N8 = 56{39/48} -> 5,6 locked for N8; R89C4+R8C5 <> 3,4
c) 7 locked in R79C5 for C5
d) Killer pair (56) locked in 10(3) @ R4C5 + R8C5 for C5
e) ! Killer quad (1234) locked in 21(4) + R789C6 for C6
-> 21(4) can only have one of (1234)
f) 21(4) = 56{19/28} -> R1C7 = 6; 5 locked for C6+N2

6. R1234
a) 20(3) = {389} -> R4C9 = 3; 8 locked for C9
b) Naked pair (89) locked in R2C59 for R2
c) 23(4) must have 8,9 and it's only possible @ R1C4 -> R1C4 = (89)
d) Naked pair (89) locked in R1C4+R2C5 for N2
e) 22(3) = {679} because R3C6 = (67) -> 9 locked for R4, 6 locked for C6
f) 13(2): R3C2 <> 4
g) 8(2): R3C3 <> 5

7. C456
a) 17(3) = 7{19/28}
b) Killer pair (12) locked in 21(4) + R7C6 for C6
c) 22(4) = {3478} because R89C6 = {34}
-> R8C7+R9C5 = {78}, {34} locked for N8

8. N69
a) R6C7 = 1, R7C7 = 3
b) 12(2) = {48/57}
c) 9 locked in 18(3) = 9{27/45}
d) 6 locked in 14(4) @ N9 = {1256} locked for C9; R6C9 <> 6
e) 32(5) must have 4 xor 7 and R5C9 = (47) -> R4C8+R5C678 <> 4,7

9. R6789
a) Naked pair (12) locked in R7C46 for R7
b) Naked pair (34) locked in R9C36 for R9
c) Killer pair (25) locked in Innies + R6C9 for R6
d) 12(2): R7C8 <> 7
e) 4 locked in R78C8 for C8

10. N69
a) Hidden Single: R5C9 = 4 @ N6
b) 32(5) = {45689} -> 5 locked for N6
c) 12(2): R7C8 <> 8
d) Hidden Single: R8C7 = 8 @ N9
e) 14(4) = {1256} -> R6C9 = 2; 5 locked for N9
f) R9C5 = 7, Hidden Single: R8C8 = 7 @ N9
g) R6C8 = 8, R7C8 = 4

11. R456
a) Hidden Single: R4C7 = 7 @ N6 -> R3C6 = 6, R4C6 = 9
b) R6C6 = 7
c) 12(3) = 2{19/46} -> R7C4 = 2
d) 12(3) = {246} -> 6 locked for R6
e) R6C1 = 9 -> 18(3) = 9[54/63/72/81]

12. N7+C456
a) Innies+Outies: 5 = R6C1 - R9C3 -> R9C3 = 4
b) 19(4) = 3{169/259/268} -> 3 locked for R8
c) R7C6 = 1 -> R7C5 = 9
d) 21(4) = {2568} -> R2C5 = 8; 2 locked for N2
e) 10(3) @ N2 = 1{36/45} -> R4C4 = (56), 1 locked for R3+N2
f) R1C4 = 9

13. R123
a) Hidden Single: R3C2 = 9 @ N1 -> R4C2 = 4
b) R6C3 = 6, R1C9 = 7
c) 23(4) = {3479} -> 7 locked for R2, 4 locked for N2
d) 10(3) = {136} -> R4C4 = 6; 3 locked for R3+N2
e) 23(4) = {3479} -> R2C3 = 3, R2C4 = 7, R1C5 = 4
f) 16(3) = {268} -> R2C2 = 6; {28} locked for R1+N1
g) 7(2) = {25} locked for R3+N3

14. Rest is singles.

Rating: 1.25. I used one Killer triple and one Killer quad to crack it.
Alt endgame by mhparker:
Jean-Christophe wrote:
Yet Another Killer...
Thanks for keeping me busy, J-C! :roll:
Afmob wrote:
Rating: 1.25.
I agree, although probably a high 1.25.
Afmob wrote:
Though I must say that it was stubborn in the endgame.
Unfortunately, my WT is too similar to Afmob's to be worth publishing. However, my endgame was different, starting from a position very similar to the grid state after Afmob's step 8b (shown below):

Grid state after Afmob's step 8b

Code:
.-----------.-----------------------.-----------------------.-----------------------.-----------------------.
| 12345789  | 12345789    12345789  | 89          1234      | 125         6         | 123457      457       |
|           |           .-----------'           .-----------'           .-----------'           .-----------:
| 1234567   | 1234567   | 1234567     123467    | 89          125       | 2457        123457    | 89        |
|           :-----------+-----------.-----------'-----------.-----------+-----------------------:           |
| 123456789 | 56789     | 12367     | 123467      1234      | 67        | 245         235       | 89        |
|           |           |           |           .-----------:           '-----------.-----------:           |
| 1245678   | 45678     | 12567     | 124567    | 1245      | 679         79        | 2456      | 3         |
:-----------'-----------'-----------'-----------:           :-----------------------'           '-----------:
| 12345678    12345678    12345678    12345678  | 123456    | 789         245789      2456789     467       |
:-----------.           .-----------------------:           :-----------.-----------.-----------.-----------:
| 6789      | 2356      | 23456789    23456789  | 2356      | 789       | 1         | 4578      | 24567     |
|           :-----------'-----------.           :-----------'           |           |           |           |
| 456789    | 456789      456789    | 12        | 789         12        | 3         | 4578      | 124567    |
|           :-----------------------+-----------'-----------.-----------'-----------+-----------:           |
| 12345     | 123456789   123456789 | 5689        56        | 34          78        | 2456789   | 12456     |
:-----------'           .-----------'           .-----------'           .-----------'           |           |
| 2345678     123456789 | 34          5689      | 78          34        | 245789      2456789   | 12456     |
'-----------------------'-----------------------'-----------------------'-----------------------'-----------'

From here, I took the following route:

9. I/O diff. N2: R2C3 + R4C4 = R3C6 + 3
9a. min. R3C6 = 6 -> min. R2C3 + R4C4 = 9
9b. -> no 1 in R4C4

10. 10(3) at R3C4 = {127/136/145}
(Note: {235} blocked by R3C78)
10b. 1 locked in R3C45 for R3 and N2
10c. cleanup: no 7 in R4C3

11. Naked pair (NP) at R12C6 = {25}, locked for C6 and N2
11a. -> R7C46 = [21]; R2C5 = 8 (cage split)
11b. -> R23C9 = [98]
...
Afmob wrote:
SS rated it 2.02 and JSudoku used XY-Chains and Turbot Fishes to crack it.
Indeed. A bit like using an atom bomb to kill a canary, you might say! (Or, as we say in Germany, "using a cannon to shoot at sparrows"...)

It will be interesting to see why these two fine programs made such heavy going of it. Would maybe make a good post when someone (possibly me) finds out.
Optimized Walkthrough by mhparker:
Jean-Christophe wrote:
At that stage, it's probably easier to:
Indeed it is! The moral of this story is not to try to fit my moves into the context of other people's walkthroughs. In my case, there were namely several other 8s still available in R4 at this stage:

Optimized YAK94 Walkthrough

Prelims:

a) 20(3) at R2C9 = {389/479/569/578} (no 1,2)
b) 13(2) at R3C2 and R7C2 = {49/58/67} (no 1..3)
c) 8(2) at R3C3 = {17/26/35} (no 4,8,9)
d) 10(3) at R3C4 and R4C5 = {127/136/145/235} (no 8,9)
e) 22(3) at R3C6 = {589/679} (no 1..4)
f) 7(2) at R3C7 = {16/25/34} (no 7..9)
g) 32(5) at R4C8 = {26789/35789/45689} (no 1)
h) 18(5) at R5C1 = {12348/12357/12456} (no 9)
i) 4(2) at R6C7 = {13}, locked for C7; cleanup: no 4,6 in R3C8 (prelim f)
j) 12(2) at R6C8 = {39/48/57} (no 1,2,6)
k) 14(4) at R6C9 = {1238/1247/1256/1346/2345} (no 9)

1. Innies N3: R1C7 + R23C9 = 23(3) = {689}, locked for N3
1a. cleanup: no 1 in R3C8

2. 20(3) at R2C9 = {69}[5]/{89}[3]
2a. -> R4C9 = {35} (no 4,6..9)
2b. 9 locked in R23C9 for C9 and N3

3. Outies C6789: R279C5 = 24(3) = {789}, locked for C5

4. Innie/Outie (I/O) diff. N7: R6C1 = R9C3 + 5
4a. -> no 1..5 in R6C1; no 5..9 in R9C3

5. 23(4) at R8C4 = {3569/4568} (no 1,2,7)
(Note: {1589/1679/2489/2579/2678/3479/3578} all blocked by R79C5)
5a. only 1 of {34}, which must go in R9C3
5b. -> no 3,4 in R8C45+R9C4
5c. {56} locked in R8C45+R9C4 for N8
5d. cleanup: no 6,7 in R6C1 (step 4)

6. 23(4) at R8C4 (step 5) and R79C5 form killer triple on {789} within N8
6a. -> no 7..9 elsewhere in N8
6b. 7 in N8 locked in R79C5 for C5

7. 21(4) at R1C6 = {1569/2568} (no 3,4,7)
(Note: {1479/2379/3459} blocked because none of these digits in R1C7;
{3567} blocked because none of these digits in R2C5;
{1389/2469/2478/3468} blocked by R789C6; {1578} unplaceable)
7a. can only have 1 of {89}, which must go in R2C5
7b. -> no 8,9 in R1C67+R2C6
7c. -> R1C7 = 6
7d. 5 locked in R12C6 for C6 and N2

8. R12C6 and R789C6 form killer quad on {1234} within C6
8a. -> no 1..4 elsewhere in C6
8b. {34} in C6 locked in N8 -> not elsewhere in N8

9. R4C9 = 3 (outie N3, or 20(3) cage split)
9a. -> R67C7 = [13]
9b. cleanup: no 5 in R3C3; no 9 in R67C8

10. Naked pair (NP) at R2C59 = {89}, locked for R2

11. I/O diff. N2: R2C3 + R4C4 = R3C6 + 3
11a. min. R3C6 = 6 -> min. R2C3 + R4C4 = 9
11b. -> no 1 in R4C4

12. 10(3) at R3C4 = {127/136/145}
(Note: {235} blocked by R3C78)
12b. 1 locked in R3C45 for R3 and N2
12c. cleanup: no 7 in R4C3

13. Naked pair (NP) at R12C6 = {25}, locked for C6 and N2
13a. -> R2C5 = 8 (cage split)

14. R23C9 = [98]
14a. cleanup: no 5 in R4C2

15. Hidden single (HS) in N8 at R7C4 = 2

16. 2 in C5 locked in 10(3) at R4C5 = {235} (no 1,4,6) (last combo), locked for C5 and N5

17. R138C5 = [416]
17a. -> split 9(2) at R34C4 = [36] (last permutation)
17b. cleanup: no 7 in R3C2; no 2 in R3C3; no 4 in R3C7; no 5 in R4C3

Rest is really just a mop-up now.
Walkthrough by Andrew:
Thanks Jean-Christophe. A fun puzzle! :D

Although I used the same key moves as the others, I missed one early move - Afmob's step 2c, step 1 in Mike's optimised walkthrough - only seeing my step 8 instead. That led to some significant differences in my solving path including a couple of fun steps later.

Missing that early step didn't seem to make the solution path any harder so I'll also rate this puzzle 1.25.

Here is my walkthrough. Thanks Afmob for pointing out that my original step 19 was flawed. I've deleted it, renumbered the next 4 steps and inserted a new step 23; step 21 has been edited for clarity and step 22 is now shorter. There is also simplification of the mop-up stage. I've inserted a clean-up in step 28 that I'd originally omitted. That removed the last 5 steps! :D

Prelims

a) R34C2 = {49/58/67}, no 1,2,3
b) R34C3 = {17/26/35}, no 4,8,9
c) R3C78 = {16/25/34}, no 7,8,9
d) R67C7 = {13}, locked for C7, clean-up: no 4,6 in R3C8
e) R67C8 = {39/48/57}, no 1,2,6
f) R7C23 = {49/58/67}, no 1,2,3
g) R234C9 = {389/479/569/578}, no 1,2
h) 10(3) cage at R3C4 = {127/136/145/235}, no 8,9
i) 22(3) cage at R3C6 = {589/679}
j) R456C5 = {127/136/145/235}, no 8,9
k) R6789C9 = {1238/1247/1256/1346/2345}, no 9
l) 18(5) cage at R5C1 = {12348/12357/12456}, no 9
m) 32(5) cage at R4C8 = {26789/35789/45689}, no 1

1. 45 rule on C1 2 innies R59C1 = 9 = {18/27/36/45}, no 9 in R9C1

2. 45 rule on C9 2 innies R15C9 = 11 = {29/38/47/56}, no 1 in R1C9
2a. 1 in N3 locked in R123C8, locked for C8
2b. 1 in N6 locked in R6C79, locked for R6

3. 45 rule on R1234 2 innies R4C58 = 7 = [16/25/34/43/52], no 7,8,9, no 6 in R4C5

4. 32(5) cage at R4C8 = {26789/35789/45689}, 8 locked in R5C6789 for R5

5. 45 rule on R6789 2 innies R6C25 = 8 = {26/35}

6. 18(5) cage at R5C1 = {12357/12456}, 1 locked in R5C1234 for R5

7. R456C5 = {127/136/145/235}
7a. 1 of {145} must be in R4C5 -> no 4 in R4C5, clean-up: no 3 in R4C8 (step 3)

8. 45 rule on N3 1 innie R1C7 = 1 outie R4C9 + 3, R1C7 = {6789}, R4C9 = {3456}
8a. R234C9 = {389/479/569/578}
8b. 3,4 of {389/479} must be in R4C9 -> no 3,4 in R23C9

9. 45 rule on N7 1 outies R6C1 = 1 innie R9C3 + 5, R6C1 = {6789}, R9C3 = {1234}

10. 45 rule on R89 3 innies R8C19 + R9C9 = 8, no 6,7,8,9 in R8C1, no 7,8 in R89C9

11. 45 rule on C6789 3 outies R279C5 = 24 = {789}, locked for C5

12. 21(4) cage at R1C6 = {1389/1479/1569/1578/2379/2469/2478/2568/3459/3468/3567}, R1C7 + R2C5 = {6789} -> no 6,7,8,9 in R12C6

13. 23(4) cage at R8C4 = {3569/4568} (cannot be {1589/1679/2489/2579/2678/3479/3578} which clash with R79C5), no 1,2,7, 5,6 locked for N8, clean-up: no 6,7 in R6C1 (step 9)
13a. R9C3 = {34} -> no 3,4 in R8C45 + R9C4

14. Killer triple 7,8,9 in R79C5 + R89C4, locked for N8
14a. 7 in N8 locked in R79C5, locked for C5

15. Naked quint {12345} in R12789C6, locked for C6
15a. 22(3) cage at R3C6 = {589/679}
15b. 5 of {589} must be in R4C7 -> no 8 in R4C7

16. 5 in C6 locked in R12C6, locked for N2
16a. 21(4) cage at R1C6 (step 12) = {1569/1578/2568} (cannot be {3459} because 3,4,5 only in R12C6, cannot be {3567} because R2C5 only contains 8,9), no 3,4
16b. R2C5 = {89} -> no 8,9 in R1C7, clean-up: no 5,6 in R4C9 (step 8)

17. 3,4 in C6 locked in R789C6, locked for N8

18. R1C7 + R4C9 (step8) = [63/74]
18a. R234C9 (step 8a) = {389} (cannot be {479} which clashes with R1C7 + R4C9, cannot be {569/578} because R4C9 only contains 3,4) -> R4C9 = 3, R1C7 = 6 (step 8), R67C7 = [13], clean-up: no 5 in R3C3, no 1 in R3C8 , no 9 in R67C8, no 8 in R15C9, no 5 in R5C9 (both step 2), no 4 in R4C8 (step 3)
18b. Naked pair {89} in R23C9, locked for C9 and N3, clean-up: no 2 in R15C9 (step 2)
18c. Naked pair {89} in R2C59, locked for R2

19. 3 in C6 locked in R89C6
19a. 22(4) cage at R8C6 = {2389/3478}, no 1,5
19b. 2,3,4 must be in R89C6 -> no 2,4 in R8C7

20. R6C1 + R9C3 (step 9) = [83/94]
20a. R678C1 = {189/279/369/378/468} (cannot be {459} which clashes with R6C1 + R9C3, cannot be {567} because R6C1 only contains 8,9), no 5
20b. 1,2,4 of {189/279/468} must be in R8C1 -> no 1,2,4 in R7C1

21. 23(4) cage at R1C4 = {1679/2579/2678/3479/3569/3578/4568} (cannot be {1589/2489} which clash with R2C5)
21a. 8,9 only in R1C4 -> R1C4 = {89}
21b. 1,2 of {1679/2579/2678} must be in R1C5 -> no 1,2 in R2C34

22. Naked pair {89} in R1C4 and R2C5, locked for N2

23. R3C6 = {67} -> 22(3) cage at R3C6 = {679} (only remaining combination), no 5,8, 6 locked in R34C6, locked for C6, 9 locked in R4C67, locked for R4, clean-up: no 4 in R3C2

24. 8 in R4 locked in R4C12, locked for N4 -> R6C1 = 9, R9C3 = 4 (step 9), clean-up: no 9 in R7C23

25. R7C5 = 9 (hidden single in R7), R2C5 = 8, R9C5 = 7, R1C4 = 9, R23C9 = [98], R3C2 = 9 (hidden single in R3), R4C2 = 4
25a. R7C5 = 9 -> R67C6 = 8 = [71], R34C6 = [69], R4C7 = 7, R5C6 = 8, R7C4 = 2, R89C6 = [43], R8C7 = 8 (step 19a), clean-up: no 4 in R1C9 (step 2), no 1 in R3C3, no 2 in R4C3, no 4 in R6C8, no 5 in R7C8

26. R6C8 = 8 (hidden single in R6), R7C8 = 4

27. R4C1 = 8 (hidden single in R4), clean-up: no 1 in R8C1 (step 20a)
27a. 4 in C1 locked in R123C1 -> R123C1 = 10 = {145}, locked for C1 and N1

28. R7C4 = 2 -> R6C34 = 10 = [64], clean-up: no 2 in R6C25 (step 5), no 2 in R3C3, no 7 in R7C2

29. R8C3 = 9 (hidden single in C3)
29a. 1 in N7 locked in 19(4) cage = {1279/1369}, no 5,8
29b. 3 of {1369} must be in R8C2 -> no 6 in R8C2 (added for completeness)

30. R7C23 = {58} (hidden pair in N7), locked for R7

31. R5C9 = 4 (hidden single in C9), R1C9 = 7 (step 2), R7C9 = 6, R7C1 = 7, R8C1 = 2 (step 20a), R59C1 = [36], R89C2 = [31], R6C25 = [53], R689C9 = [215], R8C8 = 7, R7C23 = [85], R9C4 = 8, R4C3 = 1, R3C3 = 7, R2C34 = [37], R12C2 = [26], R1C3 = 8, R5C23 = [72], R12C6 = [52]

32. 10(3) cage at R3C4 = {136/145}
32a. 1 locked in R3C45, locked for R3 and N2 -> R1C5 = 4, R1C1 = 1, R1C8 = 3, clean-up: no 4 in R3C7
32b. R3C45 = {13} -> R4C4 = 6 (step 32)


and the rest is naked singles
Examples of ALS cage block by mhparker:
sudokuEd wrote:
SudokuSolverV3 doesn't know about two-cell cage blocks yet
This is actually an example of a blocking constraint in the form of an Almost Locked Set (ALS), where N cells (N > 0) contain (N + 1) candidates. Of the Assassin forum members, Para is the specialist in using this ALS-based blocking. Here are just three further examples taken from some of his earlier walkthroughs:

Example 1 - Assassin 44 grid state after Para's step 27b:

Code:
.-------------------------------.-------.-----------------------.-------.
| 9       3       4       2     | 6     | 7       58      58    | 1     |
:-----------------------.-------:       :---------------.-------'       |
| 8       6       7     | 5     | 1     | 9       2     | 3       4     |
:-----------------------:       :-------'-------.       |       .-------:
| 5       12      12    | 3     | 4       8     | 67    | 9     | 67    |
:-------.       .-------+-------'---------------:       :-------:       |
| 237   | 4     | 189   | 79      28      15    | 67    | 167   | 23589 |
|       :-------'       :-----------------------+-------'       |       |
| 27    | 159     189   | 4       3       6     | 1589    1578  | 2589  |
|       |       .-------+-----------------------:       .-------:       |
| 237   | 159   | 6     | 79      28      15    | 1358  | 4     | 23589 |
|       :-------:       :---------------.-------+-------'       '-------:
| 4     | 8     | 3     | 6       7     | 2     | 159     15      59    |
:-------'       |       '-------.-------:       :-----------------------:
| 6       7     | 5       1     | 9     | 4     | 38      2       38    |
|       .-------'---------------:       :-------'-----------------------:
| 1     | 29      29      8     | 5     | 3       4       67      67    |
'-------'-----------------------'-------'-------------------------------'
Para wrote:
28. 16(3) in R4C4 = [925]: [781] clashes with R4C78
Here, R4C78 forms an ALS on the digits {167}. The digits 1 and 7 of [781] permutation see all of the digits 1 and 7 in the ALS (respectively), and is therefore blocked by it.

Example 2 - Assassin 74 Brick Wall grid state after Para's step 39a:

Code:
.-----------------------------------.-----------------------------------.-----------------------------------.
| 123456789   123456789   123456789 | 789         346         234       | 123456789   123456789   123456789 |
:-----------.-----------------------+-----------.-----------------------+-----------.-----------------------:
| 23456789  | 12345678    12345678  | 5789      | 3678        123468    | 123456789 | 123456789   123456789 |
|           '-----------.           |           '-----------.           |           '-----------.           |
| 23456789    23456789  | 12345678  | 5789        13        | 123468    | 123456789   123456789 | 123456789 |
:-----------.-----------'-----------+-----------.-----------'-----------+-----------.-----------'-----------:
| 13456789  | 13456789    13456789  | 278       | 14          145       | 24689     | 12356       12356     |
|           '-----------.           |           '-----------.           |           '-----------.           |
| 13456789    13456789  | 13456789  | 278         78        | 145       | 24689       24689     | 12356     |
:-----------.-----------'-----------+-----------.-----------'-----------+-----------.-----------'-----------:
| 458       | 1245        1245      | 3         | 69          69        | 17        | 14578       14578     |
|           '-----------.           |           '-----------.           |           '-----------.           |
| 5689        5689      | 458       | 1           2         | 7         | 34589       34589     | 39        |
:-----------.-----------'-----------+-----------.-----------'-----------+-----------.-----------'-----------:
| 12        | 45789       45789     | 6         | 389         389       | 12        | 45789       45789     |
|           '-----------.           |           '-----------.           |           '-----------.           |
| 123         123       | 789       | 4           5         | 89        | 126         126       | 789       |
'-----------------------'-----------'-----------------------'-----------'-----------------------'-----------'
Para wrote:
39b. 15(3) at R1C4: [843] blocked by R34C5: R1C6: no 3
This is a slightly more complicated example, in that the blocking ALS at R34C5 (= {134}) does not completely share a house with the 15(3) cage at R1C4. Nevertheless, the same logic holds: the 3 and 4 of the [843] permutation for R1C456 see all 3s and 4s (respectively) in the ALS at R34C5, and is therefore blocked by it.

Example 3 - Maverick 1 grid state after Para's step 32:

Code:
.-----------------------.-----------------------.-----------.-----------------------.-----------------------.
| 4578        123       | 5689        5689      | 4578      | 46          79        | 123         123       |
|           .-----------'-----------.-----------'           '-----------.-----------'-----------.           |
| 5689      | 4679        4679      | 1235689     1235689     139       | 4578        4578      | 123       |
:-----------+-----------------------+-----------.-----------.-----------+-----------------------+-----------:
| 12357     | 12345789    12345789  | 345789    | 12345789  | 2389      | 6           45        | 89        |
|           :-----------.           |           |           |           |           .-----------:           |
| 13567     | 123456789 | 123456789 | 345789    | 123456789 | 2389      | 23        | 12345679  | 67        |
:-----------'           :-----------'-----------:           :-----------'-----------:           '-----------:
| 45679       12345679  | 234567      234567    | 12345679  | 56          89        | 12345679    456789    |
:-----------.           :-----------.-----------:           :-----------.-----------:           .-----------:
| 6789      | 123456789 | 123456789 | 1234567   | 123456789 | 127       | 1235      | 12345679  | 23567     |
|           :-----------'           |           |           |           |           '-----------:           |
| 6789      | 456789      456789    | 2345678   | 23456789  | 278       | 1235        245       | 12356     |
:-----------+-----------------------+-----------'-----------'-----------+-----------------------+-----------:
| 123       | 456789      456789    | 123456789   123456789   1379      | 345789      345789    | 45679     |
|           '-----------.-----------'-----------.           .-----------'-----------.-----------'           |
| 123         123       | 46789       12346     | 123456789 | 45          78        | 2345679     45679     |
'-----------------------'-----------------------'-----------'-----------------------'-----------------------'
Para wrote:
33. 4 in N6 locked in 20(4) at R4C8 = {1469/147[8]/2459/246[8]/345[8]}(only place for 8 in R5C9): {3467} blocked by R4C9
33a. 20(4) can't have 2 of {245} in R456C8 because of R37C8: {2459/246[8]/345[8]} blocked
33b. 20(4) = {1469/147[8]} = {67..}: no 2,3,5; R5C9: no 7; 1 locked for N6 and C8(only place for 1 in R456C8);
This was the key move that Para found to break this puzzle. As in the first two examples, it is based on using an ALS (R37C8 = {245}) to block specific permutations of the 20(4) cage at R4C8
More Implied Cage Blocks by sudokuEd:
Andrew wrote:
Are the following thoughts correct?
Andrew wrote:
At the time that I did step 13 ... I may have used an ALS cage block without realising it
Yes! Just like you (and Afmob) did in A88
Quote:
r89c3 = {357} -> {57} blocked from 12(2)r34c3
It is a 2-cell ALS(+1) block.

A88: 2-cell Almost Locked Set (ALS) (+1) in r89c3 -> {57} blocked from 12(2)r34c3
Code:
.-----------------------------------------------------------------------.
|(17)   :       |(10)   |(17)   :       :       |(19)   |(21)   :       |
|       :  123  |   23  |  123  :  123  :  123  |   23  |  123  :  123  |
|   5   :   56  |  456  |  456  :  456  :  456  |  456  |  456  :  456  |
|  789  :  789  |  7    |  78   :  789  :  789  |  78   |  789  :  789  |
|-------:.......|.......|-----------------------|.......|.......--------|
|(29)   |       |       :       |(18)   |       :       |       |(19)   |
|       |  123  |   23  :  123  |  123  |       :   23  |  123  |  123  |
|   5   |   56  |  456  :       |  456  |       :  456  |  456  |  456  |
|  789  |  789  |  7    :       |  789  |  789  :  789  |  789  |  789  |
|.......|.......|---------------|.......|---------------|.......|.......|
|       |       |(12)   |       :       :       |( 9)   |       |       |
|       |  123  |    3  |  123  :  123  :  123  |  123  |  123  |  123  |
|   5   |   56  |  45   |  456  :  456  :  456  |  456  |  456  |  456  |
|  789  |  789  |  7    |  78   :  789  :  789  |  78   |  789  |  789  |
|.......|-------|.......|-----------------------|.......|-------|.......|
|       :       |       |(17)   |(14)   |(25)   |       |       :       |
|       :       |       |  123  |  123  |  123  |  123  |  123  :  123  |
|   5   :   5   |   5   |  456  |  456  |  456  |  456  |  456  :  456  |
|  789  :  789  |  789  |       |       |       |  78   |  789  :  789  |
|---------------|-------|.......|.......|.......|-------|---------------|
|(15)   |       :       :       |       |       :       :       |(14)   |
|    3  |   2   :  12   :  123  |  123  |    3  :   23  :       |  123  |
|    6  |   5   :   5   :  456  |  456  |  456  :  456  :  456  |  4    |
|       |  7    :  789  :  78   |  7    |  789  :  789  :  789  |       |
|.......|-----------------------|.......|-----------------------|.......|
|       :       |(12)   :       |       |(14)   :       |       :       |
|    3  :       |  12   :  123  |       |  123  :  123  |  123  :  123  |
|    6  :   4   |   5   :   56  |    6  |   56  :   56  |   56  :   56  |
|       :       |  789  :  78   |  789  |  789  :  789  |  78   :  78   |
|.......--------|-------:.......|-------|.......--------|-------:.......|
|       |(23)   :       |       |( 9)   |       |(12)   :       |       |
|       |       :       |  123  |       |  123  |    3  :    3  |  123  |
|   2   |    6  :    6  |  456  |   56  |  456  |  456  :  456  |  456  |
|       |   89  :   89  |       |  78   |       |  7    :  78   |       |
|-------|.......--------|-------|.......|-------|-------:.......|-------|
|( 5)   |       |(24)   :       |       |(21)   :       |       |(14)   |
|  1    |       |    3  :       |  123  |    3  :  123  |  123  |       |
|  4    |    6  |   5   :   9   |  4    |  456  :  456  |       |   56  |
|       |   8   |  7    :       |       |  78   :  78   |       |   8   |
|.......|-------|.......--------|-------|-------:.......|-------|.......|
|       |       :       |(15)   :       :       |       :       |       |
|  1    |    3  :    3  |  123  :  123  :  123  |  123  :       |       |
|  4    |   5   :   5   |  456  :  456  :  456  |  456  :  456  |   56  |
|       |  7    :  7    |  78   :  78   :  78   |  789  :  789  |   89  |
.-----------------------------------------------------------------------.


Presumably there can be a 2-cell ALS(+2); ALS(+3) etc which blocks a combination(s) from larger cages.
Andrew wrote:
23(4) cage at R8C4 must have at least one of 7,8,9 since {3456} only total 20. Then hidden killer triple 7,8,9 in R79C5 and R89C4 -> only one of 7,8,9 in R8(C4 -> 23(4) cage at R8C4 ={3569/4568} (all other combinations have two of 7,8,9). The rest of step 13 and step 13a would still follow as before
This is the way that Afmob used, but I think you have been a bit more technically correct calling it "hidden" killer triple. For example, SudokuSolver can't find this one since for it, a killer triple has to have 2 complete cages in the one house, or 1 complete cage and 1/2 single cells all in the same house.

Because there is one cell outside the nonet (r9c3), it cannot find a killer triple. Hidden killer triple is also in Richard's queue.
Andrew wrote:
That makes me think that some hidden killers can also be ALS cage blocks
As has happened this time - two ways to get the same result. As long as we keep clear that ALS blocks involve single cells that don't have a single cage enclosing them.
Andrew wrote:
although most hidden killers won't be
Nor will most ALS cage blocks. I think I'm right that all the examples Mike gave and this one from A88 cannot be found by (hidden) killer subsets. Sounds like Jean-Christophe has just worked with the hidden killer subset on JSudoku, not the 2-cell ALS block. I hope Richard does both with SS.
Andrew wrote:
step 14 is still required IMHO because the hidden killer triple and the killer triple do different things; one is inclusive and the other is exclusive.
I think technically these are both hidden killer subset moves since they only work because r9c3 does not have (789).

I'm not exactly sure about inclusive and exclusive part. But this could be the reason for why Richard has "killer pairs", "hidden killer pairs" and has just introduced "forced killer pairs" in SudokuSolverV3.

eg, for Bored89-Easy it says forced Killer Pair found in cage 5(2) n5 & r8c6 for c6 -> r8c6 = {12}. I'm a bit vague on what the exact difference is between "hidden" & "forced", so perhaps inclusive & exclusive belong in here somewhere also. I'm planning on just continuing to use "hidden" killer pair for this situation (when I finally get around to another walk-through!).

Bored89-Easy: Forced killer pair in 5(2) n5 & r8c6 for c6 -> r8c6 = {12}
Code:
.-----------------------------------------------------------------------.
|(17)   :       :       |(15)   :       :       |(25)   :       :       |
|  123  :  123  :  123  |    3  :  123  :    3  |  123  :  123  :  123  |
|  456  :  456  :  456  |  456  :  456  :  45   |  4 6  :  456  :  456  |
|  789  :  789  :  789  |       :       :       |  78   :  789  :  789  |
|.......----------------|-------:.......--------|---------------:.......|
|       |(22)   :       :       |       |(18)   :       :       |       |
|  123  |   23  :   23  :  12   |  123  |       :  123  :  123  |  123  |
|  456  |  456  :  456  :   5   |  456  |  45   :  4 6  :  456  |  456  |
|  789  |  789  :  789  :  7    |       |  7    :  78   :  789  |  789  |
|-------|-------:.......--------|-------|-------:.......--------|-------|
|(15)   :       |       |(14)   |(17)   :       |       |(13)   :       |
|  12   :  12   |    3  |  12   |       :       |    3  |  12   :  12   |
|   56  :   56  |  4    |   5   |       :       |  4    |   56  :   56  |
|  7    :  7    |       |  7    |   89  :   89  |       |  7    :  7    |
|.......--------|-------|.......|---------------|-------|-------:.......|
|       |(25)   |       :       |(19)   |( 5)   |(14)   |(16)   |       |
|   2   |  123  |  123  :       |    3  |  123  |       |  123  |       |
|  4    |  456  |  45   :    6  |  4    |  4    |   5   |  4    |  4 6  |
|  78   |  789  |  7    :   89  |  789  |       |    9  |  78   |  7    |
|-------|.......|---------------|.......|.......|.......|.......|-------|
|       :       |( 9)   |( 7)   |       |       |       |       :       |
|  123  :  123  |  123  |  12   |       |  123  |       |  123  :  123  |
|  456  :  456  |  456  |   56  |       |  4    |   5   |  4    :  4    |
|  789  :  789  |  78   |       |  789  |       |    9  |  78   :  78   |
|-------:.......|.......|.......|.......|-------|-------|.......--------|
|(15)   |       |       |       |       |(15)   :       |       |(18)   |
|  123  |  123  |  123  |  12   |    3  |       :  12   |  123  |       |
|  456  |  456  |  456  |   56  |  4    |   56  :  4    |  4    |  4 6  |
|  7    |  789  |  78   |       |  789  |   8   :       |  78   |  78   |
|.......|-------|-------|-------|-------|.......--------|-------|.......|
|       :       |(17)   |(13)   :       |       |(19)   |       :       |
|    3  :    3  |  12   |       :       |       |  12   |    3  :    3  |
|  456  :  456  |       |       :  456  |  456  |       |  456  :  456  |
|  789  :  789  |       |  789  :       |  78   |       |  789  :  789  |
|---------------|.......|---------------|-------|.......|---------------|
|(23)   |       :       :       |(17)   |       :       :       |(17)   |
|  123  |  123  :  123  :    3  |  123  |  123  :    3  :    3  |  123  |
|  456  |  456  :  456  :  456  |  456  |   5   :  4 6  :  456  |  456  |
|  789  |  789  :  789  :  789  |       |       :  78   :  789  |  789  |
|.......|-----------------------|.......|-----------------------|.......|
|       :       :       |       :       :       |       :       :       |
|  123  :  123  :  123  |    3  :  123  :       |  123  :  123  :  123  |
|  456  :  456  :  456  |  456  :  456  :       |  4 6  :  456  :  456  |
|  789  :  789  :  789  |       :       :  789  |  78   :  789  :  789  |
.-----------------------------------------------------------------------.


Making me think hard! Thanks Andrew :D .

Cheers
Ed


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PostPosted: Sat Jul 19, 2008 10:07 am 
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unofficial Assassin 95 (uA95) by sudokuEd (Mar 08)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:3585:3585:4610:4867:2820:2820:4613:4613:4613:3585:4610:4610:4867:2820:4614:4614:4614:1543:4360:4360:1801:4867:4874:4874:4874:3595:1543:7180:4360:1801:4867:2061:2061:3595:3595:4622:7180:7180:5135:5135:5135:5135:5135:4622:4622:7180:2064:2064:2833:2833:5650:3347:4884:4622:2325:2064:4118:4118:4118:5650:3347:4884:4884:2325:4119:4119:4119:5144:5650:3097:3097:3610:2587:2587:2587:5144:5144:5650:3097:3610:3610:
Solution:
+-------+-------+-------+
| 7 5 9 | 2 3 1 | 6 4 8 |
| 2 1 8 | 4 7 6 | 9 3 5 |
| 4 6 3 | 5 8 9 | 2 7 1 |
+-------+-------+-------+
| 9 7 4 | 8 5 3 | 1 6 2 |
| 5 8 2 | 6 1 4 | 7 9 3 |
| 6 3 1 | 9 2 7 | 5 8 4 |
+-------+-------+-------+
| 1 4 7 | 3 6 5 | 8 2 9 |
| 8 9 6 | 1 4 2 | 3 5 7 |
| 3 2 5 | 7 9 8 | 4 1 6 |
+-------+-------+-------+
Quote:
sudokuEd, lead-in: This puzzle has a ridiculously low SS(v3)score of 1.05. But it took about 6 sessions to finally find the 2 key moves...they are not hard moves, just very-hard-for-me to find. So, I give it a rating of 1.25
Afmob: I agree with Ed that this Killer should be rated above 1.0. It took me some time to find step 5a (though the step itself is not difficult) Rating: (Easy) 1.25
gary w: I'ld rate this as 1.25 at least..or maybe I'm out of practice!?
Andrew: Afmob's steps 2d and 3b are the sort of steps that are so easy not to spot..Using an innie pair and an outie pair.. isn't a particularly common step. Steps 4a and 5c were also interesting. With those steps, together with Afmob saying that step 5a was difficult to spot, I felt that it should have been rated 1.25 rather than (Easy) 1.25
mhparker: I took a very similar route to Andrew..Despite avoiding a contradiction move, I would still go along with Andrew's rating of a typical 1.25, rather than an "easy 1.25"
Walkthrough by Afmob:
I agree with Ed that this Killer should be rated above 1.0. It took me some time to find step 5a (though the step itself is not difficult) and after that the puzzle was pretty much solved. Another interesting move was step 4a which helped me to shorten the end game a bit.

By the way, I finally got the status "Addict" which more fits I think :wink:.

UA 95 Walkthrough:

1. C123
a) 28(4) = 89{47/56} -> 8,9 locked for N4
b) Outies N1 = 11(2) = [56/65/74]
c) 7(2): R3C3 <> 4,5,6
d) Hidden Triple (123) in R5C3+R6C23 for N4 -> no other candidates
e) 8(3) must have 4 xor 5 and it's only possible @ R7C2 -> R7C2 = (45)
f) 8(3) = 1{25/34} -> 1 locked for R6+N4
g) Naked triple (123) locked in R356C3 for C3
h) 9(2) <> 4,5 because {45} blocked by R7C2 = (45)
i) 10(3) <> 4 because {145} blocked by R7C2 = (45)
j) 10(3) must have 5,6 xor 7 and R9C3 = (567) -> R9C12 <> 5,6,7

2. R6789
a) Innies+Outies N7: -10 = R8C4 - R7C23
-> R8C4 = (1234) because R7C23 <= 14
-> R7C3 <> 4,5 because R7C23 must at least be 11
b) Outies N9 = 13(2) <> 2,3
c) Innies = 10(2) = [46/64/73/82]
d) Using Outies N9 = 13(2): R6C236 = 11(3) = 1{28/37} -> R6C6 = (78)
e) 11(2) <> {38} since it's a Killer pair of R6C236
f) Outies R89 = 13(2+1): R7C16 <> 6,7,8,9 because R6C6 >= 7
g) Naked triple (123) locked in R7C1+R9C12 for N7

3. R1234
a) Innies = 11(2): R4C9 <> 1,8,9
b) Using Outies N1 = 11(2): R4C478 = 15(3): R4C4 <> 1 because R4C78 @ 14(3) <= 13
c) R4C478 = 15(3) <> 7 because 7{26/35} blocked by Killer pairs (57,67) of Outies N1
d) 17(3): R3C12 <> 5 because there is no combo with {56} or {57}

4. R789 !
a) ! Innies N9 = 19(3) must have 2 of (6789), only other place possible in R7
is 16(3) -> 16(3) must have 2 of (6789)
b) 16(3) = {169/178/268/367} <> 4,5
c) Innies N9 = 19(3) <> 5 because {568} blocked by Killer pair (68) of 16(3) @ R7
d) 13(2): R6C7 <> 8
e) Outies N9 = 13(2): R6C8 <> 5

5. R456 !
a) ! Hidden Killer pair (89) in R4C1 for R4 since R4C478 can only have one of (89) -> R4C1 = (89)
b) Innies R1234 = 11(2) = [83/92]
c) Innies R6789 = 10(2) <> 2,8 since [82] is a Killer pair of Innies R1234
d) 11(2) <> {47} because it's a Killer pair of Innies R6789
e) 8(2) <> {26} since it's a Killer pair of 11(2)
f) Outies N9 = 13(2) <> {67} since it's a Killer pair of Innies R6789
g) 13(2) <> 6,7
h) 7 locked in R5C789 for R5
i) 28(4): R6C1 <> 4 because 7 only possible there

6. R456 !
a) Innies R6789 = 10(2): R6C9 <> 6
b) 4 locked in R6C789 for N6
c) 20(5) = 12{359/368/467} since other combos blocked by Killer pair (45) of 28(4)
-> 1,2 locked for R5
d) ! 18(4) <> {3456} because it's blocked by Killer pair (56) of 20(5)
e) 18(4) = 2{349/358/367/457} -> R4C9 = 2
f) Innies R1234 = [92] -> R4C1 = 9
g) 28(4) = 89{47/56} -> 8 locked for R5
h) 18(4) = 23{49/67} since {2457} blocked by Killer pair (45) of Outies N9
-> 3 locked for N6
i) R4C478 = 15(3) <> 5 because {456} blocked by Killer pair (46) of Outies N1

7. C789
a) 6(2) = {15} locked for C9+N3
b) 14(3) @ N3 = {167} since R4C78 = (168) and R3C8 <> 5 -> R3C8 = 7, {16} locked for R4+N6
c) 18(4) = {2349} -> R6C9 = 4, {39} locked for R5+N6
d) 13(2) = [58] -> R6C7 = 5, R7C7 = 8
e) 18(3) @ R1C7 = 6{39/48} -> 6 locked for R1+N3
f) R6C8 = 8 -> 19(3) = 8[29/47]

8. R456
a) 11(2) = {29} locked for R6+N5
b) 8(3) = {134} -> R7C2 = 4
c) Outies N1 = 11(2) = [74] -> R4C2 = 7, R4C3 = 4 -> R3C3 = 3
d) R6C1 = 6

9. R789
a) 19(3) = {289} -> R7C8 = 2, R7C9 = 9
b) 16(3) @ R7 = {367} -> 3 locked for R7+N8
c) 9(2) = [18] -> R7C1 = 1, R8C1 = 8
d) Hidden Single: R9C1 = 3 @ C1 -> R9C3 = 5, R9C2 = 2
e) 16(3) @ R8 = {169} -> R8C4 = 1, {69} locked for R8+N7

10. R123
a) 17(3) = 7[28/46] -> R3C2 = (68)
b) Hidden Single: R4C4 = 8 @ R4 -> 19(4) = 28{36/45} -> 2 locked for C4+N2
c) Killer pair (46) of 19(4) blocks {146} of 11(3)
d) 11(3) = {137} locked for N2
e) 19(4) = {2458} -> {45} locked for C4+N2
f) 18(3) @ R2C6 = 6{39/48} -> R2C6 = 6
g) 18(3) @ R2C6 = {369} -> {39} locked for R2+N3

11. N89
a) Hidden Single: R8C8 = 5 @ N9 -> 12(3) = {345} -> R8C7 = 3, R9C7 = 4
b) 20(3) = {479} -> R8C5 = 4, {79} locked for R9+N8

12. Rest is singles.

Rating: (Easy) 1.25
Outline by gary w:
I'ld rate this as 1.25 at least..or maybe I'm out of practice!?
The innies of n14-> r5c3=2/3,r6c23=1 2/3 so r7c2=4/5,hence r6c6=7/8.With r7c126=10 combo work in n7 places 4 in either r7c2 or r8c23.It is then fairly straightforward to eliminate 3 from r4c3 as this would place a 3 at both r4c4 and r4c8.

Regards

Gary
Walkthrough by Andrew:
Thanks for a fun puzzle Ed! :D
Afmob wrote:
By the way, I finally got the status "Addict" which more fits I think :wink:.
Congratulations! It won't take you too long to reach Expert and Master, which are also appropriate!

Afmob's steps 2d and 3b are the sort of steps that are so easy not to spot; I missed them. Using an innie pair and an outie pair to do a 45 isn't a particularly common step. Steps 4a and 5c were also interesting. With those steps, together with Afmob saying that step 5a was difficult to spot, I felt that it should have been rated 1.25 rather than (Easy) 1.25.

Gary's R7C126 = 10 is useful although both Afmob and I got the same cage eliminations using different steps; however the only possible combinations in R7C126 do lock 5 for R7 very quickly.

I used one, fairly easy to spot, contradiction move so I'll rate this puzzle 1.25.

Ed commented that SS had two key moves that gave this puzzle a low rating. I'll be interested to see what they were. I don't think I found either of them.

Here is my walkthrough

Prelims

a) R23C9 = {15/24}
b) R34C3 = {16/25/34}, no 7,8,9
c) R4C56 = {17/26/35}, no 4,8,9
d) R6C45 = {29/38/47/56}, no 1
e) R67C7 = {49/58/67}, no 1,2,3
f) R78C1 = {18/27/36/45}, no 9
g) 11(3) cage in N2 = {128/137/146/236/245}, no 9
h) R3C567 = {289/379/469/478/568}, no 1
i) 8(3) cage at R6C2 = 1{25/34}, CPE no 1 in R45C2
j) 19(3) cage at R6C8 = {289/379/469/478/568}, no 1
k) 20(3) cage in N8 = {389/479/569/578}, no 1,2
l) R9C123 = {127/136/145/235}, no 8,9
m) 28(4) cage in N4 = {4789/5689}, 8,9 locked for N4

1. 45 rule on N1 2 outies R4C23 = 11 = {56}/[74], clean-up: no 4,5,6 in R3C3
1a. 17(3) cage at R3C1 = {179/269/278/359/368/458/467}
1b. 5 of {359/458} must be in R4C2 -> no 5 in R3C12

2. Killer pair 4,5 in R4C23 and 28(5) cage, locked for N4
2a. Killer pair 6,7 in R4C23 and 28(5) cage, locked for N4
[Alternatively 45 rule on N14 3 innies R5C3 + R6C23 = 6 = {123} or another alternative hidden triple {123} in R5C3 + R6C23. Take your pick! :wink: ]

3. 8(3) cage at R6C2 = 1{25/34}
3a. 4,5 only in R7C2 -> R7C2 = {45}
3b. 1 locked in R6C23, locked for R6 and N4
3c. R78C1 = {18/27/36} (cannot be {45} which clashes with R7C2), no 4,5
[I should also have spotted that R7C2 = {45} eliminates 4 from R9C123]

4. Naked triple {123} in R356C3, locked for C3

5. 45 rule on N9 2 outies R6C78 = 13 = {49/58/67}, no 2,3

6. 45 rule on N7 2 innies R7C23 = 1 outie R8C4 + 10, max R7C23 = 14 -> max R8C4 = 4
6a. Max R8C34 = 13 -> min R8C2 = 3

7. 45 rule on R1234 2 innies R4C19 = 11 = {47/56}/[83/92], no 1,8,9 in R4C9

8. 45 rule on R6789 2 innies R6C19 = 10 = {46}/[73/82], no 5,9, no 7,8 in R6C9

9. 45 rule on N23 1 outie R4C4 = 1 innie R3C8 + 1, no 1 in R4C4, no 9 in R3C8

10. 45 rule on N78 1 outie R6C6 = 1 innie R7C2 + 3 -> R6C6 = {78}

11. Hidden killer pair 5,9 in R6C45 and R6C78. Neither can have both 5 and 9 -> R6C45 = {29/56}, R6C78 = {49/58}, clean-up: no 6,7 in R7C7
11a. R4C56 = {17/35} (cannot be {26} which clashes with R6C45), no 2,6

12. 45 rule on R89 2 outies R67C6 = 1 innie R8C1 + 4
12a. Min R67C6 = 8 -> no 1,2,3 in R8C1, clean-up: no 6,7,8 in R7C1
12b. Min R8C1 = 6 -> min R67C6 = 10, no 1 in R7C6
12c. Max R8C1 = 8 -> max R67C6 = 12, no 6,7,8,9 in R7C6

13. 45 rule on N69 1 outie R3C8 = 1 innie R5C7, no 9 in R5C7

14. 45 rule on C123 2 innies R57C3 = 1 outie R8C4 + 8, min R57C3 = 9 -> min R7C3 = 6

15. 45 rule on N5 5 innies R4C4 + R5C456 + R6C6 = 26 and must contain 4 = {14678/23489/34568} (cannot be {14579/24569/24578} which clash with R6C45)

16. Killer pair 5,7 in R4C23 and R4C56, locked for R4, clean-up: no 4,6 in R3C8 (step 9), no 4,6 in R4C19 (step 7), no 4,6 in R5C7 (step 13)

17. 7 in N6 locked in R5C789, locked for R5

18. R6C6 = R7C2 + 3 (step 10)
18a. 45 rule on N14 R7C2 = R5C3 + 2
18b. -> R6C6 = R5C3 + 5

19. R4C4 + R5C456 + R6C6 (step 15) = {14678/23489/34568}
19a. 8 of {23489} must be in R6C6 => R5C3 => 3 (step 18b) => R4C4 = 3 => R3C8 = 2 (step 9) => R5C7 = 2 (step 13) -> R4C4 + R5C456 + R6C6 cannot be {23489}
19b. R4C4 + R5C456 + R6C6 = {14678/34568}, no 2,9, 6 locked for N5, clean-up: no 1,8 in R3C8 (step 9), no 1,8 in R5C7 (step 13), no 5 in R6C45

20. Naked pair {29} in R6C45, locked for R6, clean-up: no 8 in R6C1 (step 8), no 4 in R6C78, no 4,9 in R7C7
20a. Naked pair {58} in R6C78, locked for R6 and N6 -> R6C6 = 7, R7C2 = 4 (step 10), clean-up: no 5 in R3C8 (step 13), no 6 in R4C4 (step 9), no 1 in R4C56, no 3 in R6C9 (step 8)

21. R4C2 = 7 (hidden single in R4), R4C3 = 4 (step 1), R3C3 = 3, R5C3 = 2, R6C23 = [31], R6C19 = [64]; clean-up: no 2 in R23C9, no 3 in R7C1

22. Naked pair {35} in R4C56, locked for R4 and N5 -> R4C4 = 8, R3C8 = 7 (step 9), R5C7 = 7 (step 13), R4C19 = [92]
22a. Naked pair {16} in R4C78, locked for N6

23. R9C1 = 3 (hidden single in C1), R9C23 = 7 = [16/25]

24. Naked pair {15} in R23C9, locked for C9 and N3

25. R4C4 = 8 -> R123C4 = 11
25a. 45 rule on N2 3 innies R2C6 + R3C56 = 23 = {689}, locked for N2

26. R3C567 = {289/469} -> R3C7 = {24}, 9 locked in R3C56, locked for R3 and N2

27. R4C2 = 7 -> R3C12 = 10 = {28}/[46], no 1
27a. Killer pair 2,4 in R3C12 and R3C7, locked for R3

28. R123C4 = 11 (step 25) = {137/245}
28a. R3C4 = {15} -> no 1,5 in R12C4

29. R2C678 = {369/468}, no 2, 6 locked for R2

30. R1C789 = {369/468}, no 2, 6 locked for R1 and N3 -> R2C6 = 6 (step 29)

31. R3C7 = 2 (hidden single in N3), clean-up: no 8 in R3C12 (step 27) -> R3C12 = [46]

32. 18(3) cage in N1 = {189/279}, no 5, 9 locked for N1
32a. 1,2 only in R2C2 -> R2C2 = {12}
32b. 9 locked in R12C3, locked for C3

33. Naked pair {12} in R29C2, locked for C2
33a. Naked pair {58} in R15C2, locked for C2 -> R8C2 = 9
33b. R8C34 = 7 = [52/61]
33c. Naked pair {56} in R89C3, locked for C3

34. R7C345 = {178/268/358/367} (cannot be {169/259} because R7C3 only contains 7,8), no 9

35. 9 in R7 locked in R7C89, locked for N9
35a. R6C8 = [829] (only remaining permutation), R5C89 = [93], R67C7 = [58], R7C3 = 7, R78C1 = [18], R5C12 = [58], R9C23 = [25] (step 23), R12C2 = [51], R23C9 = [51], R3C4 = 5, R8C34 = [61] (step 33b)
35b. R3C4 = 5 -> R12C4 = {24} (step 28), locked for C4 and N2 -> R5C4 = 6, R6C45 = [92], R7C4 = 3, R7C56 = [65], R9C4 = 7, R8C56 = [42], R5C56 = [14], R4C56 = [53], R1C6 = 1, R8C78 = [35], R89C9 = [76], R1C9 = 8, R12C3 = [98]

36. R1C789 (step 30) = {468}, 4,6 locked for R1 and N3

and the rest is naked singles and a couple of cage sums
Alt ending by mhparker: 2-cell ALS block:
Andrew wrote:
Thanks for a fun puzzle Ed! :D
Indeed. Thanks, Ed!
Andrew wrote:
I used one, fairly easy to spot, contradiction move so I'll rate this puzzle 1.25.
I took a very similar route to Andrew up to and including his step 17, but managed to avoid a contradiction move as follows:

Grid state after Andrew's step 17:

Code:
.-----------------------.-----------.-----------.-----------------------.-----------------------------------.
| 123456789   123456789 | 456789    | 123456789 | 12345678    12345678  | 123456789   123456789   123456789 |
|           .-----------'           |           |           .-----------'-----------------------.-----------:
| 123456789 | 123456789   456789    | 123456789 | 12345678  | 123456789   123456789   123456789 | 1245      |
:-----------'-----------.-----------:           :-----------'-----------------------.-----------:           |
| 12346789    12346789  | 123       | 123456789 | 23456789    23456789    23456789  | 123578    | 1245      |
:-----------.           |           |           :-----------------------.-----------'           :-----------:
| 89        | 567       | 456       | 234689    | 1357        1357      | 1234689     1234689   | 23        |
|           '-----------+-----------'-----------'-----------------------'-----------.-----------'           |
| 45689       45689     | 23          12345689    12345689    12345689    123578    | 123456789   123456789 |
|           .-----------'-----------.-----------------------.-----------.-----------+-----------.           |
| 4678      | 123         123       | 2569        2569      | 78        | 4589      | 4589      | 2346      |
:-----------:           .-----------'-----------------------:           |           |           '-----------:
| 123       | 45        | 6789        123456789   123456789 | 2345      | 4589      | 23456789    23456789  |
|           :-----------'-----------------------.-----------:           :-----------'-----------.-----------:
| 678       | 3456789     456789      1234      | 3456789   | 123456789 | 123456789   123456789 | 123456789 |
:-----------'-----------------------.-----------'           |           |           .-----------'           |
| 1234567     1234567     4567      | 3456789     3456789   | 123456789 | 123456789 | 123456789   123456789 |
'-----------------------------------'-----------------------'-----------'-----------'-----------------------'


18. 28(4) cage in N4 (prelim. m) = {4789/5689}
18a. 7 only available in R6C1
18b. -> no 4 in R6C1
18c. cleanup: no 6 in R6C9 (step 8)

19. 6(2) at R23C9 = {15}, locked for C9 and N3
(Note: {24} combo blocked by R46C9)
19a. no 1,5 in R5C7 (step 13)

20. 18(4) at R4C9: max. R46C9 = 7 -> min. R5C89 = 11
20a. -> no 1 in R5C8

21. 1 in N6 locked in 14(3) at R3C8 = {167} (last combo)
21a. -> R3C8 = 7; R4C78 = {16}, locked for R4 and N6
...

Note: I decided to make this post because step 19 is another good example of the use of a 2-cell ALS blocker, as discussed in the YAK94 thread.

P.S. Despite avoiding a contradiction move, I would still go along with Andrew's rating of a typical 1.25, rather than an "easy 1.25"
2 more Alt endings by sudokuEd:
Afmob wrote:
if we combine Andrew's step 11 and 16..my step 5c we can come to a short and easy walkthrough
Afmob's step 5c was the key move for me and hence the double-headed axe gif . Fun one!
...

Now, two more ways from Andrew's step 17 marks (see Mike's post). First, adapted from the way that SudokuSolver v3 (scoring routine order) makes it's big breakthrough (edit: incorrect combo's in 11(2)n5 taken out: thanks Andrew) and which leads to the low SS(v3)score of 1.05.
18. "45" n69: 3 innies r4c78 + r5c7 = h14(3) = {149/158/167/248/257/347/356} ({239} blocked by r4c9)
18a. -> no 3 in r5c7 (missing 5 or 7 in r4c78)
18b. -> no 3 in r3c8 (i/o n69)
18c. -> no 4 in r4c4 (i/o n23)

19. 4 in n5 only in r5: 4 locked for r5

20. 28(4)n4 = 89{47/56}
20a. 4 in {4789} must be in r6c1 -> no 7 in r6c1
20b. -> no 3 in r6c9 (h10(2)r6c19)

21. hidden pair {13} in r6c23 -> r7c2 = 4, r5c3 = 2
21a. & 7 in r6c6 (i/0 n1478)

Second, another move I stumbled on playing with SudokuSolver which it called by another name, but looks like Y-wing to me.
18. 3s in r5c3 & r4c9 'see' all 3's in r6 -> they cannot both be 3
18b. -> no 2 in common peers in r5c789 since this would force both r5c3 & r4c9 = 3
18c. -> no 2 in in r3c8(i/o n69)
18d. -> no 3 in r4c4 (i/o n23)

Now Andrew's (first part of) step 19
19. R4C4 + R5C456 + R6C6 (step 15) = {14678/23489/34568}
19a. 8 of {23489} must be in R6C6 => R5C3 => 3 (step 18b)
19b. but this clashes with 3 in r5 of innies n5
19c. back to Andrew's 19b

Cheers
Ed


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PostPosted: Sat Jul 19, 2008 10:11 am 
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Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1043
Location: Sydney, Australia
nd's #9 (aka Night of the Living Sudoku) presented by sudokuEd (Mar 08)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:2816:2816:5378:2307:6660:6660:6660:6151:6151:2816:5378:5378:2307:6413:6660:7183:7183:6151:2834:3859:2836:2307:6413:7183:7183:6151:6151:2834:3859:2836:4126:6413:6413:7183:7202:7202:2834:5413:2836:4126:6413:6413:5930:5930:7202:5413:5413:4126:4126:6705:5938:5938:5930:7202:8502:5413:7736:6705:6705:6705:5938:5930:5930:8502:8502:7736:7736:7736:7736:5938:5938:6215:8502:8502:8502:8502:6215:6215:6215:6215:6215:
Solution:
+-------+-------+-------+
| 3 2 7 | 1 6 8 | 5 9 4 |
| 6 9 5 | 3 4 7 | 8 2 1 |
| 1 8 4 | 5 2 9 | 6 3 7 |
+-------+-------+-------+
| 2 7 1 | 4 9 6 | 3 5 8 |
| 8 5 6 | 2 1 3 | 4 7 9 |
| 9 4 3 | 7 8 5 | 2 1 6 |
+-------+-------+-------+
| 4 3 8 | 9 7 2 | 1 6 5 |
| 5 1 9 | 6 3 4 | 7 8 2 |
| 7 6 2 | 8 5 1 | 9 4 3 |
+-------+-------+-------+
Quote:
sudokuEd, lead-in: I spent Easter '06 trying to solve this beauty and have been hopelessly hooked on (difficult) killers ever since
Afmob: you could totally ignore some nonets to crack it ....At first I wanted to rate it 1.75 but I discovered that the complex combo analysis I had used wasn't necessary to solve it so I deleted it from my wt. Rating: 1.5. I used one forcing chain and a Hidden Killer quad
mhparker: Afmob's 1.5 rating! :shock: (<-- very surprised, because I would have expected a 1.75 - or even a 2.0 :!: - here, due to need for a chain to break the deadlock)
sudokuEd: Afmob, some really great moves in steps 1-3! But your first instinct works much better for me - no way could I seriously put this classic onto the rating sticky as a 1.5 (more like a 2.0 with that type of chain)!
Afmob: I rated ND 9 only "1.5" because when I solved it, it flowed quite well meaning I didn't really came to halt despite those difficult moves. Also my wt is quite short and doesn't have this many ! moves where as my other 1.75 walkthroughs are usually quite large and have many ! moves and they also wouldn't be cracked with one chain only... So maybe it's more a hard 1.5. Compared to UA97 V2 which I'm tackling at the moment (made 4 placements so far) ND9 is way easier
Andrew (in 2012): I'm working on nd's killers again, having intended for a long time to try them all and write walkthroughs for them; I originally solved six of them back in 2006 before I was first introduced to Ruud's Assassins. This is the first time I've tried nd#9.
In Afmob's solving path I loved step 3a; I didn't look at 21(4) cage at R5C8 until much later in my solving path.
Walkthrough by Afmob:
This was an interesting Killer since you could totally ignore some nonets to crack it which is the reason why my wt is quite short since I only used those "useless" nonets in the endgame.
At first I wanted to rate it 1.75 but I discovered that the complex combo analysis I had used wasn't necessary to solve it so I deleted it from my wt.

The overlap technique (step 2 from the blog) is quite useful in this Killer though you can come to the same results with more but easier moves.

I don't know why the SS rating so high (nearly off by 1.0!), maybe the X-Chain and techniques in the "useless" areas which SudokuSolver used, raised it so high.

ND's #9 Walkthrough:

1. C1234
a) Innies = 32(2+2) <> 1,2,3,4,5; R7C4 <> 6,7
b) Innies+Outies C4 : -20 = R6C3 - R789C4 -> R6C3 = (1234); R9C4 <> 1,2,3
c) Innies+Outies N14: R6C3 = R7C2 = (1234)
d) 30(5) = 89{157/247/256/346} because of step 1a
-> 8,9 locked between R8+N7 -> R8C12 <> 8,9
-> R8C56 = (12345)
e) Innies N1 = 13(3): R3C13 <> 6,7,8 because R3C2 >= 6
f) 5 locked in 33(7) @ N7 = 12567{39/48} -> 1,2 locked for N7
g) Innies+Outies N14: R6C3 = R7C2 = (34)
h) Innies+Outies C4 : -20 = R6C3 - R789C4 -> R789C4 = 23/24(3) = 89{6/7}
-> 8,9 locked for C4+N8
i) Innies+Outies C12: 1 = R9C34 - R2C2
-> R2C2 <> 4,5 because R9C34 >= 7
-> R9C3 = (1234) because R9C4 >= 6
j) 9(3) = 3{15/24} because {126} blocked by Killer pair (12) of 16(4) -> 3 locked for C4+N2

2. R789
a) Outies R9 = 12(3+1) -> R7C1+R8C9 <> 7,8,9
b) Hidden Killer pair (89) in 24(6) for R9 since 33(7) can't have both
-> 24(6) = 1234{59/68}
c) 7 locked in 33(7) @ R9 -> R8C12 <> 7
d) Killer quad (1234) locked in 24(6) + R9C3 for R9
e) 24(6) must have one of (1234) @ R8C9 (step 3d) -> R8C9 <> 5,6
f) Outies R9 = 12(3+1): R7C1 <> 5,6 since 12{3/4} are Killer triples of 30(5)
g) R8C9 <> 1 since it sees all 1 of N8
h) 24(6) = 1234{59/68} -> 1 locked for R9

3. C123 !
a) ! Hidden Killer quad (1234) in R18C2 for C2 since 21(4) can only have two of (1234)
-> R18C2 <> 5,6,7,8
b) 21(4) must have two of (1234) @ C2 -> R6C1 <> 1,2,3,4
c) Naked quad (1234) locked in R7C12+R8C2+R9C3 for N7
d) 1 locked in 11(3) @ C3 = 1{28/37/46} <> 5
e) 5 locked in 21(3) @ C3 = {579} locked for N1
f) 15(2): R4C2 <> 6,8
g) Naked pair (79) locked in R24C2 for C2

4. C123 !
a) ! Consider combos of 15(2) -> 11(3) @ R3C1 <> 7:
- i) 15(2) = [69] -> Innies N1 = {346} -> 1 locked in 11(3) @ C3 for N2 -> 11(3) @ R3C1 <> 1
- ii) 15(2) = [87] -> 11(3) <> {137}
b) Hidden pair (79) in R69C1 for C1 -> R69C1 <> 5,6,8
c) Naked pair (79) locked in R4C2+R6C1 for N4
d) 11(3) @ C3 = 1{28/46}
e) Innies+Outies C1: -23 = R1C2 - R6789C1 -> R7C1 <> 1 because R689C1 <= 22
f) ! Innies+Outies C1: -23 = R1C2 - R6789C1
-> R7C1 <> 2 since only combo R6789C1 = {2679} blocked by Killer pair (26) of 11(3) @ R3C1
g) 33(7) = 12567{39/48} -> R8C2 = 1, R9C3 = 2
h) 11(3) @ C3 = {146} locked for C3, 6 locked for N4
i) Innies+Outies N14: R6C3 = R7C2 = 3
j) 21(4) = 39{27/45} -> R6C1 = 9

5. C123
a) 15(2) = {78} -> R3C2 = 8, R4C2 = 7
b) Innies N1 = 13(3) = {148} locked for R3+N1
c) Hidden Single: R9C2 = 6 @ C2, R8C1 = 5
d) R7C1 = 4, R9C1 = 7 -> R9C4 = 8
e) Outies = 23(3) = {689} -> R8C4 = 6, R7C4 = 9

6. N568
a) 26(4) = {2789} because R7C56 = (257) -> R6C5 = 8, {27} locked for R7+N8
b) 3 locked in 25(6) @ N5 -> 25(6) = {123469}
c) 28(4) = 89{47/56} -> 8,9 locked for N6
d) R7C3 = 8, R8C3 = 9
e) Naked pair (34) locked in R8C56 for R8+N8
f) R8C9 = 2
g) 23(5) @ R5C7 = 567{14/23} -> 7 locked for N6
h) 28(4) = {5689} locked for N6
i) 23(5) @ R5C7 must have 5 and 6 and it's only possible @ R7C89 -> {56} locked for N9

7. N56
a) 23(5) @ R6C6 = {12578} -> R7C7 = 1, R6C6 = 5, R7C6 = 2
b) 16(4) = {2347} -> {247} locked for C4+N5
c) 25(6) = {123469} -> R2C5 = 4, R3C5 = 2
d) 23(5) @ R5C7 = {14567} -> 4 locked for N6, 1 locked for C8
e) R4C7 = 3 -> 28(5) = {23689} -> R2C8 = 2, R2C7 = 8, {69} locked for R3

8. Rest is singles.

Rating: 1.5. I used one forcing chain and a Hidden Killer quad
Alt ending by sudokuEd:
Afmob wrote:
At first I wanted to rate it 1.75 ...Rating: 1.5. I used one forcing chain and a Hidden Killer quad
Oh Afmob, some really great moves in steps 1-3! But your first instinct works much better for me - no way could I seriously put this classic onto the rating sticky as a 1.5 (more like a 2.0 with that type of chain)! Did the 1.75 way you used still need a looking-3-ways-chain? I'd much, much rather combo-crunching.

If it did still need that chain, here's a way that looks simpler for step 4.

Marks at the end of Amob's step 3

Code:
.-------------------------------.-------------------------------.-------------------------------.
| 123468    1234      579       | 12345     2456789   2456789   | 23456789  123456789 123456789 |
| 123468    79        579       | 12345     12456789  2456789   | 123456789 123456789 123456789 |
| 1234      68        1234      | 12345     12456789  12456789  | 123456789 123456789 123456789 |
:-------------------------------+-------------------------------+-------------------------------:
| 12345678  79        1234678   | 124567    123456789 123456789 | 123456789 456789    456789    |
| 12345678  1234568   1234678   | 124567    123456789 123456789 | 123456789 123456789 456789    |
| 56789     1234568   34        | 124567    23456789  123456789 | 123456789 123456789 456789    |
:-------------------------------+-------------------------------+-------------------------------:
| 1234      34        6789      | 89        234567    234567    | 123456789 123456789 123456789 |
| 56        1234      6789      | 6789      12345     12345     | 123456789 123456789 234       |
| 56789     568       234       | 6789      123456    123456    | 12345689  12345689  12345689  |
'-------------------------------.-------------------------------.-------------------------------'

Code:
.-----------------------------------------------------------------------.
|(11)   :       |(21)   |( 9)   |(26)   :       :       |(24)   :       |
|  123  :  123  |       |  123  |   2   :   2   :   23  |  123  :  123  |
|  4 6  :  4    |   5   |  45   |  456  :  456  :  456  |  456  :  456  |
|   8   :       |  7 9  |       |  789  :  789  :  789  |  789  :  789  |
|.......--------|.......|.......|-------:.......--------|-------:.......|
|       |       :       |       |(25)   |       |(28)   :       |       |
|  123  |       :       |  123  |  12   |   2   |  123  :  123  |  123  |
|  4 6  |       :   5   |  45   |  456  |  456  |  456  :  456  |  456  |
|   8   |  7 9  :  7 9  |       |  789  |  789  |  789  :  789  |  789  |
|-------|---------------|.......|.......|-------|.......--------|.......|
|(11)   |(15)   |(11)   |       |       |       :       |       :       |
|  123  |       |  123  |  123  |  12   |  12   :  123  |  123  :  123  |
|  4    |    6  |  4    |  45   |  456  |  456  :  456  |  456  :  456  |
|       |   8   |       |       |  789  |  789  :  789  |  789  :  789  |
|.......|.......|.......|-------|.......|-------:.......|---------------|
|       |       |       |(16)   |       :       |       |(28)   :       |
|  123  |       |  123  |  12   |  123  :  123  |  123  |       :       |
|  456  |       |  4 6  |  456  |  456  :  456  |  456  |  456  :  456  |
|  78   |  7 9  |  78   |  7    |  789  :  789  |  789  |  789  :  789  |
|.......|-------|.......|.......|.......:.......|-------|-------:.......|
|       |(21)   |       |       |       :       |(23)   :       |       |
|  123  |  123  |  123  |  12   |  123  :  123  |  123  :  123  |       |
|  456  |  456  |  4 6  |  456  |  456  :  456  |  456  :  456  |  456  |
|  78   |   8   |  78   |  7    |  789  :  789  |  789  :  789  |  789  |
|-------|.......|-------|.......|---------------|-------:.......|.......|
|       :       |       :       |(26)   |(23)   :       |       |       |
|       :  123  |    3  :  12   |   23  |  123  :  123  |  123  |       |
|   56  :  456  |  4    :  456  |  456  |  456  :  456  |  456  |  456  |
|  789  :   8   |       :  7    |  789  |  789  :  789  |  789  |  789  |
|-------:.......|---------------|.......|-------:.......|.......|-------|
|(33)   |       |(30)   |       :       :       |       |       :       |
|  123  |    3  |       |       :   23  :   23  |  123  |  123  :  123  |
|  4    |  4    |    6  |       :  456  :  456  |  456  |  456  :  456  |
|       |       |  789  |   89  :  7    :  7    |  789  |  789  :  789  |
|.......|-------|.......|-----------------------|.......|---------------|
|       :       |       :       :       :       |       :       |(24)   |
|       :  123  |       :       :  123  :  123  |  123  :  123  |   23  |
|   56  :  4    |    6  :    6  :  45   :  45   |  456  :  456  |  4    |
|       :       |  789  :  789  :       :       |  789  :  789  |       |
|.......:.......|-------------------------------|---------------|.......|
|       :       :       :       |       :       :       :       :       |
|       :       :   23  :       |  123  :  123  :  123  :  123  :  123  |
|   56  :   56  :  4    :    6  |  456  :  456  :  456  :  456  :  456  |
|  789  :   8   :       :  789  |       :       :   89  :   89  :   89  |
.-----------------------------------------------------------------------.

ALT
4a) no 7 in r9c4 because of 7's in n1
i. 7 in r12c3 -> 7 in n7 in r9c1 -> no 7 in r9c4
ii. 7 in r2c2 -> r9c34 = 8 (i/o c12) -> no 7 in r9c4
b. r9c1 = 7 (hidden single r9)
c. r6c1 = 9 (hidden single c1)

On it goes from here.

Cheers
Ed
Alt ending as (killer) Grouped Turbot Fish by mhparker:
sudokuEd wrote:
If it did still need that chain, here's a way that looks simpler for step 4.
Love this chain, Ed! Indeed, I think it's an example of a Grouped Turbot Fish, which is a specific type of AIC. Before discussing it in more detail below, I'd like to first of all present an example of a grouped turbot fish taken from a regular Sudoku, found with the help of JSudoku (thanks J-C!):

Code:
.-----------------------.-----------------------.-----------------------.
| 8       7       6     | 5       4       1     | 23      9       23    |
| 125     125     12    | 9       3       6     | 4       78      78    |
| 9       3       4     | 78      78      2     | 56      56      1     |
:-----------------------+-----------------------+-----------------------:
| 16      4       178   | 2       15689   578   | 589     3       68    |
| 12367   128     5     | 13678   16789   4     | 289     128     268   |
| 1236    9       128   | 1368    1568    358   | 7       1258    4     |
:-----------------------+-----------------------+-----------------------:
| 17      18      3     | 1678    2       9     | 68      4       5     |
| 4       258     278   | 368     568     3578  | 1       2678    9     |
| 125     6       9     | 4       158     578   | 238     278     2378  |
'-----------------------'-----------------------'-----------------------'

From this position, the following grouped Turbot fish can be applied:
Code:
(1)R4C13=R4C5-R9C5=R9C1 => R56C1<>1

In other words, if R4C13 do not contain a 1, then R4C5 must be 1 (strong link R4), implying that R9C5 cannot be 1 (weak link C5), in turn implying that R9C1 must be 1 (strong link R9). Thus, (even) if R4C13 do not contain a 1, R9C1 must be 1. Expressed differently, at least one of the two chain ends must contain a 1, thus allowing the digit 1 to be removed from the common peers R56C1.

Note that a turbot fish is an AIC where all links are based on the same digit. In this case, it's a grouped turbot fish on (the digit) 1 with 3 links, where the term "grouped" refers to the use of a multi-cell node at R4C13. As is traditionally the case with AICs in general, the chain begins and ends with a strong link.

Now let's turn our attention to Ed's move, using the marks diagram he presented above. Here, Ed used bifurcation based on two possible locations for the digit 7 in N1, namely R2C2 and R12C3. This is, however, simply making use of the fact that there is a grouped strong link between R2C2 and R12C3, allowing us to reformulate his chain in standard AIC form as follows:
Code:
(7)R9C1=R78C3-R12C3=R2C2 => R9C4<>7

In other words, if R9C1 does not contain a 7, then R78C3 must contain a 7 (strong link N7), implying that R12C3 cannot contain a 7 (weak link C3), in turn implying that R2C2 must be 7 (strong link R9). Thus, (even) if R9C1 does not contain a 7, R2C2 must do. This allows us to eliminate the candidate 7 from R9C4, even though this is not a common peer of both chain end nodes. This is because the general rule for AICs is that we can eliminate any candidate that is weakly linked to both end nodes, which (as in this case) includes any such candidates in cells that are not directly seen by either (or even both) ends of the chain.

In this case, one of the weak links is complex, in that it depends on the possible combinations ({267/289/379/469}) for the innie/outie difference cage at R2C2+R9C34, none of which contain multiple occurrences of the digit 7. Therefore, a 7 in R2C2 precludes a 7 in R9C34
Walkthrough by Andrew (in 2012):
Prelims

a) R34C2 = {69/78}
b) 11(3) cage at R1C1 = {128/137/146/236/245}, no 9
c) 21(3) cage at R1C3 = {489/579/678}, no 1,2,3
d) 9(3) cage at R1C4 = {126/135/234}, no 7,8,9
e) 11(3) cage at R3C1 = {128/137/146/236/245}, no 9
f) 11(3) cage at R3C3 = {128/137/146/236/245}, no 9
g) 26(4) cage at R1C5 = {2789/3689/4589/4679/5678}, no 1
h) 28(4) cage at R4C8 = {4789/5689}, no 1,2,3
i) 26(4) cage at R6C5 = {2789/3689/4589/4679/5678}, no 1

1. 28(4) cage at R4C8 = {4789/5689}, 8,9 locked for N6

2. 25(6) cage at R2C5 contains 1,2, CPE no 2 in R6C5

3. 45 rule on R9 4(1+3) outies R7C1 + R8C129 = 12
3a. Max R8C129 = 11, no 9 in R8C129
3b. Min R8C129 = 6 -> max R7C1 = 6
3c. Min R7C1 + R8C12 = 6 -> max R8C9 = 6

4. 45 rule on N1 3 innies R3C123 = 13 = {139/148/157/238/256/346} (cannot be {247} which clashes with 21(3) cage at R1C3)
4a. R3C2 = {6789} -> no 6,7,8 in R3C13

5. 45 rule on C4 3 innies R789C4 = 1 outie R6C3 + 20
5a. Max R789C4 = 24 -> max R6C3 = 4
5b. Min R789C4 = 21, no 1,2,3 in R789C4

6. 1 in N8 only in R89C56, CPE no 1 in R8C9
6a. Min R8C9 = 2 -> max R7C1 + R8C12 = 10 (step 3), no 8 in R8C12

7. 33(7) cage at R7C1 = {1234689/1235679/1245678}, 1,2 locked for N7

8. 45 rule on C123 3 innies R678C3 = 1 outie R9C4 + 12
[I originally saw the next sub-step as …
8a. R789C4 = R6C3 + 20 (step 5), max R78C4 = 17 -> R9C4 at least 3 more than R6C3 -> min R78C3 = 15, no 3,4,5 in R78C3
However on looking a bit more closely one can do a bit of algebra…]
8a. Rewriting steps 5 and 8
R78C4 + R9C4 – R6C3 = 20
R78C3 + R6C3 – R9C4 = 12
Adding these together R78C3 + R78C4 = 32
8b. Max R78C3 = 17 -> min R78C4 = 15, no 4,5 in R78C4
8c. Max R78C4 = 17 -> min R78C3 = 15, no 3,4,5 in R78C3
[After looking at Afmob’s walkthrough, I see that I missed that R78C34 are 4(2+2) innies = 32 for C1234.]
[Don’t think I can get anything by subtracting step 8 from step 5, at least at this stage.]

9. R678C3 = R9C4 + 12 (step 8)
9a. 45 rule on N7 3 innies R7C2 + R78C3 = 1 outie R9C4 + 12
-> R6C3 = R7C2 = {34}
[Or, more simply, 45 rule on N14 1 innie R6C3 = 1 outie R7C2 = {34}.]

10. R789C4 = R6C3 + 20 (step 5)
10a. R6C3 = {34} -> R789C4 = 23,24 = {689/789}, no 4,5, 8,9 locked for C4 and N8

11. 16(4) cage at R4C4 = {1357/1456/2347} (cannot be {1267} because R6C3 only contains 3,4, cannot be {2356} which clashes with 9(3) cage at R1C4, ALS block)
11a. Killer pair 6,7 in 16(4) cage and R789C4, locked for C4

12. 9(3) cage at R1C4 = {135/234}, 3 locked for C4 and N2

13. 45 rule on C12 2 outies R9C34 = 1 innie R2C2 + 1
13a. Min R9C34 = 7 -> min R2C2 = 6
13b. Max R9C34 = 10 -> max R9C3 = 4

14. Killer quad 1,2,3,4 in 11(3) cage at R3C3, R6C3 and R9C3, locked for C3

15. 21(3) cage at R1C3 = {579/678}, 7 locked for N1, clean-up: no 8 in R4C2
15a. R3C123 (step 4) = {139/148/238/346} (cannot be {256} which clashes with 21(3) cage), no 5

16. 25(6) cage at R2C5 = {123469/123478/123568/124567}
16a. Double killer pair 1,2 in R123456C4 and 25(6) cage, locked for N25

17. 45 rule on N3 2 outies R3C6 + R4C7 = 1 innie R1C7 + 7, IOU no 7 in R3C6

18. 24(6) cage at R8C9 = {123459/123468/123567}, 1 locked for R9
18a. Hidden killer triple 7,8,9 in 33(7) cage at R7C1 and 24(6) cage for R9, 24(6) cage contains one of 7,8,9 -> 33(7) cage must contain two of 7,8,9 in R9 -> no 7 in R8C12 (because 33(7) cage only contains two of 7,8,9)

19. 5 in N7 only in 33(7) cage at R7C1 = {1235679/1245678}, 7 locked for R9

20. 24(6) cage at R8C9 = {123459/123468}
20a. Killer triple 2,3,4 in R9C3 and 24(6) cage, locked for R9
20b. Hidden killer triple 2,3,4 in R9C3 and 24(6) cage for R9, R9C3 = {234} -> 24(6) cage contains two of 2,3,4 in R9 -> R8C9 = {234} (only other place in cage for 2,3,4)

21. R8C9 = “sees” all 2,3,4 in N8 except for R7C56, R8C9 = {234} -> R7C56 must contain one of 2,3,4 -> 26(4) cage at R6C5 = {2789/3689/4589/4679} (cannot be {5678} which doesn’t contain any of 2,3,4)
21a. One of 2,3,4 in R7C56 -> no 3,4 in R6C5
21b. 8,9 of {4589} must be in R6C5 + R7C4 -> no 5 in R6C5

22. R9C34 = R2C2 + 1 (step 13)
22a. Min R9C34 = 8 -> min R2C2 = 7
22b. Max R9C34 = 10 -> max R9C4 = 8
22c. 9 in C4 only in R78C4, CPE no 9 in R7C3

23. 1 in C3 only in 11(3) cage at R3C3 = {128/137/146}, no 5

24. 5 in C3 only in 21(3) cage at R1C3 (step 15) = {579} (only remaining combination), locked for N1, clean-up: no 6 in R4C2
24a. Naked pair {79} in R24C2, locked for C2

25. 30(5) cage at R7C3 = {15789/24789/25689/34689/35679/45678}
25a. R7C3 + R8C34 must contain three of 6,7,8,9 -> R8C56 = {15/24/25/34/35/45}, no 6,7
25b. 45 rule on C1234 1 innie R7C4 = 2 outies R8C56 + 2
25c. Min R8C56 = 6 -> min R7C4 = 8
25d. R7C4 = {89} -> R8C56 = 6,7 = {15/24/25/34}
25e. 30(5) cage = {15789/24789/25689/34689} (cannot be {45678} because max R8C56 = 7), 9 locked for R8
25f. 30(5) cage = {15789/24789/25689/34689} -> R8C3 = {89} because one of 8,9 must be in the cell which doesn’t “see” R7C4
25g. 26(4) cage at R6C5 (step 21) = {2789/3689/4679} (cannot be {4589} which clashes with R8C56), no 5

26. 21(4) cage at R5C2 = {2469/2478/3459/3468/3567} (cannot be {1569/1578/2568} because R7C2 only contains 3,4, cannot be {1479/2379} which clash with R4C2, cannot be {1389} which clashes with R34C2, combo blocker), no 1
26a. 21(4) cage = {2469/2478/3459/3468} (cannot be {3567} which clashes with R34C2, combo blocker because 9 in N4 only in R4C2 + R6C1)
26b. 7,9 of {2469/2478/3459} must be in R6C1, 6 of {3468} must be in R6C1 (R567C2 cannot be {368/468} which clash with R3C2, R567C2 cannot be {346} which clashes with R34C2, combo blocker because 9 in N4 only in R4C2 + R6C1) -> R6C1 = {679}
26c. 21(4) cage = {2469/2478/3459/3468}, 4 locked for C2

27. 21(4) cage at R5C2 (step 26a) = {2469/2478/3459/3468}, R6C3 = R7C2 (step 9a) -> R5C2 + R6C123 = {2469/2478/3459/3468}, 4 locked for N4

28. 5 in N4 only in 11(3) cage at R3C1 or in 21(4) cage at R5C2
5 in 11(3) cage at R3C1 = 4{25}, 2 locked for N4 => 21(4) cage at R5C2 (step 26a) = {3459/3468}
or 5 in 21(4) cage at R5C2 (step 26a) = {3459}
-> 21(4) cage at R5C2 = {3459/3468}, no 2,7, 3 locked for C2
28a. 21(4) cage at R5C2 = {3459/3468} -> R5C2 + R6C123 = {3459/3468}, 3 locked for N4
28b. R6C1 = {69} -> no 6 in R56C2

29. 33(7) cage at R7C1 contains 1 in C12 -> the other 1 in C12 must be either in 11(3) cage at R1C1 or 11(3) cage at R3C1
29a. Consider combinations for 11(3) cage at R3C1
11(3) cage at R3C1 contains 1 -> no 1 in 11(3) cage at R1C1
or 11(3) cage at R3C1 = {236} = 3{26} => R6C1 = 9, R4C2 = 7, R3C2 = 8 => R1C2 = 6 (hidden single in N1)
or 11(3) cage at R3C1 = {245} = 4{25} => R3C123 = 4[63/81] (step 4) => R1C2 = 2 (hidden single in N1)
-> no 1 in R1C2

30. R8C2 = 1 (hidden single in C2)
30a. R8C56 (step 25d) = 6,7, R8C9 = {234} -> max R8C569 = 11 must contain 2, locked for R8
30b. 1 in N8 only in R9C56, locked for R9
30c. 1 in N9 only in R7C789, CPE no 1 in R5C7

[Just spotted R78C3 = 15,17 (cannot be 16 = [79] which clashes with 21(3) cage at R1C3, ALS block) -> R78C4 = 15,17, step 8a.
Alternatively R78C3 and R78C4 cannot be 16 because the 7s in R7C3 and R8C4 “see” each other. ;-)]
31. R78C3 = 15 = [69/78] => R78C4 = 17 = [98/89]
or R78C3 = 17 = [89] => R78C4 = 15 = [96]
-> no 7 in R8C4

32. 7 in R8 only in R8C78, locked for N9 and 23(5) cage at R6C6, no 7 in R6C67

33. Killer pair 7,9 in 21(3) cage at R1C3 and R78C3, locked for C3)

34. 11(3) cage at R3C3 (step 23) = {128/146}, no 3
34a. 21(4) cage at R5C2 (step 28a) = {3459} (only remaining combination, cannot be {3468} which clashes with 11(3) cage at R3C3) -> R6C1 = 9, R567C2 = {345}, 5 locked for C2 and N4, R4C2 = 7, R3C2 = 8, R2C2 = 9, R9C2 = 6, R1C2 = 2

35. Naked pair {57} in R12C3, locked for C3 -> R78C3 = [89], R7C4 = 9, R8C4 = 6
35a. R9C4 = 8 (hidden single in C4)

36. R1C2 = 2 -> R12C1 = 9 = {36}, locked for C1

37. 11(3) cage at R3C1 = {128} (only remaining combination) -> R3C1 = 1, R45C1 = {28}, locked for C1 and N4, R3C3 = 4, R6C3 = 3

38. Naked pair {45} in R78C1, locked for N7 -> R7C2 = 3, R9C13 = [72]

39. R8C78 = {78} (hidden pair in R8)
39a. R8C78 = {78} = 15 -> R6C67 + R7C7 = 8 = {125} -> R6C6 = 5, R67C7 = {12}, locked for C7, R56C2 = [54]

40. 16(4) cage at R4C4 (step 11) = {2347} (only remaining combination), 2,4,7 locked for C4 and N5

41. Naked triple {135} in 9(3) cage at R4C1, locked for N2

42. 45 rule on N5 1 remaining innie R6C5 = 1 outies R23C5 + 2
42a. Min R23C5 = [42] = 6 -> R6C5 = 8, R23C5 = [42], R7C5 = 7, R7C6 = 2 (cage sum), R67C7 = [21]

43. R12C6 = {78} (hidden pair in N2)
43a. R12C6 = {78} = 15 -> R1C57 = 11 = [65], R3C6 = 9

44. Naked triple {367} in R3C789, locked for R3 and N3 -> R2C7 = 8

45. R3C6 + R4C7 = R1C7 + 7 (step 17), R1C7 = 5, R3C6 = 9 -> R4C7 = 3
45a. R8C78 = [78], R3C7 = 6, R2C8 = 2 (cage sum)

46. 30(5) cage at R7C3 (step 25f) = {34689} (only remaining combination) -> R8C56 = [34]

and the rest is naked singles.


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PostPosted: Sat Jul 19, 2008 10:13 am 
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Yet Another Killer #96 (Unofficial Assassin 96) by Jean-Christophe (Mar 08)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:7683:7683:7683:2833:2833:2833:8708:8708:8708:7683:7683:3353:3353:3338:2066:2066:8708:8708:7683:2581:4615:4615:3338:4872:4872:1046:8708:3343:2581:4615:4615:7937:4872:4872:1046:4112:3343:1804:1804:7937:7937:7937:3597:3597:4112:3343:2583:4617:4617:7937:4870:4870:3352:4112:8453:2583:4617:4617:3595:4870:4870:3352:6146:8453:8453:2835:2835:3595:3092:3092:6146:6146:8453:8453:8453:2574:2574:2574:6146:6146:6146:
Solution:
+-------+-------+-------+
| 6 7 3 | 1 2 8 | 4 5 9 |
| 8 1 9 | 4 7 5 | 3 2 6 |
| 5 2 4 | 3 6 9 | 7 1 8 |
+-------+-------+-------+
| 9 8 6 | 5 4 1 | 2 3 7 |
| 1 5 2 | 9 3 7 | 6 8 4 |
| 3 4 7 | 2 8 6 | 1 9 5 |
+-------+-------+-------+
| 7 6 1 | 8 5 3 | 9 4 2 |
| 2 3 5 | 6 9 4 | 8 7 1 |
| 4 9 8 | 7 1 2 | 5 6 3 |
+-------+-------+-------+
Quote:
Jean-Christophe, lead-in: rating "much too easy for regular members"..SudokuSolver v3.0 scores: V1: 0.90
Afmob: It can be solved using a (very) basic Killer technique..Rating: 0.75-1.0. I used a Killer pair to crack it. I am not sure about the rating since I've never rated such an easy puzzle
Jean-Christophe: I personally would not qualify "(very) basic" such techniques as killer naked pair or combination conflicts like you used. Also consider the number of In/outies with three cells in this puzzle, most useless at first
Andrew: Using elimination solving, YAK96 was an easy puzzle. I expect it could still be solved fairly easily without using elimination solving. This puzzle only requires one killer pair ..(which can be spotted even without using elimination solving)..and a few simple 45s so I'll rate it at 0.75
gary w: I certainly wouldn't say v1 was "much too easy" for regular assassinators....Took me over an hour so I'ld rate it as harder than virtually all the "deadly" killers that appear in The Times..0.75??
Walkthrough by Afmob: Killer pair & cage block:
I think V1 is neither "reasonably hard" nor tricky. It can be solved using a (very) basic Killer technique.

JC, wouldn't it be better if you called YAK 96 UA 96 since no one else posted an UA so far and it would be a bit weird if there is a UA 95, but no UA 96 (the same goes for the YAK). Maybe we should sort out before every friday who is going to post the UA for the following week. Of course this doesn't include the Maverick Series since it doesn't appear weekly.

By the way, I broke my personal record for shortest wt again (sorry UA 93 :cry:).

UA 96 Walkthrough:

1. R5+C5
a) 13(2) <> {58} since it's a Killer pair of 14(2) @ C5
b) Killer pair (69) locked in 13(2) + 14(2) for C5
c) 31(5) = 9{1678/2578/3478/3568/4567} -> 9 locked for R5+N5
d) 14(2) @ R5 = {68} locked for R5+N6
e) 31(5) = 789{25/34} -> 7 locked for N5, 8 locked for C5+N5
f) 14(2) @ C5 = {59} locked for C5+N8
g) 13(2) = {67} locked for C5+N2
h) 7(2) <> 1
i) 16(3) = {259/349/457} <> 1
j) Hidden Single: R5C1 = 1 @ R5
j) 10(3) = 1{27/36} -> 1 locked for R9+N8
k) 11(3) = 2{18/45} -> 2 locked for R1+N2

2. C789
a) 8(2) = [17/35/53]
b) Innies N3 = 11(3) = {137} because R2C7+R3C8 = (1357)
-> {137} locked for N3, 7 locked for C7, 1 locked for R3
c) 13(2): R7C8 <> 5,7
d) Innies N9 = 21(3) = {489} locked for N9
e) 12(2), 13(2) <> 7
f) 7 locked in 16(3) = {457} locked for C9+N6
g) 13(2) = [94] -> R6C8 = 9, R7C8 = 4

3. R123
a) Hidden Single: R1C7 = 4 @ N3
b) 11(2) = {128} locked for R1+N2
c) 8(2) = {35} -> R2C6 = 5, R2C7 = 3
d) 3 locked in R3C46 for R3
e) R3C8 = 1, R3C7 = 7
f) 13(2) = {49} locked for R2
g) 10(2) = {28/46}
h) 19(4) = 27{19/46} -> 2 locked for R4
i) R3C5 = 6
j) Innies N1 = 15(3) = {249} because R2C3 = (49)
-> {249} locked for N1, 2 locked R3, 9 locked for C3

4. N47
a) R4C1 = 9 @ R4 -> 13(3) = [913] -> R6C1 = 3
b) 7(2) = {25} locked for R5+N4
c) 2 locked in R789C1 for N7
d) 10(2) @ N7 = [46/73]

5. R789
a) 4 locked in R8C46 for R8
b) 2,4,9 locked in 33(6) = 2479{38/56} -> 7 locked for N7
c) 11(2) <> {38} since it's a Killer pair of 12(2)
d) 11(2) = {56} -> R8C3 = 5, R8C4 = 6
e) 10(3) = {127} locked for R9+N8
f) 19(4) = 6{139/148/238} -> R6C6 = 6
g) Hidden Single: R7C3 = 1 @ C3

6. Rest is singles.

Rating: 0.75-1.0. I used a Killer pair to crack it.

I am not sure about the rating since I've never rated such an easy puzzle. If using a Killer pair automatically means a rating of at least 1.0 then it's an easy 1.0 Killer otherwise a 0.75
Walkthrough by Andrew: Killer Pair & cage block:
Jean-Christophe wrote:
I know the regular members here usually eat "monsters" and this V1 could look very easy in comparison. But on other forums, most will find it "just the right difficulty".
You are right that on other forums this would be "just the right difficulty". I started doing killers on http://www.sudoku.org.uk, where I still do the killers without using elimination solving, and I know that a lot of forum members there find Assassins too hard.

Using elimination solving, YAK96 was an easy puzzle. I expect it could still be solved fairly easily without using elimination solving but I won't bother to do that.
Afmob wrote:
I am not sure about the rating since I've never rated such an easy puzzle. If using a Killer pair automatically means a rating of at least 1.0 then it's an easy 1.0 Killer otherwise a 0.75.

I suppose I could say that it depends which type of killer pair. Afmob uses the term killer pair in three different ways in other walkthroughs. In this case it is the "classic" killer pair which can be spotted even without using elimination solving. The other two types, hidden killer pairs and clashes with killer pairs in other cages, are more difficult moves.

This puzzle only requires one killer pair and a few simple 45s so I'll rate it at 0.75.

Here is my walkthrough. It would have been shorter but I missed one simple 45 which Afmob used. Even so it's still one of my shortest walkthroughs.

Prelims

a) R2C34 = {49/58/67}, no 1,2,3
b) R23C5 = {49/58/67}, no 1,2,3
c) R2C67 = {17/26/35}, no 4,8,9
d) R34C2 = {19/28/37/46}, no 5
e) R34C8 = {13}, locked for C8
f) R5C23 = {16/25/34}, no 7,8,9
g) R5C78 = {59/68}
h) R67C2 = {19/28/37/46}, no 5
i) R67C8 = {49/58/67}, no 1,2,3
j) R78C5 = {59/68}
k) R8C34 = {29/38/47/56}, no 1
l) R8C67 = {39/48/57}, no 1,2,6
m) R1C456 = {128/137/146/236/245}, no 9
n) R9C456 = {127/136/145/235}, no 8,9
o) 34(6) cage in N3 = {136789/145789/235789/245689/345679}, 9 locked for N3
p) 31(5) cage in N5 = {16789/25789/34789/35689/45679}, 9 locked for N5
[I was careless with the Prelims. I should also have spotted 24(6) cage in N9 = {123459/123468/123567}, 1,2,3 locked for N9 when I would have also spotted 45 rule on N9 3 innies R7C78 + R8C7 = 21 = {489/579/678}.]

1. 45 rule on N3 3 innies R2C7 + R3C78 = {128/137/146/236} (cannot be {245} because R3C8 only contains 1,3), no 5, clean-up: no 3 in R2C6

2. R23C5 = {49/67} (cannot be {58} which clashes with R78C5), no 5,8

3. Killer pair 6,9 in R23C5 and R78C5, locked for C5

4. 9 in N5 locked in R5C46, locked for R5, clean-up: no 5 in R5C78
4a. Naked pair {68} in R5C78, locked for R5 and N6, clean-up: no 1 in R5C23, no 5,7 in R7C8

5. R456C9 = {259/349/457}, no 1

6. 45 rule on N6 4 innies R46C78 = {1239/1257/1347}
6a. 9 of {1239} must be in R6C8 = 9 -> no 9 in R46C7

7. 31(5) cage in N5 = {25789/34789} (only remaining combinations), no 1, 7,8 locked for N5, 8 locked for C5, clean-up: no 6 in R78C5

8. R5C1 = 1 (hidden single in R5), clean-up: no 9 in R3C2, no 9 in R7C2
8a. R46C1 = 12 = {39/48/57}, no 2,6

9. Naked pair {59} in R78C5, locked for C5 and N8, clean-up: no 4 in R23C5, no 2,6 in R8C3, no 3,7 in R8C7

10. Naked pair {67} in R23C5, locked for C5 and N2, clean-up: no 6,7 in R2C3, no 1,2 in R2C7
10a. 7 in N5 locked in R5C46, locked for R5

11. R5C46 = {79} (hidden pair in N5), locked for R5
11a. 31(5) cage in N5 = {34789} (only remaining combination), no 2, 3,4 locked for C5 and N5

12. R5C23 = {25} (cannot be {34} which clashes with R5C5), locked for R5 and N4, clean-up: no 8 in R3C2, no 7 in R46C1 (step 8a), no 8 in R7C2

13. R456C9 (step 5) = {349/457} (cannot be {259} because R5C9 only contains 3,4), no 2, 4 locked for C9 and N6, clean-up: no 9 in R7C8
13a. 2 in N6 locked in R46C7, locked for C7

14. R1C456 = {128/245}, no 3, 2 locked for R1 and N2, clean-up: no 6 in R2C7

15. 3 in N2 locked in R3C46, locked for R3 -> R34C8 = [13], R5C9 = 4, R5C5 = 3, clean-up: no 7 in R3C2, no 7,9 in R4C2, no 9 in R46C9 (step 13), no 9 in R6C1 (step 8a)

16. Naked pair {57} in R46C9, locked for C9 and N6, R6C8 = 9, R7C8 = 4, clean-up: no 6 in R6C2, no 1 in R7C2, no 8 in R8C6
16a. 1 in N6 locked in R46C7, locked for C7

17. R9C456 = {127/136}, no 4, 1 locked for R9 and N8

18. 4 in N8 locked in R8C46, locked for R8, clean-up: no 7 in R8C4

19. 45 rule on R12 3 outies R3C159 = 19 = {469/478/568} (cannot be {289} because R3C5 only contains 6,7), no 2
19a. 4,5 only in R3C1 -> R3C1 = {45}
19b. 8,9 only in R3C9 -> R3C9 = {89}
19c. 2 in R3 locked in R3C23, locked for N1

20. 45 rule on R1234 3 outies R4C159 = 20 = {479} (cannot be {578} because 5,7 only in R4C9) -> R4C159 = [947], R6C159 = [385], clean-up: no 6 in R4C2, no 7 in R7C2

21. Naked pair {68} in R4C23, locked for N4, clean-up: no 2 in R7C2

22. R2C7 + R3C78 (step 1) = {137} -> R23C7 = [37], R2C6 = 5, R23C5 = [76], clean-up: no 4 in R1C456 (step 14), no 8 in R2C34

Now for those who find it acceptable, there’s R6C6 = 6 to prevent UR but since I prefer to demonstrate that a puzzle has a unique solution I won’t use it. I think it’s a UR in this case because the remaining cells in the 19(4) cages at R3C6 and R6C6 can’t be used to determine the placing of 1,2 in R4C67 and R6C67.

23. R4C4 = 5 (hidden single in R4)

24. R3C6 = 9 (cage sum), R2C34 = [94], R5C46 = [97], clean-up: no 4 in R3C1 (step 19), no 7 in R8C3, no 2 in R8C4, no 5 in R8C7
24a. R3C19 = [58], R3C4 = 3, clean-up: no 8 in R8C3

25. Naked pair {26} in R2C89, locked for R2 and N3 -> R1C789 = [459], R2C12 = [81]

26. R8C6 = 4 (hidden single in C6), R8C7 = 8, R5C78 = [68], R8C4 = 6, R8C3 = 5, R78C5 = [59], R79C7 = [95], R5C23 = [52], R3C23 = [24], R4C2 = 8, R4C3 = 6, R6C3 = 7, R6C2 = 4, R7C2 = 6, R1C123 = [673], R89C2 = [39], R79C3 = [18], R67C4 = [28], R6C67 = [61], R4C67 = [12], R1C456 = [128], R9C45 = [71], R9C6 = 2 (step 17)

and the rest is naked singles
Outline by gary w:
I certainly wouldn't say v1 was "much too easy" for regular assassinators.

It was relatively easy to show that the 13(2) cage N2 ={67} but then I didn't spot for quite a while that the 11(3) cage couldn't contain a 3.Given that the innies in N3 are{137} this meant that r2c7=3,r3c7=7 and r34c8=13.It's all over now.[/size].
Took me over an hour so I'ld rate it as harder than virtually all the "deadly" killers that appear in The Times..0.75??

Regards

Gary


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PostPosted: Sat Jul 19, 2008 10:15 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1043
Location: Sydney, Australia
YAK96 v2 (aka uA96v2) by Jean-christophe (Mar 08)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:8707:8707:8707:3345:3345:3345:7684:7684:7684:8707:8707:2329:2329:2826:3602:3602:7684:7684:8707:1813:4359:4359:2826:3848:3848:2070:7684:4111:1813:4359:4359:7681:3848:3848:2070:2320:4111:3340:3340:7681:7681:7681:3853:3853:2320:4111:1559:5129:5129:7681:6662:6662:2840:2320:7429:1559:5129:5129:2571:6662:6662:2840:7170:7429:7429:1811:1811:2571:2836:2836:7170:7170:7429:7429:7429:4110:4110:4110:7170:7170:7170:
Solution:
+-------+-------+-------+
| 5 8 3 | 7 4 2 | 1 9 6 |
| 7 2 1 | 8 6 9 | 5 3 4 |
| 9 4 6 | 3 5 1 | 8 2 7 |
+-------+-------+-------+
| 8 3 7 | 1 9 4 | 2 6 5 |
| 2 9 4 | 6 3 5 | 7 8 1 |
| 6 1 5 | 2 7 8 | 9 4 3 |
+-------+-------+-------+
| 1 5 9 | 4 2 3 | 6 7 8 |
| 3 6 2 | 5 8 7 | 4 1 9 |
| 4 7 8 | 9 1 6 | 3 5 2 |
+-------+-------+-------+
Quote:
Jean-Christophe: rating "not sure it's hard enough for regular members"..SudokuSolver v3.0 scores: V2: 1.79 JSudoku cannot solve V2..I designed ...(tricky) moves..
Afmob: UA 96 V2 was quite challenging and interesting ..It had a regular X-Wing which you don't find that often in Killers...Compared to ND #9 my moves wheren't much more complicated but it took me some time to find them ... That's why I rate UA 96 V2 higher..Rating: 1.75. I used combo analysis and a forcing chain
Andrew (in 2012): J-C's comments on the tricky moves designed into this puzzle are interesting. I missed both of them, I rarely spot crossovers, but I found the other tricky move innies-outies for C5 (not mentioned by J-C) very helpful. Afmob found a better area for detailed combination analysis, giving a shorter solving path than mine although not necessarily using easier steps. I agree with Afmob's rating of 1.75.
Walkthrough by Afmob:
UA 96 V2 was quite challenging and interesting at the same time. It had a regular X-Wing which you don't find that often in Killers. Thanks JC!

Compared to ND 9 my moves wheren't much more complicated but it took me some time to find them where as ND 9 flowed quite well. That's why I rate UA 96 V2 higher.

UA 96 V2 Walkthrough:

1. R456
a) 13(2) <> {67} since it's a Killer pair of 15(2)
b) Killer pair (89) locked in 13(2) + 15(2) for R5
c) 7(2) <> {25} because it's a Killer pair of 6(2)
d) Killer pair (14) locked in 7(2) + 6(2) for C2
e) 13(2): R5C3 <> 9
f) Innies R1234 = 22(3) = 9{58/67} -> 9 locked for R4; R4C15 <> 5,6
g) 9(3) = 1{26/35} because R4C9 = (56) -> 1 locked for C9+N6; R56C9 <> 5,6
h) 8(2): R3C8 <> 7
i) Innies R6789 = 16(3): R6C15 <> 1,2,3 because R6C9 <= 3

2. R123
a) Outies R12 = 21(3) <> 1,2,3
b) 11(2): R2C5 <> 8,9
c) Innies N1 = 11(3) <> 9
d) Innies N3 = 15(3): R3C7 <> 3 because 4,7 only possible there

3. C4789
a) Innies C1234 = 22(3) = 9{58/67} -> 9 locked for C4
b) Innies C1234 = 22(3): R19C4 <> 5 because R5C4 <> 8,9
c) 13(3): R1C56 <> 6,7,8,9 because R1C4 >= 6
d) Outies C89 = 11(3) <> 9; R19C8 <> 5,6,7,8
e) 15(2): R5C8 <> 6

5. R5+C5
a) Hidden Killer triple (123) in R5C19 + 30(5) for R5 -> R5C1 = (123); 30(5) <> {45678}
b) 30(5) = 9{1578/2478/2568/3468} -> 9 locked for C5+N5
c) 11(2) <> 2
d) 10(2) <> 1

6. R789
a) Innies N7 = 16(3): Hidden Killer triple (789) in R7C3 -> R7C3 = (789)
b) Innies N7 = 16(3): R8C3 <> 1 because R7C23 <= 14
c) 7(2): R8C4 <> 6
d) Outies R89 = 11(3) <> 9
e) Outies R89 = 11(3): R7C1 <> 7,8 because R7C59 >= 5

7. C5+R5 !
a) Innies+Outies R5: 13 = R46C5 - R5C19 -> R6C5 <> 4,5,6
b) Killer quad (6789) locked in 11(2) + 10(2) + R46C5 for C5
c) 13(2) + 15(2) = h28(4) = 89{47/56}
d) ! 30(5) <> 1 since {15789} blocked by Killer pair (57) of h28(4)
e) 6 in C5 must be in 11(2) xor 10(2) -> 11(2) + 10(2) = h21(4) = 6{258/348/357}
-> 11(2) <> {47}
f) 30(5): R5C6 <> 7 because R5C4 <> 2,4

8. N123 !
a) 9(2) <> {36} since R2C5 + 14(2) must have two of (356)
b) ! Innies N2 = 21(4): R3C6 <> 7 because:
- <> 7{158/239/248/356} because if R3C6 = 7 -> Outies R12 = 21(3) = {489} -> 11(2) = [38]
- <> {1479} since only placement is [1947] (since 14(2) = [95] -> 9(2) <> 4)
-> blocked by Outies R12 = 21(3) = {489}
c) 7 locked in R123C4 for C4

9. R456
a) 7 locked in 15(2) = {78} locked for R5+N6
b) 13(2) = {49} -> R5C2 = 9, R5C3 = 4
c) 30(5) = 569{28/37} -> 5,6 locked for N5
d) 8(2) <> 1
e) 7(2): R3C2 <> 3
f) 6(2): R7C2 <> 2

10. C456
a) Innies C1234 = 22(3): R19C4 <> 6 because R5C4 = (56)
b) 9(2): R2C4 <> 5
c) 7(2): R8C4 <> 3

11. C1289+C57 !
a) Outies C89 = 11(3) = 1{28/37} -> 1 locked for C7
b) Outies C12 = 15(3) = 4{29/38/56} <> 1,7
c) ! X-Wing (1) in R19C57 -> 1 locked for R19

12. N13
a) Innies N1 = 11(3): R3C3 <> 7 because 3 only possible there, R3C3 <> 1 because R2C3 <> 4,6
b) Innies N3 = 15(3): R3C7 <> 6,9 because (47) only possible there

13. R789 !
a) ! Consider placement of 1 in R9 -> R7C2 <> 1:
- i) R9C5 = 1 -> 7(2): R8C3 <> 6 -> Innies N7 = 16(3) <> 1
- ii) R9C7 = 1 -> R2C8 = 1 (HS @ N3) -> R3C2 = 1 (HS @ N1) -> R7C2 <> 1
b) 1 locked in 29(6) for C1
c) 6(2): R6C2 <> 5

14. N14
a) 1 locked in Innies N1 = 11(3) = 1{28/37/46} <> 5
b) Innies N1 = 11(3): R3C2 <> 6 because 4 only possible there
c) 7(2): R4C2 <> 1
d) 16(3) = 8[26/35] because R4C2 = (36) blocks {367} -> R4C1 = 8

15. R456
a) Innies R1234 = 22(3) = {589} -> R4C5 = 9, R4C9 = 5
b) 9(3) = {135} locked for C9+N6
c) 8(2) = {26} locked for C8
d) 11(2) = {47} -> R6C8 = 4, R7C8 = 7

16. C789
a) Innies N9 = 17(3) = 7{28/46}
b) 11(2): R8C6 <> 2,4,6,8
c) 5 locked in Innies N3 = 15(3) = 5{28/46} for N3; R23C7 <> 2,6 because R3C8 = (26)
d) Hidden Single: R6C7 = 9 @ N6
e) Naked pair (26) locked in R4C78 for R4

17. N47
a) R4C2 = 3 -> R3C2 = 4, R5C1 = 2 -> R6C1 = 6, R6C2 = 1, R7C2 = 5
b) Hidden Single: R7C3 = 9 @ R7
c) Innies N7 = 16(3) = {259} -> R8C3 = 2
d) 7(2) @ N7 = {25} -> R8C4 = 5
e) R4C3 = 7, R6C3 = 5
f) 20(4) = {2459} -> R6C4 = 2, R7C4 = 4

18. Rest is singles.

Rating: 1.75. I used combo analysis and a forcing chain
Tricky moves in design by Jean-Christophe:
Thanks for the WT, I'll study it.

Here are the "tricky" moves which could help simplifying the WT. Indeed I designed both versions around these:


For V2:
In/Outies @ r5 -> r46c5-r5c19 = 13
Max r46c5 = 17 -> Max r5c19 = 17-13 = 4
Min r5c19 = 3 -> Min r46c5 = 13+3 = 16
-> r46c5 = 16|17 = {9(7|8)} -> 9 locked for n5, c5
r5c19 = 3|4 = {1(2|3)} -> 1 locked for r5

Overlaps @ r5&c5 -> r159c5+r5c19 = 11 = {11225|11234|12233} = {12(125|134|233)}
-> r19c5 = {1234}, r5c5 = {2345}
2012 walkthrough by Andrew:
Prelims

a) R2C34 = {18/27/36/45}, no 9
b) R23C5 = {29/38/47/56}, no 1
c) R2C67 = {59/68}
d) R34C2 = {16/25/34}, no 7,8,9
e) R34C8 = {17/26/35}, no 4,8,9
f) R5C23 = {49/58/67}, no 1,2,3
g) R5C78 = {69/78}
h) R67C2 = {15/24}
i) R67C8 = {29/38/47/56}, no 1
j) R78C5 = {19/28/37/46}, no 5
k) R8C34 = {16/25/34}, no 7,8,9
l) R8C67 = {29/38/47/56}, no 1
m) 9(3) cage at R4C9 = {126/135/234}, no 7,8,9
n) 26(4) cage at R6C6 = {2789/3689/4589/4679/5678}, no 1
o) 34(6) cage at R1C1 must contain 9

Steps resulting from Prelims
1a. 34(6) cage at R1C1 contains 9, locked for N1
1b. R34C2 = {16/34} (cannot be {25} which clashes with R67C2), no 2,5
1c. R5C23 = {49/58} (cannot be {67} which clashes with R5C78), no 6,7
1d. Killer pair 1,4 in R34C2 and R67C2, locked for C2, clean-up: no 9 in R5C3
1e. Killer pair 8,9 in R5C23 and R5C78, locked for R5

2. 45 rule on R12 3 outies R3C159 = 21 = {489/579/678}, no 1,2,3, clean-up: no 8,9 in R2C5

3. 45 rule on R1234 3 innies R4C159 = 22 = {589/679}, 9 locked for R4
3a. 9(3) cage at R4C9 = {126/135} (cannot be {234} because R4C9 only contains 5,6), no 4, 1 locked for C9 and N6, clean-up: no 7 in R3C8
3b. R4C9 = {56} -> no 5,6 in R56C9
3c. R4C9 = {56} -> no 5,6 in R4C15
3d. Min R4C1 = 7 -> max R56C1 = 8, no 9 in R6C1

4. 45 rule on R89 3 outies R7C159 = 11 = {128/137/146/236/245}, no 9, clean-up: no 1 in R8C5

5. 45 rule on R6789 3 innies R6C159 = 16 = {169/178/259/268/349/358/367} (cannot be {457} because R6C9 only contains 1,2,3)
5a. R6C9 = {123} -> no 1,2,3 in R6C15
5b. Max R6C19 = 11 -> min R6C5 = 5

6. 45 rule on C1234 3 innies R159C4 = 22 = {589/679}, 9 locked for C4
6a. 5 of {589} must be R5C4 -> no 5 in R19C4

7. 45 rule on C89 3 outies R159C7 = 11 = {128/137/146/236} (cannot be {245} because no 2,4,5 in R5C7), no 5,9, clean-up: no 6 in R5C8
7a. R5C7 = {678} -> no 6,7,8 in R19C7

8. R1C456 = {139/148/157/238/247/256/346}
8a. R1C4 = {6789} -> no 6,7,8,9 in R1C56

9. 30(5) cage at R4C5 cannot contain more than one of 1,2,3
9a. Hidden killer triple 1,2,3 in R5C1, 30(5) cage and R5C9 for R5 -> R5C1 = {123}, 30(5) cage must contain one of 1,2,3
9b. 45 rule on N5 4 innies R46C46 = 15 = {1248/1257/1347/1356/2346} (cannot be {1239} which clashes with 30(5) cage), no 9
9c. 9 in N5 only in R46C5, locked for C5, clean-up: no 2 in R2C5, no 1 in R7C5

10. R5C23 = 13, R5C78 = 15 -> combined cage R5C2378 = 28 = {4789/5689}

11. 45 rule on C5 2 outies R5C46 = 2 innies R19C5 + 6
11a. Max R5C46 = {47/56} (cannot be {57/67} which clash with R5C2378) = 11 -> max R19C5 = 5, no 5,6,7,8,9 in R9C5
11b. Min R19C5 = 3 -> min R5C46 = 9, no 1 in R5C6
11c. Max R9C45 = 13 -> min R9C6 = 3
[With hindsight I should also have spotted 45 rule on R5 2 outies R46C5 = 2 innies R5C19 + 13 -> R46C5 = 16,17 = {79/89}, R5C19 = 3,4 = {12/13} …]

12. 45 rule on N7 3 innies R7C23 + R8C3 = 16 = {169/259/268/349/358/457} (cannot be {178} because 7,8 only in R7C3, cannot be {367} because no 3,6,7 in R7C2)
12a. 7,8,9 can only be in R7C3 -> R7C3 = {789}
12b. 6 of {169} must be in R8C3 -> no 1 in R8C3, clean-up: no 6 in R8C4

13. 9 in N5 only in 30(5) cage at R4C5 = {24789/25689/35679} (cannot be {15789/34689} which clash with R5C2378), no 1
13a. 8,9 of {24789/25689} must be in R46C5, 7,9 of {35679} must be in R46C5 (R5C456 cannot be {357/367} which clash with R5C2378) -> R46C5 = {789}
13b. Killer triple 6,7,8 in R23C5, R46C5 and R78C5, locked for C5
13c. 7 of {24789} must be in R5C4, 7 of {35679} must be in R46C5 -> no 7 in R5C6

14. R7C159 (step 4) = 11
14a. Min R7C59 = 5 -> max R7C1 = 6

15. R23C5 = [38]/{47}{56}, R78C5 = {28/37/46} -> combined cage R2378C5 = [38]{46}/{56}{28}/{56}{37} (cannot be {47}{28} which clashes with R46C5) -> R23C5 = [38]/{56}, no 4,7
15a. R3C159 (step 2) = {489/579/678}
15b. 5 of {579} must be in R3C5 -> no 5 in R3C19

16. 30(5) cage at R4C5 (step 13) = {24789/25689/35679}
16a. 1 in C5 only in R19C5 -> R19C5 = {12/13/14} = 3,4,5
16b. R5C46 = R19C5 + 6 (step 11) -> R5C46 = 9,10,11
16c. R5C456 = {247/256/356} -> R5C46 = [56/63/65/72/74] = 9,11 -> R19C5 = 3,5 = {12/14} -> no 3 in R19C5

17. 16(3) cage at R9C4 = {169/178/259/268/349/358/367/457}
17a. 4 of {349/457} must be in R9C5 -> no 4 in R9C6

18. 45 rule on N3 3 innies R2C7 + R3C78 = 15 = {159/168/249/258/267/348/357/456}
18a. 3 of {348/357} must be in R3C8 (because 5 of {357} must be in R2C7) -> no 3 in R3C7

19. 4 in N6 only in R4C7 + R6C78
19a. 45 rule on N6 4 innies R46C78 = 21 = {2469/2478/3459} (cannot be {3468} which clashes with R5C78)
19b. 4 of {2469} must be in R6C8 (R46C8 cannot be {26} which clashes with R34C8, CCC, R46C8 cannot be [29] which clashes with R67C8, CCC, R46C8 cannot be [69] which clashes with R3467C8, CCC), 4 or 9 of {3459} must be in R6C8 (R46C8 cannot be{35} which clashes with R34C8, CCC) -> no 3,5,6 in R6C8, clean-up: no 5,6,8 in R7C8
19c. 9 of {2469} must be in R6C7 (because 4 must be in R6C8, step 19b) -> no 6 in R6C7

[This was how far I got when this puzzle first appeared. A few of the earlier steps have been re-written in my current style; some have been slightly extended.]

20. R46C78 (step 19a) = {2469/2478/3459}
20a. 4,9 of {2469} must be in R6C78 (steps 19b and 19c)
20b. 2 of {2478} must be in R4C78 + R6C7 (R467C8 cannot be [729] which clashes with R5C78 = [69]) -> no 2 in R6C8, clean-up: no 9 in R7C8
20c. 4,9 of {2469} must be in R6C78, 2 of {2478} must be in R4C8 (cannot be [2748/4728] which clash with R159C7 (step 7) = {146/236}) -> no 7 in R4C8, no 2 in R6C7, clean-up: no 1 in R3C8
20d. {2478} must be [4278]/[72]{48} (cannot be [8274] which clashes with R4C159 = {589} since 9(3) cage at R4C9 must be 5{13} when 2 in R46C78), no 8 in R4C7

21. R2C7 + R3C78 (step 18) = {159/168/249/258/267/348/357/456}
21a. 1,4 of {159/249} must be in R3C7 -> no 9 in R3C7
21b. 1,4,7 of {168/267/456} must be in R3C7 -> no 6 in R3C7
[Can eliminate combination {267} using interactions with R23C5 and R3C159, but I’ll leave that for now because it doesn’t give any candidate eliminations.]

22. 45 rule on N9 3 innies R7C78 + R8C7 = 17 = {269/278/359/368/458/467}
22a. 3 of {359/368} must be in R7C8 -> no 3 in R78C7, clean-up: no 8 in R8C6
22b. 7 of {278} must be in R7C8 (R78C7 cannot be {78} because R5C78 = [69] clashes with R67C8 = [92]), 7 of {467} must be in R7C8 (R78C7 cannot be {67} because R5C78 = [87] clashes with R67C8 = [74]) -> no 7 in R78C7, clean-up: no 4 in R8C6
22c. R7C78 + R8C7 = {269/278/359/467} (cannot be {368} because R5C78 = [78] clashes with R67C8 = [83], cannot be {458} because R67C8 = [74] and R78C7 = {58} clashes with R46C78 = {2478})
22d. 7 of {467} must be in R7C8 -> no 4 in R7C8, clean-up: no 7 in R6C8

23. 45 rule on C6789 3 innies R159C6 = 13
23a. Consider placements for R1C4 = {6789}
R1C4 = 6 => R1C56 = 7 = [25/43]
or R1C4 = 7 => R1C56 = 6 = [15/24/42]
or R1C4 = 8 => R59C4 = [59] (step 6) => R9C56 = 7 = [16/25/43] => R159C6 = {25}6/{34}6/[265]/[463] (cannot be [166/355]
or R1C4 = 9 => R1C56 = 4 = [13]
-> no 1 in R1C6
23b. Min R15C6 = 5 -> max R9C6 = 8

24. 1 in C6 only in R34C6, locked for 15(4) cage at R3C6, no 1 in R3C7

25. X-Wing for 1 in R19C57, no other 1 in R19

26. R159C7 (step 7) contains 1 = {128/137/146}
26a. R46C78 (step 19a) = {2469/2478/3459}
26b. {2478} must be [7284] (cannot be [4278/7248] which clashes with R159C7 = {146} when R46C78 contains 7,8) -> no 7 in R6C7, no 8 in R6C8, clean-up: no 3 in R7C8

27. R7C78 + R8C7 (step 22c) = {269/278/467}, no 5, clean-up: no 6 in R8C6

28. R6C159 (step 5) = {169/178/259/268/358/367} (cannot be {349} which clashes with R6C8), no 4

29. Variable hidden killer triple 3,5,6 in R2C34, R2C5 and R2C67 for R2, R2C5 = {356}, R2C67 contains one of 5,6 -> R2C34 cannot contain more than one of 3,5,6 = {18/27/45}, no 3,6

30. R46C78 (step 19a) = {2469/2478/3459}
30a. Consider combinations for R46C78
R46C78 = {2469/2478} => R4C9 = 5 (hidden single in N6)
or R46C78 = {3459} => R34C8 = {35}
-> either R34C8 or R4C9 must contain 5
30b. R34C8 or R4C9 must contain 5, 5 in N9 only in 28(6) cage at R7C9 in C89 -> no other 5 in C89 -> no 5 in 30(5) cage at R1C7
[I could probably have written step 30a as combination analysis but it felt clearer as a forcing chain.]

31. 5 in N3 only in R2C7 + R3C78 (step 18) = {258/357/456}, no 9, clean-up: no 5 in R2C6

32. R46C78 (step 19a) = {2469/3459} (cannot be {2478} = [7284] because R2C7 + R3C78 (step 31) = [546] clashes with R159C7 (step 26) = {146}), no 7,8
[The rest is fairly straightforward.]

33. R5C78 = {78} (hidden pair in N6), locked for R5, clean-up: no 5 in R5C23
33a. R5C23 = [94], clean-up: no 5 in R2C4, no 3 in R3C2, no 2 in R7C2, no 3 in R8C4
33b. R4C5 = 9 (hidden single in R4)
33c. 5,6 in R5 only in R5C456, locked for N5
33d. 6 in N6 only in R4C789, locked for R4, clean-up: no 1 in R3C2
33e. R159C7 (step 26) = {128/137}, no 4
33f. 45 rule on C12 2 remaining outies R19C3 = 11 = {29/38/56}, no 7

34. 15(4) cage at R3C6 contains 1 = {1248/1257/1347/1356} (cannot be {1239} which clashes with R159C7), no 9

35. 26(4) cage at R6C6 = {2789/3689/4589/4679/5678}
35a. {2789} must be [79]{28} (cannot be [2978/8972] which clash with R67C8 = [47]), no 2 in R6C6

36. 45 rule on N1 3 innies R2C3 + R3C23 = 11 = {146/236/245} (cannot be {128/137} because R3C2 only contains 4,6), no 7,8, clean-up: no 1,2 in R2C4
36a. 1 of {146} must be in R2C3 -> no 1 in R3C3

37. R2C7 + R3C78 (step 31) = {258/357/456}
37a. 6 of {456} must be in R2C7 (R3C78 cannot be [46] which clashes with R3C2), no 6 in R3C8, clean-up: no 2 in R4C8
37b. R46C78 (step 32) = {2469/3459}
37c. 2 of {2469} must be in R4C7 -> no 6 in R4C7

[Only just spotted …]
38. 1 in R3 only in R3C46, locked for N2
38a. R9C5 = 1 (hidden single in C5), R1C7 = 1 (hidden single in R1), R8C8 = 1 (hidden single in N9), clean-up: no 6 in R8C3
38b. R9C5 = 1 -> R9C46 = 15 = [78/87/96]

39. R7C23 + R8C3 (step 12) = {259/349/358/457}, no 1, clean-up: no 5 in R6C2

40. 1 in C2 only in R46C2, locked for N4
40a. Naked triple {123} in R46C2 + R5C1, locked for N4
40b. R5C9 = 1 (hidden single in R5)

41. R159C4 (step 6) = {589/679}
41a. R5C4 = {56} -> no 6 in R1C4

42. 13(3) cage at R1C4 = {238/247}, no 5,9, 2 locked for R1 and N2
42a. R9C4 = 9 (hidden single in C4), R9C6 = 6 (step 38b), clean-up: no 5 in R1C3 (step 33f), no 8 in R2C7, no 4 in R78C5
42b. R1C5 = 4 (hidden single in C5) -> R1C46 = [72], R2C4 = 8, R2C3 = 1, R2C6 = 9, R2C7 = 5, R5C4 = 6 (hidden single in R5), clean-up: no 3 in R2C5, no 6 in R3C5, no 3 in R4C8, no 2,9 in R8C7
42c. R23C5 = [65]

43. Naked pair {13} in R3C46, locked for R3 -> R3C8 = 2, R4C8 = 6, R7C8 = 7, R6C8 = 4, R2C8 = 3, R5C78 = [78], R9C7 = 3 (step 33e), R46C7 = [29], R46C9 = [53], R19C8 = [95], R3C3 = 6, clean-up: no 3 in R8C5

44. R3C2 = 4, R4C2 = 3, R5C1 = 2, R67C2 = [15]
44a. R34C7 = [82] = 10 -> R34C6 = 5 = [14]

and the rest is naked singles.

I'll rate my walkthrough at 1.75. I used combination/permutation analysis and two forcing chains, although the latter was only because it was simpler/clearer to write the step that way than to use combination analysis.

J-C's comments on the tricky moves designed into this puzzle are interesting. I missed both of them, I rarely spot crossovers, but I found the other tricky move innies-outies for C5 (not mentioned by J-C) very helpful. J-C's tricky moves are useful shortcuts; fortunately it didn't take much effort to get the same results.


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PostPosted: Sat Jul 19, 2008 10:17 am 
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Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1043
Location: Sydney, Australia
unofficial Assassin 96v1.5 by mhparker (Mar 08)
Puzzle pic: 1-9 cannot repeat on the diagonals:
Image
Code: Select, Copy & Paste into solver:
3x3:d:k:4096:4096:2562:2562:1796:5125:5125:3079:3079:4096:5130:5130:2562:1796:5125:5391:5391:3079:2322:5130:5130:5653:11542:3607:5391:5391:3354:2322:2322:5653:5653:11542:3607:3607:3354:3354:2596:2596:11542:11542:11542:11542:11542:2603:2603:2861:2861:4911:4911:11542:3634:3634:4916:4916:2861:4919:4919:4911:11542:3634:5436:5436:4916:5183:4919:4919:3650:2627:3908:5436:5436:3655:5183:5183:3650:3650:2627:3908:3908:3655:3655:
Solution:
+-------+-------+-------+
| 7 5 3 | 6 2 8 | 9 1 4 |
| 4 9 2 | 1 5 3 | 8 6 7 |
| 6 8 1 | 9 7 4 | 2 5 3 |
+-------+-------+-------+
| 1 2 8 | 5 9 7 | 3 4 6 |
| 3 7 6 | 4 8 2 | 5 9 1 |
| 5 4 9 | 3 1 6 | 7 2 8 |
+-------+-------+-------+
| 2 6 5 | 7 3 1 | 4 8 9 |
| 8 1 7 | 2 4 9 | 6 3 5 |
| 9 3 4 | 8 6 5 | 1 7 2 |
+-------+-------+-------+
Quote:
mhparker, lead-in: Est. rating: 1.5..SudokuSolver v3.0 scores this beauty at 1.83, but that's probably making a bit too much of a meal of it!
Afmob: It seems Mike found another Killer where the SS rating is quite off..Rating: (Easy) 1.25. I used a Killer triple to crack it
Andrew: I rate the way I solved this puzzle as Hard 1.25. However if the key move is used, then it becomes Easy 1.25 as rated by Afmob
Optimized Walkthrough by Jean-Christophe w/o killer subsets:
I don't have steel teeth Image, but enjoyed solving it. Thanks

1. The easy part
a. Innies @ r1234 -> r34c5 = 16 = {79} (NP @ c5, 45/9)
b. Innies @ r6789 -> r67c5 = 4 = {13} (NP @ c5, 45/9)
c. Innies @ c5 -> r5c5 = 8
d. 10/2 @ r89c5 = {46} (NP @ n8, c5)
e. 7/2 @ r12c5 = {25} (NP @ n2)
f. Innies @ c1234 -> r5c34 = 10 = {46} (NP @ r5)
g. r5c67 = 7/2 = {25} (NP @ r5)

2. X-Wing on 9
a. 22/3 @ r34c4+r4c3 = {9..} and 16/2 @ r34c5 = X-Wing on 9
b. -> no 9 elsewhere in r34
c. 9 @ r3 locked @ r3c45 -> locked for n2

3. n123
a. 20/3 @ r1c67+r2c6 = {389|479|578} = {5|9..} -> r1c7 = {59}, r12c6 = {3478}
b. Innies @ n3 -> r1c7+r3c9 = 12 -> r3c9 = {37}
c. 10/3 @ r1c34+r2c4 = {1(27|36|45)} (no {89}); Since r12c4 <> {25} -> r1c3 <> {47}
d. 9/3 @ r34c1+r4c2 -> no {789}
e. Innies @ n1 -> r1c3+r3c1 = 9 = {36} | [54]
f. 10/3 @ r1c34+r2c4 = {1(36|45)} -> 1 locked @ r12c4 for n2, c4

4. r3
a. {125} @ r3 locked @ r3c2378
b. Outies @ r12 -> r3c2378 = 16 = {1258} (NQ @ r3)

5. r34
a. 22(3): R3C4 <> 6 because {679} blocked by R4C5 = (79) (Afmob step 2i)
b. r3c45 = NP {79} @ r3, n2
c. r3c9 = 3, r1c7 = 9, r12c6 = {38} (NP @ n2, c6)
d. Since r3c1 = {46}, 9/3 -> r4c12 = {2(1|3)} -> 2 locked for n4, r4
e. 13/3 @ r34c9+r4c8 -> r4c89 = {46} (NP @ n6, r4)
f. 22/3 @ r34c4+r4c3 = [958], , r34c5 = [79], r5c67 = [25]

6. c6, n6, n9
a. r36c6 = HP {46} @ c6
b. r5c4&r6c6 = NP {46} @ n5
c. Two 14/3 @ c67 -> r46c7 = {137}
d. r6c89 = HP {28}; 19/3 -> r7c9 = 9
e. Innies @ n9 -> r9c7 = 1, 15/3 -> r89c6 = {59}
f. 10/2 @ r5c89 = [91] (HS @ n6)
g. 11/3 @ r6c12+r7c1 -> no 9; r6c3 = 9 (HS @ r6)
...[/quote]

So, it does not require any Killer subset, but a X-Wing and a contradiction will unlock it.
Original, harder Walkthrough by Jean-christophe:
Steps 1 to 4 as above

5. c6
a. 8 @ n2 locked @ r12c6 -> locked for c6, 20/3 = {8(39|57)}
b. {46} @ c6 locked @ r346c6
c. 14/3 @ r34c6+r4c7 <> {46}+4 -> Killer HP {46} @ c6
d. -> r6c6 = {46}, 14/3 = {4|6..} within r34c6
e. r5c4&r6c6 = NP {46} @ n5
f. r36c6 = HP {46} @ c6

6. n9, c6
a. Innies @ n9 -> r7c9+r9c7 = 10 -> no 5
b. 19/3 @ r6c89+r7c9 -> r7c9 <> 1 -> r9c7 <> 9
c. 15/3 @ r89c6+r9c7 = {159|249|258|267|357} = {2|5..}
d. Since r89c6 <> {468} -> r9c7 <> 2
e. -> r5c6 & r89c6 = Killer NP {25} @ c6

7. c6, n6
a. Two 14/3 @ c67 -> no 8 because <> {158|248}
b. Two 14/3 @ c67 -> r46c7 <> 6 because r36c6 = {46}
c. {68} @ n6 locked @ r46c89
d. 13/3 @ r34c9+r4c8 <> {68..}
e. Since r7c9 <> 5 (6a); 19/3 -> r6c89 <> {68}
f. -> Killer HP {68} @ n6, each of 13/3 & 19/3 must include one of {68} within r46c89
g. -> 13/3 @ r34c9+r4c8 = {238|346} (no 7)
h. r3c9 = 3, r1c7 = 9, r12c6 = {38} (NP @ n2, c6)

8. Almost done
a. r3c45 = HP {79} @ n2
b. Since r3c1 = {46}, 9/3 -> r4c12 = {2(1|3)} -> 2 locked for n4, r4
c. 13/3 @ r34c9+r4c8 -> r4c89 = {46} (NP @ n6, r4)
d. r4c3 = 8 (HS @ r4), 22/3 -> r34c4 = [95], r34c5 = [79], r5c67 = [25]
e. r6c89 = HP {28}; 19/3 -> r7c9 = 9
f. Innies @ n9 -> r9c7 = 1, 15/3 -> r89c6 = {59}
g. 10/2 @ r5c89 = [91] (HS @ n6)
h. 3 @ n5 locked @ r6c45 -> locked for r6
i. -> r46c7 = [37]
..
Walkthrough by Afmob:
It seems Mike found another Killer where the SS rating is quite off. Though this one is in a different league than UA 96 V2 they nearly got the same rating :shock:, in fact this one is "0.04 tougher".

UA 96 V1.5 Walkthrough

1. R6789
a) Innies = 4(2) = {13} locked for C5 + 45(9)
b) 10(2) <> 7,9
c) Innies N7 = 6(2) = {15/24}
d) Innies N9 = 10(2) <> 5; R9C7 <> 9

2. R1234
a) Innies = 16(2) = {79} locked for 45(9)
b) 7(2) = {25} locked for C5+N2
c) 9 locked Innies + 22(3) = 9{58/67} for R34
d) Innies N1 = 9(2) = {27/36/45}; R1C3 <> 2
e) 10(3) = 1{36/45} -> 1 locked for C4+N2
f) Innies N1 = 9(2) <> 2
g) 10(3): R1C3 <> 4 because R12C4 <> 5
h) Innies N1 = 9(2): R3C1 <> 5
i) 22(3): R3C4 <> 6 because {679} blocked by R4C5 = (79)
j) 9 locked in R3C45 for N2

3. R456+N8
a) Hidden Killer pair (13) in both 10(2) for R5 -> Both 10(2) = {19/37}
b) Innies C6789 = 7(2) = {25} locked for R5
c) Innies C1234 = 10(2) = {46} locked for R5
d) R5C5 = 8
e) 10(2) @ N8 = {46} locked for N8

4. N123 !
a) 20(3) <> 6 because 5,9 only possible @ R1C7; 20(3) = {389/479/578}
b) ! Killer triple (789) locked in R3C45+20(3) for N2
-> 20(3) must have exactly one of (789) @ N2
c) 20(3) must have 2 of (789) -> R1C7 <> 3,4,5
d) 20(3) = 9{38/47} -> R1C7 = 9
e) Innies N3 = 12(3) = {39} -> R3C9 = 3
f) 13(3) = 3{28/46}
g) 9(3) = 2{16/34} because R3C1 = (46) -> 2 locked R4+N4; R4C12 <> 4,6
h) 13(3) = {346} -> {46} locked for R4+N6
i) 22(3) = {589} -> 5 locked for R4
j) 14(3) = 7{16/34} -> 7 locked for R4

5. N12
a) Innies N1 = 9(2): R1C3 <> 6
b) 10(3) must have 3 xor 5 and R1C3 = (35) -> R12C4 <> 3
c) 3 locked in 20(3) @ N2 = {389} -> {38} locked for N2+C6
d) 22(3) = {589} -> R3C4 = 9, R4C4 = 5, R4C3 = 8

6. N478
a) Killer triple (123) locked in R4C12 + 10(2) for N4
b) Hidden Killer pair (12) in 11(3) @ R7C1 -> R7C1 = (12)
c) Innies N7 = 6(2) = [15/24]
d) R5C6 = 2, R5C7 = 5
e) 15(3) = 5{19/37} because R89C6 = (1579) -> 5 locked for N8; R89C6 <> 1
f) 1 locked in R7C56 for R7
g) Innies N7 = 6(2) = [24] -> R7C1 = 2, R9C3 = 4
h) 11(3) = {245} -> {45} locked for R6
i) 19(3) @ N8 = {379} -> R6C3 = 9, {37} locked for C4

7. N369
a) Innies N9 = 10(2) = [73/91]
b) 19(3) = 9{28/37} -> R7C9 = 9; R6C8 <> 7
c) 14(3) @ R6C6 = {167} -> R6C6 = 6
d) 14(3) @ R3C6 = {347} -> R3C6 = 4, R4C6 = 7, R4C7 = 3
e) R9C7 = 1
f) 21(4) @ N3 = 28{47/56} because R3C7 = (26) -> 2 locked for N3

8. Rest is singles.

Rating: (Easy) 1.25. I used a Killer triple to crack it
Walkthrough by Andrew:
Thanks Mike. A fun puzzle. Unfortunately I missed one key move (J-C's step 2a, Afmob's step 2c) which I ought to have spotted. When I went through the other walkthroughs I realised that this is a design feature of this puzzle. Sorry Mike for missing it. :oops:

I'm pleased to see that J-C kept his original walkthrough as well as posting his improved version. There are some interesting steps in the original which weren't required in the improved version.

I rate the way I solved this puzzle as Hard 1.25. However if the key move is used, then it becomes Easy 1.25 as rated by Afmob.

Here is my walkthrough. It often happens that if one misses one important move, then other interesting moves are brought into play.

Prelims

a) R12C5 = {16/25/34}, no 7,8,9
b) R5C12 = {19/28/37/46}, no 5
c) R5C89 = {19/28/37/46}, no 5
d) R89C5 = {19/28/37/46}, no 5
e) 10(3) cage at R1C3 = {127/136/145/235}, no 8,9
f) 20(3) cage at R1C6 = {389/479/569/578}, no 1,2
g) 9(3) cage at R3C1 = {126/135/234}, no 7,8,9
h) 22(3) cage at R3C4 = {589/679}
i) 11(3) cage at R6C1 = {128/137/146/236/245}, no 9
j) 19(3) cage at R6C3 = {289/379/469/478/568}, no 1
k) 19(3) cage at R6C8 = {289/379/469/478/568}, no 1
l) 20(3) cage in N7 = {389/479/569578}, no 1,2

1. 45 rule on R1234 2 innies R34C5 = 16 = {79}, locked for C5 and 45(9) cage, clean-up: no 1,3 in R89C5
[This would give a UR no 6 in R4C3 because it would be impossible to determine the placement of 7,9 in R34C45. Of course I don’t use such moves.]

2. 45 rule on R6789 2 innies R67C3 = 4 = {13}, locked for C5 and 45(9) cage, clean-up: no 4,6 in R12C5

3. Naked pair {25} in R12C5, locked for C5 and N2, clean-up: no 8 in R89C5

4. Naked pair {46} in R89C5, locked for C5 and N8

5. R5C5 = 8 (naked single), locked for both diagonals, clean-up: no 2 in R5C12, no 2 in R5C89

6. 45 rule on C1234 2 innies R5C34 = 10 = {46} (only remaining combination), locked for R5
[At this stage I realised that there’s potential for more URs. There are in fact already one candidate elimination and one other combination elimination in a different cage that could be made using UR.]

7. 45 rule on N1 2 innies R1C3 + R3C1 = 9 = {36/45}/[72], no 1, no 2 in R1C3

8. 45 rule on N3 2 innies R1C7 + R3C9 = 12 = {39/48/57}, no 1,2,6

9. 45 rule on N7 2 innies R7C1 + R9C3 = 6 = {15/24}

10. 45 rule on N9 2 innies R7C9 + R9C7 = 10 = {28/37/46}/[91], no 5, no 9 in R9C7

11. 10(3) cage at R1C3 = {136/145}, no 7, 1 locked in R12C4, locked for C4 and N2, clean-up: no 2 in R3C1 (step 7)
11a. 5 of {145} must be in R1C3 -> no 4 in R1C3, clean-up: no 5 in R3C1 (step 7)

12. 9(3) cage at R3C1 = {126/135/234}
12a. 6 of {126} must be in R3C1 -> no 6 in R4C12

13. 20(3) cage at R1C6 = {389/479/569/578}
13a. 4 of {479} must be in R12C4 (R12C4 cannot be {79} which clashes with R3C5), no 4 in R1C7, clean-up: no 8 in R3C9 (step 8)

14. 22(3) cage at R3C4 = {589/679}
14a. 6 of {679} must be in R4C34 (R4C34 cannot be {79} which clashes with R4C5), no 6 in R3C4

15. 13(3) cage at R3C9 = {139/148/157/238/247/256/346}
15a. 3 of {139} must be in R3C9 (cannot be 9{13} which clashes with R5C89), no 9 in R3C9, clean-up: no 3 in R1C7 (step 8)

16. 20(3) cage at R1C6 = {389/479/569} (cannot be {578} which clashes with R3C45, 2-cell or ALS cage block)
16a. Killer triple 7,8,9 in R12C6 and R3C45, locked for N2

17. 14(3) cage at R3C6 = {149/167/239/248/347/356} (cannot be {158/257} because R3C6 only contains 3,4,6)
17a. 6 of {167/356} must be in R3C6 (R4C67 cannot be {56} which clashes with R3C34), no 6 in R4C67

18. 1,2 in R3 locked in R3C2378
18a. 45 rule on R12 4 outies R3C2378 = 16 = {1249/1258/1267}, no 3
18b. Killer triple 7,8,9 in R3C2378 and R3C45, locked for R3, clean-up: no 5 in R1C7 (step 8)

19. 20(3) cage at R1C6 (step 18) = {389/479}, no 6

20. 13(3) cage at R3C9 = {139/148/238/247/256/346} (cannot be {157} which clashes with R5C89)
20a. 5 of {256} must be in R3C9 -> no 5 in R4C89

21. 45 rule on N4 3 innies R456C3 = 2 outies R37C1 + 15
21a. Min R37C1 = 4 -> min R456C3 = 19, max R45C3 = 15 -> min R6C3 = 4
21b. R456C3 can only total 19,20,21,23 (cannot be 22 because {679} clashes with R5C12) -> R37C1 can only total 4,5,6,8 = [31/32/35/41/42/62], no 4 in R7C1, clean-up: no 2 in R9C3 (step 9)

22. 14(3) cage at R8C4 = {158/248/257/347} (cannot be {149} because 1,4 only in R9C3, cannot be {239} because R9C3 only contains 1,4,5), no 9

23. 15(3) cage at R8C6 = {159/168/249/258/267/348/357} (cannot be {456} because 4,6 only in R9C7)
23a. 2,4,6 of {168/258/348} must be in R9C7 (R89C6 cannot be {25} which clashes with R5C6), no 8 in R9C7, clean-up: no 2 in R7C9 (step 10)

24. 2 in C3 locked in R2378C3
24a. 45 rule on C12 4 outies R2378C3 = 15 = {1239/1248/1257} (cannot be {2346} which clashes with R5C3), no 6, 1 locked for C3, clean-up: no 5 in R7C1 (step 9)

25. Hidden killer triple 7,8,9 in R2378C3 and R46C3 for C3 -> R46C3 = {789}
25a. Killer triple 7,8,9 in R46C3 and R5C12, locked for N4
25b. 8 in N4 locked in R46C3, locked for C3, clean-up: no 4 in R2378C3 (step 24a)

26. 22(3) cage at R3C4 = {589/679}
26a. 5,6 only in R4C4 -> R4C4 = {56}

27. 11(3) cage at R6C1 = {236/245} (cannot be {146} which clashes with R5C3) -> R7C1 = 2, R6C12 = {36/45}
27a. R9C3 = 4 (step 9), R5C34 = [64], R89C5 = [46], clean-up: no 3 in R3C1 (step 7), no 3 in R6C12 (step 27)
27b. Naked pair {45} in R6C12, locked for R6 and N4

28. R4C2 = 2 (hidden single in N4)

29. 10(3) cage at R1C3 (step 13) = {136} (only remaining combination) -> R1C3 = 3, R3C1 = 6 (step 7), R4C1 = 1 (step 12), R12C4 = {16}, locked for C4 -> R4C4 = 5, locked for D\, R5C67 = [25], clean-up: no 7 in R3C2378 (step 18a), no 9 in R2378C3 (step 24a), no 9 in R5C12

30. Naked pair {37} in R5C12, locked for R5 and N4
30a. Naked pair {19} in R5C89, locked for N6

31. 22(3) cage at R3C4 = {589} (only remaining combination), no 7

32. R3C5 = 7 (hidden single in R3), R4C5 = 9, R46C3 = [89], R3C4 = 9, clean-up: no 4 in R3C2378 (step 18a)

33. 20(3) cage at R1C6 (step 19) = {389} (cannot be {479} because 7,9 only in R1C7) -> R1C67 = [89], R2C6 = 3, R34C6 = [47], 7 locked for D/, R4C7 = 3, R3C9 = 3 (step 8)

34. R6C3 = 9 -> R67C4 = 10 = [37], 3 locked for D/, R6C56 = [16], 6 locked for D\, R7C5 = 3

35. R6C6 = 6 -> R6C7 + R7C6 = 8 -> R6C7 = 7, R7C6 = 1, R7C3 = 5, locked for D/, R7C7 = 4, locked for D\, R1C1 = 7, locked for D\, R5C12 = [37], R89C1 = [89], R789C2 = [613], 1 locked for D/, R8C3 = 7, R3C7 = 2, R23C3 = [21], 1 locked for D\, R2C2 = 9, locked for D\

and the rest is naked singles


It's interesting that J-C and Afmob didn't use URs in their solutions. Maybe they aren't very helpful.

Now to have another go at J-C's V2 to see if I can make further progress


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PostPosted: Sat Jul 19, 2008 10:20 am 
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Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1043
Location: Sydney, Australia
unofficial Assassin 97 by Afmob (April 08)
Puzzle pic:
Image
Code: Select, Copy & Paste into solver:
3x3::k:3840:3840:3840:5635:3332:5125:4614:4614:4614:3593:5635:5635:5635:3332:5125:5125:5125:3601:3593:4883:3348:2325:3332:3863:1816:5657:3601:3593:4883:3348:2325:3359:3863:1816:5657:3601:5668:4883:3110:3110:3359:4905:4905:5657:5932:5668:4883:4883:3110:2609:4905:5657:5657:5932:5668:5668:3128:3128:2609:3387:3387:5932:5932:1599:5440:3128:4418:4418:4418:3387:3142:2887:1599:5440:5440:3403:3403:3403:3142:3142:2887:
Solution:
+-------+-------+-------+
| 6 5 4 | 9 2 1 | 8 7 3 |
| 3 7 1 | 5 4 8 | 2 9 6 |
| 9 2 8 | 3 7 6 | 4 5 1 |
+-------+-------+-------+
| 2 4 5 | 6 8 9 | 3 1 7 |
| 7 1 6 | 2 5 3 | 9 8 4 |
| 8 9 3 | 4 1 7 | 6 2 5 |
+-------+-------+-------+
| 4 3 2 | 1 9 5 | 7 6 8 |
| 5 8 9 | 7 6 4 | 1 3 2 |
| 1 6 7 | 8 3 2 | 5 4 9 |
+-------+-------+-------+
Quote:
Afmob: Here is the first Killer I've created and published so far..(Estimated) Rating: SudokuSolver rates this one 0.96 but it can be solved in an easier way
Nasenbaer: It took me a lot longer than I had thought. Somehow I always got sidetracked..with all the the things I might not have needed
sudokuEd: I'd call this one a hard 1.0 rating since it took a long time to find my break-through. Not the type of move I look for very early. But admittedly, not that difficult
Jean-Christophe: I personally did not found it really hard. I would even say it's easy if you're familiar with Kakuro
gary w: I found this one fairly easy.Took me 35 minutes to complete which was OK,long enough for a Saturday evening!!If we rate the Times "deadly" killers as about 0.5 I'ld say this one is about 0.75
Andrew: I also found uA97 hard going (I guess my "killer brain" had partly switched off!) until I realised that hidden cages .. can be used for clashes ... rather than just for clean-up eliminations. Then I restarted and found it a straightforward puzzle. Based on my re-worked solution I'll rate.. uA97 at 1.0
Walkthrough by Nasenbaer:
Wow, that was a very interesting puzzle. Thanks, Afmob!

It took me a lot longer than I had thought. Somehow I always got sidetracked. So here is my walkthrough, up to the first placements. The rest was solved so fast that I couldn't remember what was next. :wink:

Be warned: it's the way I solved it, with all the the things I might not have needed, so it's not very nice.

Walkthrough UA097

1. Preliminaries
1a. n14: 13(2) = {49|58|67} -> no 1,2,3
1b. n5: 13(2) = {49|58|67} -> no 1,2,3
1c. n25: 9(2) = {18|27|36|45} -> no 9
1d. n25: 15(2) = {69|78} -> no 1,2,3,4,5
1e. n36: 7(2) = {16|25|34} -> no 7,8,9
1f. n58: 10(2) = {19|28|37|46} -> no 5
1g. n7: 6(2) = {15|24} -> no 3,6,7,8,9
1h. n9: 11(2) = {29|38|47|56} -> no 1
1i. n56: 19(3) = {289|379|469|478|568} -> no 1
1j. n7: 21(3) = {489|579|678} -> no 1,2,3

2. 45 on c5: r89c5 = h9(2) = {18|27|36|45} -> no 9

3. 45 on r89: r8c37 = h10(2) = {19|28|37|46} -> no 5

4. 45 on c1234: r89c4 = h15(2) = {69|78} -> no 1,2,3,4,5

5. 45 on c6789: r89c6 = h6(2) = {15|24} -> no 3,6,7,8,9

6. cage placement in n8: 13(3): no 6,7,8 in r9c5
6a. -> (step 2) no 1,2,3 in r8c5
6b. 17(3): no 3 -> {359|368} removed

7. 45 on c1 (1 innie, 1 outie): r1c1 - r7c2 = 3 -> no 1,2,3 in r1c1, no 7,8,9 in r7c2

8. 45 on c9 (1 innie, 1 outie): r7c8 - r1c9 = 3 -> no 1,2,3 in r7c8, no 7,8,9 in r1c9

9. 45 on c9 (3 outies): r1c78 + r7c8 = 21 -> no 1,2,3 in r1c7, no 1,2 in r1c8

10. n14: 14(3): {149|257} removed, blocked by 6(2) in c1

11. n56: 19(3): no 2,3,5 in r5c7, blocked by 15(2) in c6

12. 45 on n8: r7c456 = h15(3) = {159|249|348|357} (other combinations blocked by h15(2) and h6(2) -> no 6
12a. -> no 4 in r6c5
12b. 13(3): {139} removed, blocked by h15(3) -> no 9
12c. -> h15(2): no 6 in r8c4
12d. 17(3): {458} removed, blocked by h15(3) -> no 5 -> no 4 in r8c5
12e. -> h6(2): no 1 in r9c6
12f. -> h9(2): no 4,5 in r9c5
12g. 13(3): {247} removed, blocked by 17(3)
12h. h15(3): {249} removed, blocked by 17(3) -> no 2
12i. -> no 8 in r6c5

13. c5: 13(2): {67} removed, blocked by 13(3), 10(2) and h9(2) -> no 6,7
(explanation: 13(3), 10(2) and h9(2) each need one of {6789} -> only one of {6789} left for 13(2) -> {67} removed)
13a. -> 13(3) @ N2: {148} removed, blocked by 13(2)

14. 45 on r1: r1c456 = h12(3) = {129|138|147|156|237|246|345}

15. no 3 in r7c4, can be seen by all 3's in n7

16. 45 on n8 (3 outies): r7c37 + r6c5 = 10 -> no 9 in r7c37 and r6c5
16a. -> no 1 in r7c5

17. n8: h15(3): no 9 in r7c46

18. 45 on n9 (1 outie, 2 innies): r7c89 - r7c6 = 9 -> no 7,8 in r7c6, no 9 in r7c8, no 1,9 in r7c9
18a. -> (step 8) no 6 in r1c9
18b. -> (step 9) no 3 in r1c8

19. n78: 12(3): {147} removed, blocked by 6(2) and 21(3)
19a. -> no 7 in r78c3
19b. -> no 3 in r8c7

20. n8: 17(3): {269} removed, blocked by h15(2) -> 7 locked in r8c45 for 17(3), r8 and n8
20a. -> h15(2): no 8 in r8c4
20b. -> r8: h10(2): no 3 in r8c3
20c. -> no 3 in r6c5
20d. -> 13(3): {157} removed, {148|346} removed, blocked by 17(3), h9(2) -> 2 locked in r9c56 for 13(3), r9 and n8
20e. -> 17(3): {278} removed -> no 8 in r8c5
20f. -> h15(3): {357} removed
20g. -> no 4 in r8c1
20h. -> no 9 in r8c9, no 4 in r9c9
20i. -> no 1 in r9c5, no 4 in r9c6

21. c5: 10(2): {37} removed, blocked by h9(2)
21a. 8 locked in 13(2) and 10(2) for c5
21b. -> 13(3): {238} removed, {256} removed, blocked by h9(2)

22. n78: 12(3): {237} removed

23. n47: 22(4): {1489|2569|2578|4567} removed, blocked by 6(2)

24. n8: h15(3): no 4 r7c6

25. n89: 13(3): {247} removed
25a. h15(3) and 17(3) restrict placement in 13(3): no 1,5,8 in r7c7, no 6 in r8c7
25b. -> no 4 in r8c3

26. n78: 12(3): {345} removed
26a. h15(3) and 17(3) restrict placement in 12(3): no 1,4,5,8 in r7c3, no 8 in r7c4
26b. -> h15(3): no 4 in r7c5
26c. -> no 6 in r6c5

27. c5: killer pair {89} locked in 13(2) and 10(2) for c5
27a. -> 13(3): {139} removed

28. n7: {138} in 12(3) only possible with r7c4 = 1 -> {579} in 21(3) -> {24} in 6(2) -> can't

place 1 in r7c12 -> {138} removed from 12(3) -> no 8 in r8c3, no 3 in r7c3
28a. -> no 2 in r8c7
28b. -> n89: 13(3): {256} removed

29. n7: killer pair {12} in 6(2) and r78c3 -> no 1,2 in r7c12
29a. 3 locked in r7c12 for 22(4), r7 and n7
29b. -> 22(4): {1579|1678|2479} removed -> no 1

30. single: r9c5 = 3, r9c46 = [82], r8c456 = [764], r67c5 = [19]
...


EDIT:Corrections in blue. Thanks to Afmob!
EDIT2: Removed tiny text, added solution. Thanks for the reminder, Andrew!

EDIT3: corrections added, thanks to Andrew

I hope you learned from my mistakes... :wink:

Cheers,
Nasenbaer
Walkthrough by sudokuEd:
[edit: forgot to say congratulations to Afmob on your first killer!! ]

Afmob wrote:
(Estimated) Rating: SudokuSolver rates this one 0.96 but it can be solved in an easier way
Not by me! I'd call this one a hard 1.0 rating since it took a long time to find my break-through. Not the type of move I look for very early. But admittedly, not that difficult.

This walk-through gets straight to the break-through first placements and is then basically just a very long clean-up. [edit: simplified the early steps to get to the first placement quicker Edit 2 to get step 7 clearer (thanks Andrew)]

unofficial Assassin 97 (uA97)

Prelims
i. n1
13(2) no 123

ii. n2
9(2) no 9
15(2) = {69/78}

iii. n3
7(2) no 789

iv. n5
13(2) no 123
19(3) no 1
10(2) no 5

v. n7
6(2) = {15/24}
21(3) no 123

vi. n9
11(2) no 1

1. "45" c1234: 2 innies r89c4 = h15(2) = {69/78}

2. "45" c6789: 2 innies r89c6 = h6(2) = {15/24} = [4/5..]

3. "45" c5: 2 innies r89c5 = h9(2) = {18/27/36}(no 459) ({45} clashes with h6(2)r89c6)

steps 4-6 deleted: not needed. Hope i got the clean-up OK later.

7. 17(3)n8 = {179/269/467}(no 3,5,8) ({278}=[872] clashes with r89c4 = [87] in h15(2)r89c4);{359/368} blocked by r8c6;{458} has no {45} in r8c45)
7a. = [971/962]/{67}[4]
7b. no 8 in r8c4 -> no 7 in r9c4 (h15(2))
7c. r8c5 = {67} -> r9c5 = {23}(h9(2))
7d. no 1 in r9c6 (h6(2)r89c6)

8. 13(3)n8 = {238/256}(no 4,9) ({346}=[634] blocked by h9(2)r89c5)
8a. = [832/625]
8b. r9c4 = {68} -> r8c6 = {79} (h15(2)r89c4)
8c. r9c6 = {25} -> r8c6 = {14} (h6(2)r89c6)

9. 13(3)n8 = 2{38/56} -> 2 locked for r9 & n8
9a. no 4 in r8c1
9b. no 9 in r8c9
9c. no 8 in r6c5

10. 17(3)n8 = {179/467} (only valid combos)
10a. = 7{19/46}
10b. 7 locked for n8 & r8
10c. no 4 in r9c9
10d. no 3 in r6c5

11. "45" r89: 2 innies r8c37 = h10(2) = {19/28/46} (no 35)

12. 3 in n7 only in r7: 3 locked for r7

13. r9c5 = 3 (hidden single n8)
13a. no 8 in r8c9
13b. no 7 in r6c5

14. r8c5 = 6 (h9(2)r89c5)
14a. no 4 in r67c5
14b. no 5 in r9c9
14c. no 4 in r8c37 (h10(2)r8c37)
14d. no 7 in 13(2)n5

15. r9c4 = 8 (naked single)
15a. no 3 in r8c9
15b. no 1 in 9(2)n2
15c. no 2 r6c5

16. r8c4 = 7 (h15(2)r89c4
16a. no 2 in 9(2)n2

(note: should have done r89c6 now. Not too long a wait)
16. 10(2)n5 = {19}: both locked for c5

17. 13(2)n5 = {58}: both locked for c5 & n5
17a. no 7 in r3c6
17b. no 4 in r3c4

18. 13(3)n2 = {247}: all locked for n2

19. r9c6 = 2 (hidden single n8)
(2 in c4 is now only in 12(3)n4: but didn't seem to help a great deal so left out)

20. r8c6 = 4 (h6(2)r89c6)
20a. no 7 in r9c9

21. naked triple {159} in r7c456: all locked for r7

22. r8c8 = 3 (hidden single n9)
22a. r9c78 = {45}: both locked for n9 & r9

23. r89c9 = [29] (haven't included all the clean-up as singles coming up shortly do it better)

24. r89c1 = [51]

25. r9c23 = {67}: both locked for n7 & r8c2 = 8 (cage sum)

26. r8c37 = [91] (naked singles)
26a. no 4 in 13(2)n1
26b. no 6 in 7(2)n3

27. 12(3)n7 must have 9 -> r7c34 = [21] (only permutation)

28. r67c5 = [19]

29. r7c6 = 5 -> r7c7 = 7 (cage sum)

30. r7c89 = {68} = 14 -> r56c9 = 9 = {45} ({18} blocked by 8 in r7c89)
30a. {45} locked for c9 & n6
30b. no 23 in r3c7

31. "45" c9: r7c8 - 3 = r1c9
31a. -> r7c8 = 6, r1c9 = 3
31b. r7c9 = 8

32. naked pair {34} in r7c12: locked for 22(4) cage
32a. r56c1 = {69/78}(no 2) = [6/7..]

33. "45" c1: r7c2 + 3 = r1c1
33a. r1c1 = {67}

34. Killer pair {67} in r156c1: both locked for c1

35. 18(3)n3 must have 3 = {69/78}[3](no 1245) = [6/7..]
35a. Killer pair {67} in r1c1 & 18(3)
35b. both locked for r1
35c. Killer pair {67} in 18(3)n3 & r23c1: both locked for n3

36. "45" r1: r1c456 = h12(3)
36a. = [921] (only permutation)

37. 18(3)n3 = [873] (only permutation)

rest is hidden and naked singles & clean-up

Cheers
Ed
Walkthrough by Jean-Christophe:
I usually do not rate puzzles, but I personally did not found it really hard. I would even say it's easy if you're familiar with Kakuro.

1. n8:
a. Innies @ c1234 -> r89c4 = 15 = {69|78}
b. Innies @ c6789 -> r89c6 = 6 = {15|24} = {4|5..}
c. Innies @ c5 -> r89c5 = 9 <> {45} = {18|27|36}
d. 13/3 @ r9c456: Min r9c4 = 6 -> Max r9c56 = 7 -> r9c5 <> {678} = {123}
e. h9/2 @ r89c5 -> r8c5 = {678}
f. 17/3 @ r8c456: Min r8c45 = {67} = 13 -> Max r8c6 = 4, r8c6 = {124}
g. h6/2 @ r89c6 -> r9c6 = {245}
h. 13/3 @ r9c456: r9c6 <> {13} -> r9c4 <> 9 = {678}
i. h15/2 @ r89c4 -> r8c4 = {789}
j. 17/3 @ r8c456 <> [962] because it would conflict with h15/2 @ r89c4 = [96] (two 6)
k. 17/3 @ r8c456 <> {782} because it would conflict with h15/2 @ r89c4 = {78} (two {78})
l. 17/3 @ r8c456 = [971|764] -> 7 locked @ r8c45 for n8, r8
m. hidden cages -> 13/3 @ r9c456 = [625|832] -> 2 locked for n8, r9

2. r89
a. Innies @ r89 -> r8c37 = 10 <> {37} (step 1l)
b. 6/2 & 21/3 @ n7 -> no 3
c. 3 @ r8 locked @ r8c89 for n9
d. r9c5 = 3 (HS @ r9), 13/3 -> r9c46 = [82]
e. 17/3 @ r8c456 = [764]

3. c5
a. 10/2 @ r67c5 = {19} (NP @ c5)
b. 13/2 @ r45c5 = {58} (NP @ n5, c5)
c. 13/3 @ r123c5 = {247} (NT @ n2)

4. r78
a. r7c456 = NT {159} @ r7
b. h10/2 @ r8c37 = {19|28}
c. 13/3 @ r7c67+r8c7 = {148|157|256} (no {39})
d. h10/2 @ r8c37 -> r8c3 <> 1
e. 12/3 @ r7c34+r8c3 = {1(29|38)} (no {4567})
f. -> r7c4 = 1, r7c56 = [95], r6c5 = 1

5. n79, c9
a. 21/3 @ n7 -> no 1
b. 1 @ n7 locked @ 6/2 @ r89c1 = {15} (NP @ n7, c1)
c. 21/3 @ r89c2+r9c3 = {8(49|67)} -> r8c2 = 8
d. 12/3 -> r78c3 = [29], 13/3 & h10/2 @ r8c37 -> r78c7 = [71], r89c1 = [51]
e. 21/3 @ n7 -> r9c23 = {67} (NP @ n7, r9)
f. 11/2 @ r89c9 = [29], r8c8 = 3, r9c78 = {45} (NP @ n9)
g. r7c89 = {68} = 14, 23/4 @ n69 -> r56c9 = 9 = {45} (NP @ n6, c9)
h. Innies @ c9 -> r17c9 = 11 = [38], r7c8 = 6

6. c6, n36
a. 19/3 @ r5c67+r6c6 = {379} -> 7 locked @ r56c6 for n5, c6
b. 15/2 @ c6 = {69} (NP @ c6), r56c6 = {37} (NP @ n5, c6), r5c7 = 9
c. r12c6 = {18} (NP @ 20/4) -> r2c78 <> {18}
d. 7/2 @ c7 -> no 8
e. 8 @ n6 locked @ 22/5 -> r3c8 <> 8
f. -> 8 @ n3 locked @ 18/3 -> r1c78 = [87], r12c6 = [18]
g. r4c9 = 7 (HS), r23c9 = NP {16} @ n3
h. 20/4 -> r2c78 = [29], 7/2 @ r34c7 = [43], r3c8 = 5, r9c78 = [54], r6c7 = 6
i. 9/2 @ r34c4 = [36], 15/2 @ r34c6 = [69], r23c9 = [61]
j. r56c4 = {24} = 6, 12/3 -> r5c3 = 6, r12c4 = [95]
...
Walkthrough by Andrew:
I also found uA97 hard going (I guess my "killer brain" had partly switched off!) until I realised that hidden cages R89C4 and R89C6 can be used for clashes with R8C456 and R9C456, rather than just for clean-up eliminations. Then I restarted and found it a straightforward puzzle. I've included comments about interesting moves I spotted while I was struggling.

After completing this puzzle I got "sidetracked" into solving J-C's V1.5 and have only gone through the posted walkthroughs for Afmob's puzzle today.

Based on my re-worked solution I'll rate Afmob's uA97 at 1.0.

Here is my walkthrough. Edit: extra CPE added for step 24.

Prelims

a) R34C3 = {49/58/67}, no 1,2,3
b) R34C4 = {18/27/36/45}, no 9
c) R34C6 = {69/78}
d) R34C7 = {16/25/34}, no 7,8,9
e) R45C5 = {49/58/67}, no 1,2,3
f) R67C5 = {19/28/37/46}, no 5
g) R89C1 = {15/24}
h) R89C9 = {29/38/47/56}, no 1
i) 19(3) cage at R5C6 = {289/379/469/478/568}, no 1
j) 21(3) cage in N7 = {489/579/678}, no 1,2,3

1. 45 rule on C1234 2 innies R89C4 = 15 = {69/78}

2. 45 rule on C6789 2 innies R89C6 = 6 = {15/24}

3. 45 rule on C5 2 innies R89C5 = 9 = {18/27/36} (cannot be {45} which clashes with R89C6), no 4,5,9

[Initially I found this puzzle hard because I was using steps 1, 2 and 3 for elimination but not realising that they also cause clashes and force direct one-to-one relationships between combinations in R8C456 and R9C456. I’m not sure whether the direct one-to-one relationships provide any extra clashes; probably not for this puzzle. The remaining steps come from a complete restart.]

4. R9C456 = {139/148/238/256/346} (cannot be {157/247} because R9C56 = {15/24} clash with R89C6 = {15/24}), no 7, clean-up: no 8 in R8C4 (step 1), no 2 in R8C5 (step 3)
4a. R9C4 = {689} -> no 6,8 in R9C5, clean-up: no 1,3 in R8C5 (step 3)

5. 45 rule on N8 3 innies R7C456 = 15 = {159/348/357} (cannot be {168/267} which clash with R89C4, cannot be {249} which clashes with R9C456, cannot be {258/456} which clash with R89C6), no 2,6, clean-up: no 4,8 in R6C5

6. R8C456 = {179/467} (cannot be {269/278} because R8C45 = [78/96] clashes with R89C4 = [78/96], cannot be {458} because 4,5 only in R8C6), no 2,5,8, clean-up: no 1 in R9C5 (step 3), no 1,4 in R9C6 (step 2)
6a. 7 locked in R8C45, locked for R8 and N8, clean-up: no 3 in R6C5, no 4 in R9C9

7. R9C456 (step 4) = {238/256}, no 9, clean-up: no 6 in R8C4 (step 1)
7a. 2 locked in R9C56, locked for R9, clean-up: no 4 in R8C1, no 9 in R8C9

8. 45 rule on R89 2 innies R8C37 = 10 = {19/28/46}, no 3,5

9. 3 in N7 locked in R7C123, locked for R7, clean-up: no 4,8 in R7C456 (step 5), no 2,6,7 in R6C5

10. Naked triple {159} in R7C456, locked for R7 and N8 -> R8C456 = [764], R9C456 = [832], clean-up: no 1,2 in R34C4, no 7 in R45C5, no 3,8 in R8C9, no 5,7 in R9C9

11. Naked pair {19} in R67C5, locked for C5, clean-up: no 4 in R45C5

12. Naked pair {58} in R45C5, locked for C5 and N5, clean-up: no 4 in R3C4, no 7 in R3C6
12a. Naked triple {247} in R123C5, locked for N2

13. R8C8 = 3 (hidden single in R8), R9C78 = 9 = {45} (only remaining combination), locked for R9 and N9 -> R89C9 = [29], R89C1 = [51]

14. Naked pair {67} in R9C23, locked for N7, R8C2 = 8 (cage sum), R8C3 = 9, R8C7 = 1, clean-up: no 4 in R34C3, no 6 in R34C7
14a. R8C3 = 9 -> R7C34 = 3 = [21], R7C56 = [95], R6C5 = 1, R7C7 = 7 (cage sum)

15. Killer pair 4,5 in R34C7 and R9C7, locked for C7

16. 45 rule on C1 1 innie R1C1 = 1 outie R7C2 + 3 -> R1C1 = {67}

17. 45 rule on C9 1 outie R7C8 = 1 innie R1C9 + 3 -> R1C9 = {35}

18. R1C789 = {369/378/459/567} (cannot be {189/279/468} because R1C9 only contains 3,5), no 1,2
18a. R1C9 = {35} -> no 3 in R1C7, no 5 in R1C8

[At this stage I originally had two powerful in-line IOUs from applying the 45 rule on N7 and N9. There was also the use of overlapping split-cage R7C3467 and hidden-cage R7C456. I had also used combined cage R4589C5 for clashes in C5. Unfortunately they were all removed when the earlier steps were simplified.]

19. R7C12 = {34} = 7 -> R56C1 = 15 = {69/78}, no 2,3,4

20. Killer pair 6,7 in R1C1 and R56C1, locked for C1

21. Naked pair {68} in R7C89, locked for 23(4) cage at R5C9 -> no 6,8 in R56C9
21a. R7C89 = 14 -> R56C9 = 9 = {45} (only remaining permutation), locked for C9 and N6 -> R1C9 = 3, R7C8 = 6 (step 17), R7C9 = 8, clean-up: no 2 in R3C7

22. R1C9 = 3 -> R1C78 = 15 = [69/87], no 4, no 9 in R1C7, no 8 in R1C8
22a. Killer pair 6,7 in R1C1 and R1C78, locked for R1

23. Killer pair 6,7 in R1C78 and R23C9, locked for N3
23a. Hidden killer pair 6,7 in R1C78 and R23C9 for N3 -> R23C9 = {16/17}, 1 locked for C9 and N3

24. 19(3) cage at R5C6 = {379} (only remaining combination, cannot be {289} because 2,8 only in R5C7), no 2,6,8, CPE no 3,9 in R5C4
24a. 7 locked in R56C6, locked for C6, clean-up: no 8 in R3C6

25. Naked pair {69} in R34C6, locked for C6
25a. Naked pair {37} in R56C6, locked for C6, N5 and 19(3) cage -> R5C7 = 9, clean-up: no 6 in R3C4, no 6 in R6C1 (step 19)

26. Naked pair {18} in R12C6, locked for 20(4) cage at R1C6 -> R2C7 = 2, R2C8 = 9 (cage sum), R1C8 = 7, R1C7 = 8 (step 22), R1C1 = 6, R12C6 = [18], R4C7 = 3, R3C7 = 4, R3C8 = 5, R6C7 = 6, R4C9 = 7, R9C78 = [54], R3C4 = 3, R4C4 = 6, R12C4 = [95], R34C6 = [69], R23C9 = [61], clean-up: no 7 in R3C3, no 8 in R4C3, no 9 in R6C1 (step 19)
26a. R34C3 = [85], R1C3 = 4, R1C5 = 2, R1C2 = 5, R23C5 = [47], R2C1 = 3, R7C12 = [43], R45C5 = [85], R4C1 = 2, R4C8 = 1, R4C2 = 4, R3C12 = [92], R56C9 = [45], R56C4 = [24], R56C8 = [82], R56C1 = [78], R56C6 = [37], R6C23 = [93]

27. R56C4 = [24] = 6 -> R5C3 = 6

and the rest is naked singles


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