Thanks Tarek for your first Assassin.
I found this more challenging than I'd expected. I'll accept that it's straightforward if one finds both of Afmob's key steps easily but it took me a long time to find the second one, in fact I left this puzzle to try other ones and only came back to it this week.
I'll rate A147 the way I solved it at Easy 1.25 to 1.25 because of steps 10a, 14 and 20; I've included steps 10a and 20 at this level because they each extend into two nonets and into two rows or columns. Also it has a narrow solving path until one has found both key steps.
Here is my walkthough for A147.
Prelims
a) R1C34 = {18/27/36/45}, no 9 b) R23C5 = {49/58/67}, no 1,2,3 c) R34C1 = {13}, locked for C1 d) R5C23 = {89}, locked for R5 and N4 e) R5C78 = {17/26/35}, no 4 f) R67C9 = {15/24} g) R78C5 = {14/23} h) R9C67 = {18/27/36/45}, no 9 i) 19(3) cage in N1 = {289/379/469/478/568}, no 1 j) 9(3) cage in N3 = {126/135/234}, no 7,8,9 k) 7(3) cage at R3C6 = {124} l) 19(3) cage at R6C7 = {289/379/469/478/568}, no 1 m) 27(4) cage at R1C5 = {3789/4689/5679}, no 1,2
1. 45 rule on N5 2 innies R4C6 + R6C4 = 13 -> R4C6 = 4, R6C4 = 9, clean-up: no 5 in R9C7 1a. R3C6 + R4C7 = {12}, CPE no 1,2 in R3C7 1b. X-Wing for 1 in R34C1 and R4C6 + R6C4, locked for R34 1c. R6C4 = 9 -> R6C3 + R7C4 = 9 = [18]/{27/36/45}, no 1 in R7C4
2. 45 rule on N3 2 innies R1C7 + R3C9 = 12 = {39/48/57}, no 2,6
3. 45 rule on N7 2 innies R7C1 + R9C3 = 11 = {29/47/56}/[83], no 1,8 in R9C3
4. 45 rule on R1 3 outies R2C169 = 19 = {289/379/469/478/568}, no 1 4a. 2,3 of {289/379} must be in R2C9, no 2 in R2C1, no 3 in R2C6
5. 45 rule on R9 3 outies R8C149 = 19 = {289/379/469/478/568}, no 1
6. 45 rule on C9 3 outies R149C8 = 10 = {127/136/145/235}, no 8,9
7. R4C9 = 9 (hidden single in R4), clean-up: no 3 in R1C7 (step 2)
8. 8 in R4 locked in R4C45, locked for N5 8a. 45 rule on R1234 2 innies R4C45 = 1 outie R5C9 + 11 8b. Max R4C45 = 15 -> max R5C9 = 4 8c. Min R5C9 = 1 -> min R4C45 = 12, no 2,3 in R4C45 8d. Min R4C45 = {58} = 13, min R5C9 = 2
9. 24(4) cage at R3C9 = {2589/2679/3489/3579/4569} 9a. Max R345C9 = 21 -> min R4C8 = 3 9b. Max R4C89 + R5C9 = 20 and contains 4 -> min R3C9 = 5, clean-up: no 8,9 in R1C7 (step 2) 9c. Min R14C8 = 4 -> max R9C8 = 6 (step 6)
10. 27(4) cage at R1C5 = {3789/4689/5679}, 9 locked for N2, clean-up: no 4 in R23C5 10a. 27(4) cage at R1C5 = {3789/5679} (cannot be {4689} which clashes with R23C5), no 4, CPE no 7 in R1C4, clean-up: no 2 in R1C3, no 8 in R3C9 (step 2) 10b. 5 of {5679} must be in R1C7 (R1C56 + R2C6) cannot be {569} which clashes with R23C5), no 5 in R1C56 + R2C6 10c. Killer pair 6,8 in R1C56 + R2C6 and R23C5, locked for N2, clean-up: no 1,3 in R1C3 10d. 4 in N2 locked in R123C4, locked for C4, clean-up: no 5 in R6C3 (step 1c) [I could also lock 7 for N2 using interactions between the 13(2) and 27(4) cages but that’s a higher rated step so I won’t use it.]
11. Naked pair {57} in R1C7 + R3C9, locked for N3 11a. 9(3) cage in N3 = {126/234}, 2 locked for N3 11b. 24(4) cage at R3C9 (step 9) = {2679/3579/4569} 11c. R5C9 = {234} -> no 3 in R4C8 11d. 3 in R4 locked in R4C123, locked for N4, clean-up: no 6 in R7C4 (step 1c) 11e. Min R14C8 = 6 -> max R9C8 = 4 (step 6) 11f. Min R49C8 = 6 -> max R1C8 = 4 (step 6)
12. 8 in C9 locked in R89C9, locked for N9, clean-up: no 1 in R9C6 12a. 16(3) cage in N9 = 8{17/26/35}, no 4 12b. R9C8 = {123} -> no 1,2,3 in R89C9
13. R8C149 (step 5) = {289/379/478/568} (cannot be {469} because 4,9 only in R8C1) 13a. 4,9 of {289/379/478} must be in R8C1 -> no 2,7 in R8C1
14. Hidden killer triple 1,2,3 in R4C1, R4C23 and R4C7 for R4 -> R4C23 must contain one of 2,3 -> R4C23 must contain one of 5,6,7 [The final part of this could also be obtained from hidden killer triple 5,6,7 in R4C23, R4C45 and R4C8 for R4]
15. 20(4) at R5C1 = {1469/1478/1568/2459/2468/2567} (cannot be {1289} because 8,9 only in R6C1) 15a. 8,9 of {1469/1478/2459/2468} must be in R7C1 -> no 4 in R7C1, clean-up: no 7 in R9C3 (step 3) 15b. 2 of {2567} must be in R5C1 + R6C12 (R5C1 + R6C12 cannot be {567} which clashes with R4C23), 8,9 of {2459/2468} must be in R7C1 -> no 2 in R7C1, clean-up: no 9 in R9C3 (step 3) 15c. Killer triple 1,2,3 in R4C1, R4C23 and R5C1 + R6C12, locked for N4, clean-up: no 7,8 in R7C4 (step 1c)
16. 13(3) cage at R3C3 = {238/247/256/346}, no 9
17. 45 rule on R123 4 remaining outies R4C1237 = 1 innie R3C9 + 6 17a. R3C9 = {57} -> R4C1237 = 11,13 = {1235/1237}, no 6
18. 20(4) at R5C1 (step 15) = {1469/1478/1568/2459/2468/2567} 18a. 6 of {2567} must be in R5C1 + R6C12 (R5C1 + R6C12 cannot be {257} which clashes with R4C23), 8,9 of {1469/1478/2459/2468} must be in R6C1 -> no 6 in R7C1, no 5 in R9C3 (step 3)
19. 13(3) cage at R3C3 (step 16) = {238/247/256/346} 19a. 6,8 of {238/256/346} must be in R3C3 -> no 3,5 in R3C3
20. 24(4) cage at R3C9 (step 11b) = {2679/3579} (cannot be {4569} which clashes with R67C9), no 4, clean-up: no 7 in R4C45 (steps 8 and 8a) [I missed that clash earlier; {4569} could have been eliminated in step 9.] 20a. R5C1 = 4 (hidden single in R5), clean-up: no 5 in R7C3 (step 1c) 20b. 6 in N4 locked in R6C123, locked for R6 [After fixing R5C1, Afmob found 45 rule on R6789 2 innies R6C56 = 5 = {23}, locked for R6 and N5, which makes the later stages quicker.]
21. R78C5 = {14} (cannot be {23} which clashes with R7C4), locked for C5 and N8
22. 20(4) at R5C1 (step 15) = {1469/1478/2459/2468} 22a. 8,9 only in R7C1 -> R7C1 = {89}, clean-up: no 4,6 in R9C3 (step 3) 22b. 1 of {1478} must be in R6C2 -> no 7 in R6C2
23. 22(4) cage at R8C4 = {2389/2569/2578/3568} 23a. 9 of {2389} must be in R9C5, 2,3 of other combinations must be in R9C3 -> no 2,3 in R9C5
24. 9 in C5 locked in R19C5 24a. 45 rule on C5 5 innies R14569C5 = 27 = {23589/23679} 24b. 2 locked in R56C5, locked for N5 24c. 6 of {23679} must be in R4C5 -> no 6 in R159C5
25. Killer triple 1,2,3 in R4C7, R5C78 and R5C9, locked for N6, clean-up: no 4,5 in R7C9
26. 3 in R6 locked in R6C56, locked for N5 26a. Hidden killer pair 1,2 in R6C12 and R6C56 for R6, R6C12 contains one of 1,2 -> R6C56 must contain one of 1,2 and also 3 (step 26) -> R6C5 = {23}, R6C6 = {13} 26b. 7 in N5 locked in R5C456, locked for R5, clean-up: no 1 in R5C78
27. R4C7 = 1 (hidden single in N6), R3C6 = 2, R4C1 = 3, R3C1 = 1, clean-up: no 7 in R1C3, no 8 in R9C6, no 7 in R9C7 27a. 2 in N6 locked in R5C789, locked for R5 27b. R6C5 = 2 (hidden single in C5), R6C6 = 3 (hidden single in R6), R6C2 = 1 (hidden single in R6), clean-up: no 6 in R9C7 27c. R1C5 = 3 (hidden single in C5), R9C5 = 9 (hidden single in C5), clean-up: no 6 in R1C3 27d. Killer pair 5,7 in R23C5 and R5C5, locked for C5
28. R1C5 = 3 -> 27(4) cage at R1C5 (step 10a) = {3789}, no 5,6 -> R1C7 = 7, R3C9 = 5, R6C9 = 4, R7C9 = 2, R5C9 = 3, R12C9 = [16], R1C8 = 2 (step 11a), R7C4 = 3, R6C3 = 6 (step 1c), clean-up: no 8 in R1C3, no 8 in R2C5, no 7 in R3C5, no 5,6 in R5C7, no 5 in R5C8 28a. R5C78 = [26], R4C8 = 7, clean-up: no 7 in R9C6
29. Naked pair {89} in R12C6, locked for C6 and N2, clean-up: no 5 in R2C5 29a. R23C5 = [76], R45C5 = [85], R4C4 = 6, R3C4 = 4, R1C34 = [45], R2C4 = 1, R5C46 = [71] 29b. Naked pair {28} in R89C4, locked for 22(4) cage at R8C4 -> R9C3 = 3, R9C7 = 4, R9C6 = 5, R9C8 = 1, R7C1 = 8 (step 3), R6C1 = 7 (step 22)
30. R3C4 = 4 -> R34C3 = 9 = [72], R4C2 = 5, R2C1 = 5, R2C8 = 4 (hidden singles in R2) 30a. R2C1 = 5 -> R1C12 = 14 = [68], R12C6 = [98], R89C1 = [92], R89C4 = [28], R89C9 = [87], R9C2 = 6, R5C23 = [98], R23C2 = [23], R2C3 = 9, R2C7 = 3
31. 5 in R6 locked in R6C78, CPE no 5 in R8C7 31a. R8C67 = [76], R7C6 = 6, R67C7 = 13 = [85]
and the rest is naked singles
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