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Since I didn't plan on making an Assassin this week, I made this one a little bit harder than my usual Killers. But it shouldn't be too hard, so I hope you have a satisfying solving time!

Assassin 166



3x3::k:4097:7426:7426:7426:3077:3077:3863:3863:4886:7426:4097:2307:2307:7426:3077:6412:3863:4886:4097:6662:6662:2307:3076:3076:6412:6412:4886:6662:6662:6662:7176:5139:5385:6412:6412:1802:2055:7176:7176:7176:5139:5385:5385:5385:1802:2055:7179:7179:7176:5139:5385:5645:5645:5645:4116:7179:7179:1808:1808:3345:5645:5645:3854:4116:2325:7179:4626:7695:3345:3345:3854:7695:4116:2325:2325:4626:4626:7695:7695:7695:3854:


SS Score: 1.50
Estimated rating: 1.25.

Thanks Afmob, that was a fun and satisfying Assassin! Hope you won't stay gone too long -- you will be missed.

Your puzzle also had an unusual characteristic which I've commented on below. I'll try to put together a coherent wt this weekend, but hope other members won't wait for me. Sometimes life gets in the way, and I get v-e-r-y s-l-o-w.



Regards,

Ronnie

Here's my wt. As usual, it took me longer to write the walk-thru than it did to solve the puzzle! I'm just not very proficient at it.

Here's my corrected wt. Thanks again,Joe Casey, for catching my mistake so quickly and sparing me further humiliation! Must learn to keep better notes when first solving a puzzle, rather than going back and trying to remember what I'd done. Also thanks to Andrew for catching yet another mistake in Step 9, and his suggestions for clarifying step 19.

Thanks for a very encouraging puzzle Afmob! I found this one easier than recent Assassins. It seemed to just keep flowing with lots of big chunks.

Here's a different way to do Ronnie's puzzle-cracker step 9 to get the same result. I've included a pic which makes it easy to follow. Thanks Ronnie for doing the full WT!Cheers
Ed

Thanks Afmob! I enjoyed that one and didn't find it harder than your usual killers. As Ed said it flowed; I didn't have to stop for long periods thinking what to do next. At the same time there seems to be a fairly narrow solving path; Ronnie's walkthrough and my one use many of the same steps.

The other way is to write the walkthrough as one goes along, sometimes going back to change things but generally representing how I solved the puzzle. It works for me but obviously won't for people who write optimised walkthroughs; notes must be better for those ones. It takes longer to solve the puzzle my way but checking the walkthrough after is quicker.


Here is my walkthrough for A166.

Prelims

a) R3C56 = {39/48/57}, no 1,2,6
b) R45C9 = {16/25/34}, no 7,8,9
c) R56C1 = {17/26/35}, no 4,8,9
d) R7C45 = {16/25/34}, no 7,8,9
e) 9(3) cage at R2C6 = {126/135/234}, no 7,8,9
f) R123C9 = {289/379/469/478/568}, no 1
g) R456C5 = {389/479/569/578}, no 1,2
h) 9(3) cage in N7 = {126/135/234}, no 7,8,9

1. 45 rule on N12 2 innies R3C23 = 12 = {39/48/57}, no 1,2,6

2. 45 rule on N3 3 innies R2C7 + R3C78 = 11 = {128/137/146/236/245}, no 9
2a. 45 rule on N3 2 outies R4C78 = 14 = {59/68}

3. 45 rule on N7 2 outies R6C23 = 8 = {17/26/35}, no 4,8,9
3a. 45 rule on N7 3 innies R7C23 + R8C3 = 20 = {389/479/569/578}, no 1,2

4. 45 rule on N89 2 innies R7C78 = 7 = {16/25/34}, no 7,8,9

5. 45 rule on N1247 2 innies R5C23 = 15 = {69/78}
5a. Killer triple 5,6,7 in R56C1, R5C23 and R6C23, locked for N4
5b. 7 in R4 locked in R4C456, locked for N5

6. 4 in N4 locked in R4C123, locked for R4 and 26(5) cage at R3C2, clean-up: no 8 in R3C23 (step 1), no 3 in R5C9
6a. 45 rule on N12 3 outies R4C123 = 14 = {149/248}, no 3
6b. Killer pair 8,9 in R4C123 and R4C78, locked for R4
6c. R456C5 = {389/479/569/578}
6d. 3 of {389} must be in R4C5 -> no 3 in R56C5

7. 45 rule on N3689 2 innies R5C78 = 9 = {18/27/36/45}, no 9

8. 45 rule on C9 2 innies R68C9 = 1 outie R8C8 + 4, IOU no 4 in R6C9

9. 45 rule on N2 2 innies R1C4 + R2C5 = 1 outie R2C3 + 12
9a. Min R1C4 + R2C5 = 13, no 1,2,3
9b. Max R2C4 + R2C5 = 17 -> max R2C3 = 5

10. 45 rule on N89 3 outies R6C789 = 15 = {159/168/249/267/348/357} (cannot be {258/456} which clash with R4C78)
10a. Hidden killer triple 7,8,9 in R4C78, R5C78 and R6C789 for N6, R4C78 must contain one of 8,9, R6C789 must contain one of 7,8,9 -> R5C78 must contain one of 7,8 = {18/27} (step 7), no 3,4,5,6
[Alternatively there was killer triple 4,5,6 in R4C78, R45C9 and R6C789, locked for N6 as in Ronnie’s walkthrough.]

11. R5C23 (step 5) = {69} (cannot be {78} which clashes with R5C78), locked for R5, N4 and 28(5) cage at R4C4, clean-up: no 1 in R4C123 (step 6a), no 1 in R4C9, no 2 in R56C1, no 2 in R6C23 (step 3)
11a. Naked triple {248} in R4C123, locked for R4, clean-up: no 6 in R4C78 (step 2a), no 5 in R5C9
11b. Naked pair {59} in R4C78, locked for R4, N6 and 25(5) cage at R2C7, clean-up: no 2 in R5C9
11c. 1 in R4 locked in R4C456, locked for N5

12. R5C23 = 15 (step 5) -> R456C4 = 13 = {148/238/247} (cannot be {157} because 1,7 only in R4C4), no 5
12a. 3 of {238} must be in R4C4 -> no 3 in R56C4

13. R456C5 = {389/479/569/578}
13a. 9 of {479/569} must be in R6C5 -> no 4,6 in R6C5

14. R5C78 = {18/27} (step 10a) = 9 -> R456C6 = 12 = {138/156/237} (cannot be {129/147} which clash with R5C78, cannot be {246/345} which clash with R456C4), no 4,9
14a. 1,7 only in R4C6 -> R4C6 = {17}
14b. 6 of {156} must be in R6C6 -> no 5 in R6C6
14c. 21(5) cage at R4C6 = {12378/12567}, CPE no 2 in R5C4
14d. 2 in R5 locked in R5C678 for 21(5) cage, no 2 in R6C6

15. R6C5 = 9 (hidden single in N5), clean-up: no 3 in R3C6

16. R7C23 + R8C3 (step 3a) = {389/479/569} (cannot be {578} which clashes with R6C23), 9 locked for N7
[I ought to have spotted this move after step 11.]
16a. 9 in C1 locked in R123C1, locked for N1, clean-up: no 3 in R3C23 (step1)
16b. Naked pair {57} in R3C23, locked for R3 and N1

17. 12(3) cage in N2 = {129/147/156/237/246} (cannot be {138/345} which clash with R3C56), no 8

18. Min R1C4 + R2C5 = 13 (step 9a), cannot be {49} which clashes with R3C56, no 4 in R1C4 + R2C5

19. R6C789 (step 10) = {168/267/348}
19a. Killer quad 1,3,5,7 in R6C1, R6C23 and R6C789, locked for R6

20. R456C6 (step 14) = {138/156} (cannot be {237} because R6C6 only contains 6,8), no 2,7 -> R4C6 = 1, clean-up: no 8 in R5C78 (step 10a)
20a. 3 of {138} must be in R5C6 -> no 8 in R5C6
20b. Naked pair {27} in R5C78, locked for R5 and N6, clean-up: no 1 in R6C1

21. R6C789 (step 19) = {348} (only remaining combination, cannot be {168} which clashes with R6C6), locked for R6, N6 and 22(5) cage at R6C7 -> R45C9 = [61], R6C46 = [26], R5C6 = 5 (step 14), R5C1 = 3, R6C1 = 5, clean-up: no 5 in R7C5

22. 7 in C1 locked in R789C1, locked for N7
22a. R789C1 = {178} (only remaining combination), locked for C1 and N7
22b. 9(3) cage in N7 = {234} (only remaining combination), locked for N7
22c. 6 in C1 locked in R123C1, locked for N1

23. 16(3) cage in N1 = {169/268/349}
23a. 1,3,8 only in R2C2 -> R2C2 = {138}

24. R123C9 = {289/379/478}, no 5
24a. 5 in C9 locked in R789C9, locked for N9, clean-up: no 2 in R7C78 (step 4)
24b. Naked pair {16} in R7C78, locked for R7 and N9
24c. Naked pair {59} in R7C23, locked for R7 and N7 -> R8C3 = 6, R5C23 = [69], R7C23 = [95], R3C23 = [57], R6C23 = [71], clean-up: no 2 in R7C5

25. Naked pair {34} in R7C45, locked for R7 and N8
25a. Killer pair 3,4 in R45C4 and R7C4, locked for C4
25b. Killer pair 3,4 in R45C5 and R7C5, locked for C5 -> R3C5 = 8, R3C6 = 4, R5C5 = 4, R4C5 = 7 (step 13), R45C4 = [38], R7C45 = [43]

26. 18(3) cage in N8 = {279/567}, no 1, 7 locked in R89C4, locked for C4 and N8

27. R8C5 = 1 (hidden single in N8)
27a. 30(5) cage at R8C5 = {15789} (only remaining combination) -> R8C9 = 5, 7 locked in R9C78, locked for R9 and N9
[I probably ought to have also locked {789} for R9 but omitting it doesn’t make much difference.]

28. Naked pair {28} in R7C69, locked for R7 -> R7C1 = 7, R89C1 = [81]

29. Naked triple {289) in R789C6, locked for C6 and N8 -> R8C4 = 7
29a. 2 locked in R78C6, locked for 13(3) cage at R7C6 = {238} (only remaining combination) -> R8C7 = 3, R78C6 = [82], R7C9 = 2, R8C2 = 4, R8C8 = 9, R9C9 = 4 (cage sum), R4C78 = [95], R9C6 = 9

30. R12C6 = {37}, R1C5 = 2 (cage sum)

31. R1C4 = 9 (hidden single in C4)

32. R3C1 = 9 (hidden single in C1), R1C1 + R2C2 = 7 = [43/61], no 8

33. R3C9 = 3, R6C9 = 8, R6C78 = [43], R12C9 = [79], R12C6 = [37]

34. 2 in R3 locked in R3C78, locked for N3
34a. R2C7 + R3C78 (step 2) = {128} (only remaining combination) -> R2C7 = 8, R3C78 = {12}, locked for R3 and N3 -> R3C4 = 6, R2C45 = [15], R2C2 = 3, R1C1 = 4 (step 32)

and the rest is naked singles.