Cyclone Killer #2 was a really challenging puzzle. It took me a few sessions but I eventually got it out.
Mike's step 15b was a nice one; it really broke the puzzle open. I also missed Mike's grouped X-wing (step 12a) but found a couple of other ones. I realised later that my step 27 is the complement of Mike's step 12a.
Mike rated this puzzle at 1.5, after feedback from Afmob. I agree with that. It was Hard 1.5 the way I solved it.
Here is my walkthrough. I hope I've made the more difficult moves, particularly the ones that cover two octets, clear enough. Edit: Step 45 re-phrased for clarity.
Edit2: Mike pointed out that there were flaws in the original step 37 and the first part of step 40, both now in red. Fortunately I found a workaround for step 37 and was able to include Mike's suggestion for the first part of step 40. Mike also gave a quicker way to the first placement, which I've included after step 32. Thanks for all of those, Mike!
Prelims
a) R23C2 = {16/25/34}, no 7,8 b) R2C67 = {16/25/34}, no 7,8 c) R34C3 = {38/47/56}, no 1,2 d) R6C34 = {48/57}, no 1,2,3,6 e) R67C7 = {28/37/46}, no 1,5 f) R7C23 = {17/26/35}, no 4,8 g) 17(3) cage at R4C2 = {278/368/458/467}, no 1 h) 7(3) cage in Octet 8 (O8) = {124}, locked for O8, clean-up: no 6,8 in R6C7
1. 36 rule on C8 3 outies R138C7 = 8 = {125/134}, 1 locked for C7, clean-up: no 6 in R2C6
2. 36 rule on R12 2 outies R3C24 = 7 = {16/25/34}, no 7,8 in R3C4
3. 36 rule on O35 4 innies R3C24 + R45C4 = 13, R3C24 = 7 (step 2) -> R45C4 = 6 = {15/24}, no 3,6,7,8 3a. R45C4 = 6 -> R45C5 = 11 = {38/47/56}, no 1,2
4. 36 rule on R78 2 outies R6C57 = 8 = [17/53/62], R6C5 = {156}, no 4 in R6C7, clean-up: no 6 in R7C7 4a. Killer pair 2,3 in R138C7 and R67C7, locked for C7, clean-up: no 4,5 in R2C6
5. 36 rule on C12 2 outies R57C3 = 7 = [25/43/52/61], no 7,8, no 3 in R5C3, no 6 in R7C3, clean-up: no 1,2 in R7C2
6. 36 rule on C78 2 outies R24C6 = 3 = {12}, locked for C6, clean-up: no 4 in R2C7, no 7,8 in R3C5, no 7,8 in R56C6
7. 17(3) cage at R4C2 = {278/368/458/467} 7a. 2 of {278} must be in R5C3 -> no 2 in R45C2
8. 36 rule on R1 3 outies R2C138 = 16 = {178/358/367/457} (cannot be {268} which clashes with R2C67), no 2
9. 26(5) cage at R7C6 = {23678/34568} (cannot be {14678/24578} which clash with 7(3) cage in O8), no 1 9a. R8C34 must contain 2 or 4
10. 1 in 7(3) cage in O8 must be in R8C78 (R8C78 cannot be {24} which clashes with R8C34), no 1 in R7C8 10a. 1 in O8 locked in R8C78, locked for R8 10b. Killer pair 2,4 in R8C34 and R8C78, locked for R8
11. 15(3) cage in O7 = {168/258/267/348/357/456} 11a. 1,2,4 of {168/258/267/348/456} must be in R7C1 -> no 6,8 in R7C1
12. 36 rule on C1 3 outies R168C2 = 11 = {128/137/146/245} (cannot be {236} which clashes with R23C2) 12a. 5,6,8 in {128/146/245} must be in R8C2 -> no 5,6,8 in R16C2
13. 16(3) cage in O2 = {178/358/367/457} (cannot be {268} which clashes with R2C67), no 2 13a. 1 of {178} must be in R1C7 -> no 1 in R12C8
14. 21(5) cage at R3C7 = {12567/13458/13467/23457} (cannot be {12378} which clashes with 16(3) cage in O2, cannot be {12468} which clashes with 8(3) cage in O8) 14a. 16(3) cage in O2 (step 13) = {358/367/457} (cannot be {178} which clashes with 21(5) cage at R3C7), no 1
15. R138C7 (step 1) = {125/134} 15a. 5 of {125} must be in R1C7 -> no 5 in R3C7
16. 36 rule on R8 3 outies R7C168 = 12 = {147/246/345} (cannot be {138/156} because R7C8 only contains 2,4, cannot be {237} which clashes with R7C23), no 8, 4 locked for R7 16a. 1 of {147} must be in R7C1 -> no 7 in R7C1
17. 26(5) cage at R7C6 (step 9) = {23678/34568}, 8 locked in R8C3456, locked for R8
18. 15(3) cage in O7 (step 11) = {267/357/456}, no 1 [I missed a clean-up (using step 16) here, see comment after step 26.]
19. 8 in C2 locked in R45C2, locked in 17(3) cage (step 7) = {278/368/458} 19a. 6 of {368} must be in R5C3 -> no 6 in R45C2
20. R168C2 (step 12) = {137/146/245} 20a. R23C2 = {16/25} (cannot be {34} which clashes with R168C2), no 3,4, clean-up: no 3,4 in R3C4 (step 2)
21. 36 rule on R12 3 innies R2C245 = 13 = {148/238/247/346} (cannot be {157/256} which clash with R2C67), no 5, clean-up: no 2 in R3C2, no 5 in R3C4 (step 2) 21a. R2C2 = {126} -> no 1,2,6 in R2C45
22. Hidden pair {12} in R1C5 and R2C6 for O2 -> R1C5 = {12}
23. 36 rule on O2 3 innies R1C56 + R2C5 = 13 = {148/238/247} (cannot be {157/256} which clash with R2C67, cannot be {346} because R1C5 only contains 1,2), no 5,6
24. 8 in O7 locked in R7C4 + R8C34 24a. 36 rule on O7 3 innies R7C4 + R8C34 = 13 = {148/238}, no 5,6,7 24b. R8C34 must contain 2 or 4 (step 9a) -> no 2 in R7C4
25. 8 in R7 locked in R7C457 25a. 36 rule on R78 3 innies R7C457 = 16 = {178/358}, no 6 25b. 5 of {358} must be in R7C5 -> no 3 in R7C5
26. 1 in R7 must be in R7C23 = [71] or in R7C457 = 1{78} -> 7 locked in R7C257, locked for R7 [I then realised that I only got this because I’d missed the clean-up after step 18. I’ve left it like this because it’s an interesting step.]
27. 2 in C56 locked in R13C5 and R24C6, locked for B24
28. Hidden killer pair 1,2 in R6C57 and R56C8 for O6 -> R6C57 and R56C8 must each contain one of {12} (R56C8 cannot be {12} which clashes with R78C8) 28a. R6C57 (step 4) = [17/62] (cannot be [53] which doesn’t contain 1 or 2), clean-up: no 7 in R7C7 28b. Killer pair 1,2 in R56C8 and R78C8, locked for C8 28c. 4 of 7(3) cage must be in R78C8 (R78C8 cannot be {12} which clashes with R56C8), no 4 in R8C7 28d. 4 in O8 locked in R78C8, locked for C8
29. Hidden grouped X-Wing in 1 for C78 -> 21(5) cage at R3C7 and 7(3) cage in O8 must both contain 1 29a. 21(5) cage at R3C7 (step 14) = {12567/13458/13467} (cannot be {23457} which doesn’t contain 1) [This was there after step 14a but I’ve only just spotted it. Since it doesn’t lead to any immediate candidate eliminations I haven’t moved it.]
30. 16(3) cage in O2 (step 14a) = {358/367} (cannot be {457} which clashes with 21(5) cage at R3C7), no 4, 3 locked for O2
31. R138C7 (step 1) = {125/134} 31a. 4 of {134} must be in R3C7 -> no 3 in R3C7
32. 36 rule on R123 4 innies R3C1378 = 20 = {1478/3458/3467} (cannot be {1568/2468/2567} which clash with R3C24, cannot be {2378} because R3C7 only contains 1,4), no 2, 4 locked for R3, clean-up: no 5 in R3C56
[Mike pointed out that from here there is a much quicker route to my first placement. 33. 14(3) at R6C5+R7C45 = [185/617/635] 33a. R67C5 = {(5/6)..} 33b. -> {56} combo blocked for h11(2) at R45C5 (step 3a) 33c. -> no 5,6 in R45C5 34. 5 in C5 locked in R78C5 for O8 35. 5 in C6 locked in 9(2) at R5C6 = {45}, locked for C6 and N6 36. HS in O2 at R2C5 = 4 I'm not sure why I didn't look at the permutations for the 14(3) cage at R6C5; I'd looked at them for R7C457.]
33. R7C457 (step 25a) = {178/358} 33a. 5,7 can only be in R7C5 -> R7C5 = {57}
34. 4 in C5 can only be in R2C5 or R45C5 34a. If 4 in R45C5, then R45C5 = {47} 34b. -> no 7 in R2C5
35. R2C245 (step 21) = {148/238/247/346} 35a. 13(3) cage at R2C4 = {148/238/247/346} 35b. 4 of {148} must be in R2C5 (R23C4 cannot be [41] which clashes with R45C4) 35c. 3,7 of {247/346} must be in R2C4 35d. -> no 4 in R2C4
36. Combined cage R12368C2 = 18 = {12357/12456}, 5 locked for C2, clean-up: no 4 in R5C3 (step 19), no 3 in R7C3 36a. R34C3 = {38/47} (cannot be {56} which clashes with R57C3), no 5,6
37. Killer singles 8 in R45C2 (step 19), R34C3 or R6C34, locked for O35 37a. 19(5) cage at R3C1 = {12367/12457/13456}
[Mike pointed out that there is a flaw in step 37. Because of the geometrical arrangement it’s possible for R34C3 to be {47} with R6C34 = [57] when there is an 8 in the 19(5) cage = {12358}. Fortunately I found a workaround which showed that this combination is impossible.]
37. 8 locked in R45C2 (step 19) 37a. If R34C3 or R6C34 contain 8 => no 8 in 19(5) cage at R3C1 = {12367/12457/13456} 37b. If neither of R34C3 or R6C34 contain 8 then both must contain 7 => R34C3 = {47} => R6C34 = [57] => 19(5) cage at R3C1 must contain 8 = {12358} with 5 in R34C1 => R3C24 = {16}, locked for R3 => R3C7 = 4 => R3C56 = [27] -> R3C57 clash with R3C3 37c. -> R3C1 = {12367/12457/13456}, no 8
38. 8 in C1 locked in R12C1, locked for O1 38a. 13(3) cage at R1C1 = {148/238}, no 5,6,7
39. R2C245 (step 21) = {238/247/346} (cannot be {148} because R2C4 only contains 3,7), no 1, clean-up: no 6 in R3C2, no 1 in R3C4 (step 2)
40. Hidden killer singles 7 in 19(5) cage at R3C1, 17(3) cage at R4C2, R34C3 and R6C34 for O35, R34C3 or R6C34 contain 7 -> 19(5) cage at R3C1 or 17(3) cage at R4C2 must contain 7 40a. 2 and 7 are linked in 19(5) cage at R3C1 (step 37a) and 17(3) cage at R4C2 (step 19) -> 19(5) cage at R3C1 or 17(3) cage at R4C2 contains 2 and 7 40b. Hidden killer singles 2 in 19(5) cage at R3C1, 17(3) cage at R4C2 and R345C4, 19(5) cage at R3C1 or 17(3) cage at R4C2 contains 2 -> R345C4 must contain 2 40c. 2 locked in R345C4, locked for C4
[After checking my workaround for step 37, Mike pointed out that there is a similar flaw in this step and in this case provided a workaround using the same basic approach that I’ve put into the first part of step 40.]
40. Hidden killer pairs 7,8 in 19(5) cage at R3C1, 17(3) cage at R4C2, R34C3 and R6C34 for O35, R34C3 and R6C34 must contain two occurrences of 7,8 -> 19(5) cage at R3C1 and 17(3) cage at R4C2 must contain two occurrences of 7,8 of which one is 8 locked in R45C2 so either 19(5) cage at R3C1 or 17(3) cage at R4C2 contains 7 40a. 2 and 7 are linked in 19(5) cage at R3C1 (step 37a) and 17(3) cage at R4C2 (step 19) -> either 19(5) cage at R3C1 or 17(3) cage at R4C2 contains 2 and 7 40b. Hidden killer singles 2 in 19(5) cage at R3C1, 17(3) cage at R4C2 and R345C4, 19(5) cage at R3C1 or 17(3) cage at R4C2 contains 2 -> R345C4 must contain 2 40c. 2 locked in R345C4, locked for C4
41. R7C4 + R8C34 (step 24a) = {148/238} 41a. 2 of {238} must be in R8C3 -> no 3 in R8C3 41b. 4 of {148} must be in R8C3 (R78C4 cannot be [14] which clashes with R45C4], no 8 in R8C3, no 4 in R8C4 41c. 8 in O7 locked in R78C4, locked for C4, clean-up: no 4 in R6C3
42. Killer pair 2,6 in R2C2 and R2C67, locked for R2
43. R2C138 (step 8) = {178/358/457} 43a. 4 of {457} must be in R2C1 -> no 4 in R2C3
44. 36 rule on C123 4 innies R1268C3 = 18 = {1467/2358/2457} (cannot be {1278/2367} which clash with R34C3, cannot be {1368} because R8C3 only contains 2,4, cannot be {1458/3456} which clash with R57C3) 44a. 6 of {1467} must be in R1C3 -> no 1 in R1C3 44b. 2,4 of {2457} must be in R18C3 44c. Combining steps 44a and 44b, no 7 in R1C3
45. 13(3) cage at R2C4 (step 35a) = {238/247/346} 45a. Hidden killer triple 1,2,3 in R23C4, R45C4 and R78C4 for C4, R45C4 must contain 1 or 2, R78C4 must contain 1 or 3 -> R23C4 can only contain one of 2,3 -> no 8 in R2C5 (step 45) 45b. R2C5 = 4, R23C4 = [36/72] (step 45), clean-up: no 7 in R45C5 45c. Killer triple 1,2,3 in R23C4, R45C4 and R78C4, locked for C4 45d. R2C5 = 4 -> R1C56 = [18/27] (step 23)
46. 5 in O1 locked in R1C34 + R2C3 -> 23(5) cage at R1C3 must contain 5 46a. 23(5) cage at R1C3 = {12578/13568/23567} (cannot be {13478/23468} which don’t contain 5, cannot be {14567} which clashes with R1C56), no 4 [I could now make further candidate eliminations but the next step is more direct.]
47. 4 in O1 locked in R1C12 47a. 13(3) cage at R1C1 (step 38a) = {148} (only remaining combination), locked for O1
48. Grouped X-Wing on 1 in 13(3) cage at R1C1 and 19(5) cage at R3C1, locked for C12 -> R3C2 = 5, R2C2 = 2, R2C6 = 1, R2C7 = 6, R2C1 = 8, R4C6 = 2, R1C5 = 2, R1C6 = 7 (step 45c), R2C4 = 7 (step 39), R3C4 = 2 (step 45a), clean-up: no 4 in R45C4, no 1 in R5C4 (both step 3) 48a. R45C4 = [15], R16C4 = [64], R6C3 = 8, clean-up: no 3 in R34C3, no 6 in R45C5 (step 3a)
49. R1C8 = 8 (hidden single in R1)
50. R7C3 = 1 (hidden single in C3), R7C2 = 7, R7C5 = 5, R56C2 = [31], R1C12 = [14], R4C2 = 8, R45C5 = [38], clean-up: no 6 in R3C56
and the rest is naked singles
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