SudokuSolver Forum

537 892 641
826 413 975
194 765 823
912 346 587
678 259 134
453 178 269
745 621 398
369 584 712
281 937 456

My breakthrough was the sort of step I expect in one of manu's puzzles. Even so it wasn't particularly obvious so, as manu said, this is a genuine Assassin. As I've commented, the breakthrough could have been found earlier but, in that case, I might not have used some other interesting steps.

It's probably fair to describe the puzzle as a "one trick pony". I assume that SudokuSolver couldn't find step 16 (not actually used) and step 16a, which is why the SS score is high. The rest of my walkthrough was fairly long but straightforward.

I'll rate my walkthrough for A229 at 1.5. I used a forcing chain; it was related to "clones" but didn't actually use them.

Thanks Ed for pointing out some typos

Prelims

a) R12C9 = {15/24}
b) R23C1 = {18/27/36/45}, no 9
c) R23C2 = {29/38/47/56}, no 1
d) R23C3 = {19/28/37/46}, no 5
e) R6C12 = {18/27/36/45}, no 9
f) R78C1 = {19/28/37/46}, no 5
g) R7C23 = {18/27/36/45}, no 9
h) R7C78 = {39/48/57}, no 1,2,6
i) R78C3 = {19/28/37/46}, no 5
j) R8C45 = {49/58/67}, no 1,2,3
k) R89C6 = {29/38/47/56}, no 1
l) R8C78 = {17/26/35}, no 4,8,9
m) R9C45 = {39/48/57}, no 1,2,6
n) R9C78 = {18/27/36/45}, no 9
o) 22(3) cage at R4C1 = {589/679}
p) 11(3) cage at R5C8 = {128/137/146/236/245}, no 9
q) 10(3) cage at R6C3 = {127/136/145/235}, no 8,9
r) 11(3) cage at R6C6 = {128/137/146/236/245}, no 9
s) 12(4) cage at R1C6 = {1236/1245}, no 7,8,9
t) 28(4) cage at R1C8 = {4789/5689}, no 1,2,3
u) 44(8) cage at R3C8 = {23456789}, no 1
v) And, of course, 45(9) cage at R1C4 = {123456789}

Steps resulting from Prelims
1a. 12(4) cage at R1C6 = {1236/1245}, CPE no 1,2 in R1C45
1b. 28(4) cage at R1C8 = {4789/5689}, 8,9 locked for N3
1c. 22(3) cage at R4C1 = {589/679}, 9 locked for N4
1d. 7,8,9 in N2 only in R1C45 + R2C5 + R3C456, locked for 45(9) cage at R1C4, no 7,8,9 in R4C234
1e. 9 in R6 only in R6C59, CPE no 9 in R5C7
1f. 9 in N6 only in R4C789 + R56C9, locked for 44(8) cage at R3C8, no 9 in R4C6
[Alternatively 36(7) cage at R4C5 must contain 9, locked for N5]

2. Killer pair 4,5 in 28(4) cage at R1C8 and R12C9, locked for N3

3. 1 in N8 only in R7C456, locked for R7, clean-up: no 8 in R7C23, no 9 in R8C1
3a. 45 rule on N8 3 innies R7C456 = 9 = {126/135}, no 4,7,8
3b. R7C23 = {27/45} (cannot be {36} which clashes with R7C456
3c. Killer pair 2,5 in R7C23 and R7C456, locked for R7, clean-up: no 7 in R7C78, no 8 in R8C1
3d. R89C6 = {29/38/47} (cannot be {56} which clashes with R7C456), no 5,6

4. R7C456 (step 3a) = {126/135}
4a. 3 of {135} must be in R7C56 (11(3) cage at R6C6 cannot be 5{15}), no 3 in R7C4
4b. 45 rule on N8 1 outie R6C6 = 1 innie R7C4 + 2 -> R6C6 = {3478}
4c. 10(3) cage at R6C3 = {127/136/145/235}
4d. 6 of {136} must be in R7C4 (R6C34 cannot be {36} which clashes with R6C6 + R7C4 = [31], IOD blocker), no 6 in R6C34

5. 45 rule on R89 2 outies R7C19 = 15 = {69/78}, clean-up: no 6,7 in R8C1

6. 16(3) cage at R7C9 = {169/178/268} (cannot be {259/457} which clash with R12C9, cannot be {349/358} which clash with R7C78, cannot be {367} which clashes with R8C78), no 3,4,5
6a. Killer pair 1,2 in R12C9 and 16(3) cage, locked for C9
6b. Killer pair 8,9 in R7C78 and 16(3) cage, locked for N9, clean-up: no 1 in R9C78

7. 3 in C9 only in R3456C9, locked for 44(8) cage at R3C8, no 3 in R3C8 + R4C678

8. 45 rule on N3 3 innies R1C7 + R3C89 = 11 = {137/236}
8a. 7 of {137} must be in R3C8 -> no 7 in R3C9

9. Hidden killer pair 4,5 in R12C9 and R456C9 for C9, R12C9 contains one of 4,5 -> R456C9 must contain one of 4,5
9a. 11(3) cage at R5C8 = {128/137/146/236} (cannot be {245} which clashes with R456C9), no 5

10. 5 in N9 only in R8C78 = {35} or R9C78 = {45} -> R9C78 = {27/45} (cannot be {36}, locking-out cages), no 3,6

11. R9C45 = {39/48} (cannot be {57} which clashes with R9C78), no 5,7
11a. R8C45 = {58/67} (cannot be {49} which clashes with R9C45), no 4,9
11b. R89C6 = {29/47} (cannot be {38} which clashes with R9C45), no 3,8
11c. R6C6 + R7C4 cannot be [42] (clashes with R89C6, IOD blocker), no 4 in R6C6, no 2 in R7C4

12. 11(3) cage at R6C6 = {128/137/236}, no 5

13. 16(3) cage at R8C2 = {169/178/268/358/367} (cannot be {259/457} which clash with R7C23, cannot be {349} because that would leave only {28} for both the 10(2) cages in N7), no 4

14. 45 rule on R6789 2 innies R6C59 = 1 outie R5C8 + 13
14a. Max R6C59 = 17 -> max R5C8 = 4
14b. Min R6C59 = 14, no 1,2,3,4 in R6C59

15. 45 rule on N8 3 outies R6C346 = 12 = {138/147/237/345}
15a. 9 in R6 only in R6C59
15b. 45 rule on R6789 4 innies R6C5789 = 24 = {1689/2589/2679/4569} (cannot be {3489/3579} which clash with R6C346), no 3
15c. 7 of {2679} must be in R6C59 (R6C78 cannot be {27} because 11(3) cage at R5C8 cannot be 2{27}), no 7 in R6C78

[Just spotted the next move; it’s been available in this form after step 6.]
16. 3 innies for N2 R1C6 + R2C56 are “clones” of R4C234 because of 45(9) cage at R1C4
16a. Consider placements for 2 in 45(9) cage at R1C4
2 in R2C4 + R3C456, locked for N2 => 2 in 12(4) cage at R1C6 must be in R1C7
or 2 in R4C234, locked for R4 => 2 in 44(8) cage at R3C8 only in R3C8
-> 2 in R1C7 + R3C8, locked for N3, clean-up: no 4 in R12C9
[I later realised that step 16a didn’t actually use the “clones” in the previous line, but I’ve left it in anyway. It gave me the idea for step 16a.]
[Cracked!]

17. Naked pair {15} in R12C9, locked for C9 and N3, clean-up: no 6 in 28(4) cage at R1C8, no 7 in R3C8 (step 8)

18. 16(3) cage at R7C9 (step 6) = {268} (only remaining combination), locked for C9 and N9 -> R3C9 = 3, clean-up: no 6 in R2C1, no 8 in R2C2, no 7 in R2C3, no 6,8 in R7C1 (step 5), no 2,4 in R8C1, no 4 in R7C78, no 7 in R9C78

19. Naked triple {479} in R456C9, locked for N6 and 44(8) cage at R3C8, no 4,7 in R4C6

20. Naked pair {39} in R7C78, locked for R7 and N9 -> R7C1 = 7, R8C1 = 3, R7C9 = 8 (step 5), clean-up: no 2 in R2C1, no 2,6 in R3C1, no 2,6 in R6C2, no 2 in R7C23, no 5 in R8C78

21. Naked pair {45} in R7C23, locked for R7 and N7, clean-up: no 7 in R6C6 (step 4b), no 6 in R89C3

22. Naked triple {126} in R7C456, locked for N8, clean-up: no 7 in R8C45, no 9 in R89C6

23. Naked pair {45} in R9C78, locked for R9 -> R89C6 = [47], clean-up: no 8 in R9C45

24. Naked pair {58} in R8C45, locked for R8, clean-up: no 2 in R9C3
24a. Naked pair {17} in R8C78, locked for R8
24b. Naked pair {39} in R9C45, locked for R9

25. 12(4) cage at R1C6 = {1236/1245}, 1 locked for N2
25a. 1 in 45(9) cage at R1C4 only in R4C234, locked for R4

26. 5,8 of 44(8) cage at R3C8 only in R4C678, locked for R4

27. 5 in 45(9) cage at R1C4 only in R1C45 + R2C4 + R3C456, locked for N2

28. 12(4) cage at R1C6 = {1236} (only remaining combination), no 4, 3 locked for N2, CPE no 6 in R1C45

29. 4 in N2 only in R1C45 + R2C4 + R3C456, locked for 45(9) cage at R1C4, no 4 in R4C234
29a. 3 in 45(9) cage only in R4C234, locked for R4

30. R3C8 = {26} -> R4C678 must contain one of 2,6
30a. Killer pair 2,6 in R4C234 and R4C678, locked for R4 -> R4C1 = 9

31. 11(3) cage at R5C8 (step 9a) = {128/236}, 2 locked for N6
31a. 3 in N6 only in R5C78, locked for R5
31b. Killer triple 5,6,8 in R4C78 and 11(3) cage, locked for N6
31c. 5 in N6 only in R4C78, locked for R4
31d. Naked pair {26} in R1C7 + R3C8, CPE no 6 in R4C7

32. R16C7 = {26} (hidden pair in C7)
32a. 11(3) cage at R5C8 (step 31) = {128/236}
32b. 2 of {128} must be in R6C7, 3 of {236} must be in R5C8 -> no 2 in R5C8
32c. Naked pair {13} R5C78, locked for R5 and N6
32d. 2 in N6 only in R6C78, locked for R6, clean-up: no 7 in R6C2

33. 1 in N5 only in R46C4, locked for C4 -> R7C4 = 6, R6C6 = 8 (step 4b), clean-up: no 1 in R6C12

34. R7C4 = 6 -> R6C34 = 4 = {13}, locked for R6, clean-up: no 6 in R6C1

35. Naked pair {26} in R6C78, locked for N6, R5C8 = 3 (step 31), R5C7 = 1, R7C78 = [39], R8C78 = [71]

36. Naked pair {45} in R6C12, locked for R6 and N4

37. 22(3) cage at R4C1 = {679} (only remaining combination) -> R5C12 = [67], R5C3 = 8 (hidden single in N4), R9C3 = 1, R8C3 = 9, R6C34 = [31], R4C23 = [12], R4C4 = 3, R4C6 = 6, R3C8 = 2, R1C7 = 6, R9C45 = [93], clean-up: no 4,9 in R2C2, no 4 in R3C2, no 7 in R3C3

38. Naked pair {46} in R23C3, locked for C3 and N1 -> R7C23 = [45], R6C12 = [45], R1C3 = 7, clean-up: no 5 in R23C1

39. Naked pair {18} in R23C1, locked for C1 and N1 -> R9C1 = 2, R1C1 = 5, R1C2 = 3 (cage sum)

and the rest is naked singles.