I was going to start after step 25 of my Assassin 253 walkthrough, but then realised that there were a couple of earlier sub-steps which don’t work for this cage pattern, so I’ve started from the beginning and used as much of my Assassin 253 walkthrough as possible.
Prelims
a) 21(3) cage at R2C2 = {489/579/678}, no 1,2,3
b) 23(3) cage at R3C6 = {689}
c) 10(3) cage at R7C2 = {127/136/145/235}, no 8,9
d) 21(3) cage at R7C8 = {489/579/678}, no 1,2,3
e) 20(3) cage at R9C1 = {389/479/569/578}, no 1,2
1. 45 rule on N12 2 innies R3C36 = 7 -> R3C3 = 1, R3C6 = 6
1a. Naked pair {89} in R3C7 + R4C6, CPE no 8,9 in R4C7
1b. R3C3 = 1 -> R4C34 = 12 = {39/48/57}, no 2,6
1c. 12(3) cage at R1C1 = {237/246/345}, no 8,9
1d. Killer pair 4,7 in 12(3) cage and 21(3) cage at R2C2, locked for N1
2. 45 rule on N2 2 remaining innies R12C4 = 8 = {17/35}, no 2,4,8,9
2a. 45 rule on N1 2 remaining innies R1C23 = 11 = {29/38/56}
3. 45 rule on N36 2 innies R36C7 = 13 = [85/94]
3a. 18(3) cage at R6C6 = {459/468/567} (other combinations don’t contain 4 or 5 for R6C7), no 1,2,3
3b. 6 of {468/567} must be in R7C7 -> no 7,8 in R7C7
3c. Omitted, unnecessary after step 6a
4. 45 rule on N47 2 innies R47C3 = 11 = {38/47}/[56/92], no 5,9 in R7C3
5. 45 rule on N89 2 innies R7C47 = 9 = [36/45/54]
6. 18(3) cage at R6C6 = {459/468/567}
6a. 7,8,9 only in R6C6 -> R6C6 = {789}
7. 45 rule on N5 4 innies R46C46 = 26 = {2789/3689/4589/4679/5678}, no 1
8. 12(3) cage at R6C4 = {237/246/345}, no 8,9, clean-up: no 3 in R4C3 (step 4), no 9 in R4C4 (step 1b)
8a. 7 of {237} must be in R7C3 (cannot be [723] which clashes with R12C4), no 7 in R6C4
8b. R7C34 cannot total 9 which clashes with R7C47 = 9 (step 5), CCC -> no 3 in R6C4
9. 45 rule on N9 3 innies R7C7 + R9C78 = 9 = {126/135/234}, no 7,8,9
9a. R7C7 = {456} -> no 4,5,6 in R9C78
9b. 16(4) cage at R8C6 cannot contain more than two of 1,2,3, R9C78 = {123} -> no 1,2,3 in R89C6
10. 45 rule on N47 3 remaining outies R467C4 = 13 = {238/247/346} (cannot be {256} because 2,6 only in R6C4), no 5, clean-up: no 7 in R4C3 (step 1b), no 4 in R7C3 (step 4), no 4 in R7C7 (step 5)
10a. Killer pair 3,7 in R12C4 and R467C4, locked for C4
11. 12(3) cage at R6C4 (step 8) = {237/246}, CPE no 2 in R6C3
11a. R7C4 = {34} -> no 3,4 in R6C4 + R7C3, clean-up: no 8 in R4C3 (step 4), no 4 in R4C4 (step 1b)
12. R7C7 + R9C78 (step 9) = {126/135}, 1 locked for R9 and N9
13. R46C46 (step 7) = {2789/3689}, 9 locked for C6 and N5, 8 also locked for N5
14. 16(4) cage at R8C6 = {1258/1348/1357/2347}
14a. Killer triple 7,8,9 in R46C6 and R89C6, locked for C6
15. 14(3) cage at R1C5 must contain one of 7,8,9 -> R1C5 = {789}
16. 45 rule on N8 3 innies R7C4 + R89C6 = 16 = {358/457}, 5 locked for C6 and N8
16a. R7C4 = {34} -> no 4 in R89C6
17. 45 rule on N3 3 innies R2C9 + R3C79 = 15 = {159/249/258/348} (cannot be {267/357/456} because R3C7 only contains 8,9, cannot be {168} because 1,6 only in R2C9), no 6,7
17a. R3C7 = {89} -> no 8,9 in R23C9
18. 45 rule on N8 2 outies R9C78 = 1 innie R7C4
18a. R7C4 + R9C78 = 3{12}/4{13}, CPE no 3 in R7C9 + R9C5
[With hindsight, this step was available after step 9.]
[Order of steps changed for simplification.]
19. 20(3) cage at R9C1 = {389/479/569} (cannot be {578} which clashes with R9C6), 9 locked for R9 and N7
20. 17(3) cage at R8C4 = {269/467} (cannot be {179} because 1,9 only in R8C4, cannot be {278} which clashes with R89C6, ALS block), no 1,8, 6 locked for N8
20a. 7 of {467} must be in R9C5 -> no 4 in R9C5
20b. 9 of {269} must be in R8C4 -> no 2 in R8C4
21. 45 rule on C1 1 innie R9C1 = 2 outies R46C2 + 1
21a. Min R46C2 = 3 -> min R9C1 = 4
21b. Max R46C2 = 8, no 8,9 in R46C2
22. 17(3) cage at R2C5 = {179/278/359/458}
22a. Killer pair 5,7 in R12C4 and 17(3) cage, locked for N2
23. 16(3) cage at R1C7 = {169/178/259/268/349/358/367} (cannot be {457} which clashes with R2C9 + R3C79)
23a. Killer triple 6,8,9 in R1C23, R1C5 and 16(3) cage, locked for R1
23b. Hidden killer triple 6,8,9 in R1C12, R1C5 and 16(3) cage for R1, R1C12 contains one of 6,8,9, R1C5 = {89} -> 16(3) cage = {178/259/349/358/367} (cannot be {169/268} which contain two of 6,8,9)
24. 19(4) cage at R1C1 (steps 2 and 2a) = {29}{17}/{29}{35}/{38}{17}/{56}{17} -> combined cage 19(4) cage + R1C5 = {29}{17}8/{29}{35}8/{38}{17}9/{56}{17}8/{56}{17}9
24a. 16(3) cage at R1C7 (step 23b) = {349/358/367} (cannot be {178/259} which clash with combined cage), no 1,2, 3 locked for R1 and N3, clean-up: no 8 in R1C23 (step 2a), no 5 in R2C4 (step 2)
24b. 8 in N1 only in 21(3) cage at R2C2 = {489/678}, no 5
24c. 1 in R1 only in R1C46, locked for N2, clean-up: no 7 in R1C4 (step 2)
25. 3 in N1 only in R23C1, locked for C1
25a. 12(3) cage at R1C1 (step 1c) = {237/345}, no 6
26. Hidden killer pair 1,5 in R12C4 and R35C4 for C4, R12C4 contains one of 1,5 -> R35C4 must contain one of 1,5
26a. 45 rule on C1234 2 innies R35C4 = 1 outie R9C5 + 7
26b. R9C5 = {267} -> R35C4 = 9,13,14 = {45}/[81]/{58}/[95] (other combinations don’t contain 1 or 5) -> no 2,6 in R35C4
27. 45 rule on N7 3 innies R7C13 + R8C1 = 15 = {168/258/267/456}
27a. 20(3) cage at R9C1 (step 19) = {389/479} (cannot be {569} which clashes with R7C13 + R8C1), no 5,6
28. 18(3) cage at R6C6 = {459/468/567}
28a. 45 rule on N7 4(3+1) outies R689C6 + R6C7 = 25 = 21(3)[4]/{20(3)[5] = [9]{57}[4]/[7]{58}5 (because 18(3) cage = [756] when R6C7 = 5) -> R6C6 = {79}
28b. 18(3) cage = {459/567}, 5 locked for C7
29. R1C23 = 11 (step 2a) = {29/56}
29a. Consider combinations for R1C23
R1C23 = {29} => 14(3) cage at R1C5 = 8{24}=> R1C4 = 1 (hidden single in R1)
or R1C23 = {56}, locked for R1 => R1C4 = 1
-> R1C4 = 1, R2C4 = 7 (step 2), clean-up: no 5 in R4C3 (step 1b), no 6 in R7C3 (step 4)
30. Killer pair 8,9 in R4C34 and R4C6, locked for R4
31. 14(3) cage at R1C5 = {248/239}, 2 locked for C6 and N2
32. 45 rule on N3 2 outies R4C89 = 2 innies R3C7 + 2
32a. Min R3C7 = 8 -> min R4C89 = 10, no 1,2 in R4C89
33. 10(3) cage at R7C2 = {136/145/235} (cannot be {127} which clashes with R7C3), no 7
33a. Killer pair 3,4 in 10(3) cage and 20(3) cage at R9C1, locked for N7
34. R7C13 + R8C1 (step 27) = {258/267} (cannot be {168} because R7C3 only contains 2,7), no 1, 2 locked for N7
35. 1 in C1 only in R456C1, locked for N4
35a. R9C1 = R46C2 + 1 (step 21)
35b. Min R46C2 = 5 -> no 4 in R9C1
35c. Max R46C2 = 8, no 7 in R46C2
36. 18(3) cage (step 28b) = {459/567}
36a. R7C13 + R8C1 (step 34) = {258/267} -> R78C1 = {26/58/67}
36b. 19(4) cage at R6C1 = {1567/2368/2458} (cannot be {1279/1369/1378/1459/1468/2359/3457} which don’t contain both of {26/58/67}, cannot be {2467} = [74]{26} which clashes with 18(3) cage) -> R6C12 = [15/24/42/83]
37. Variable hidden killer pair 1,6 in 13(3) cage at R4C1 and 19(4) cage at R6C1 for C1, 13(3) cage cannot contain both of 1,6 -> 19(4) cage must contain at least one of 1,6 -> 19(4) cage = {1567/2368} (cannot be {2458} which doesn’t contain one of 1,6), no 4, 6 locked for C1 and N7
37a. 10(3) cage at R7C2 (step 33) = {145} (only remaining combination), locked for N7
37b. 20(3) cage at R9C1 (step 27a) = {389} (only remaining combination), locked for R9 and N7
38. Naked pair {12} in R9C78, locked for R9 and N9
39. 17(3) cage at R8C4 (step 20) = {467} (only remaining combination) -> R9C5 = 7, R89C4 = {46}, locked for C4 and N8 -> R6C4 = 2, R7C3 = 7, R7C4 = 3, R7C7 = 6 (step 5), R7C6 = 1, R78C1 = [26], R89C6 = [85], R9C9 = 4, R89C4 = [46], R8C23 = [15], R7C2 = 4, R4C6 = 9, R6C6 = 7, R6C7 = 5 (cage sum), R3C7 = 8, R4C34 = [48], R78C5 = [92], R1C5 = 8, R12C6 = 6 = {24} (locked for C6 and N2), R5C46 = [53], R3C4 = 9, R3C2 = 7, R6C2 = 3, R6C1 = 8 (cage sum), R9C1 = 9
40. 2 in N1 only in R1C23 (step 2a) = {29}, locked for R1 and N2 -> R12C6 = [42], R1C1 = 5
41. R2C9 + R3C79 = 15 (step 17), R3C7 = 8 -> R23C9 = 7 = [52], R7C9 = 8, R8C9 = 3 (cage sum)
42. R23C9 = [52] = 7 -> R4C89 = 10 = [37], R1C9 = 6
43. Naked pair {19} in R56C9, locked for N6, R6C8 = 6 (cage sum)
and the rest is naked singles.
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