Prelims
a) R1C56 = {16/25/34}, no 7,8,9
b) R1C78 = {17/26/35}, no 4,8,9
c) R2C67 = {18/27/36/45}, no 9
d) R45C2 = {89}
e) R4C67 = {29/38/47/56}, no 1
f) R5C67 = {18/27/36/45}, no 9
g) R5C89 = {16/25/34}, no 7,8,9
h) R67C4 = {69/78}
i) R6C78 = {18/27/36/45}, no 9
j) R9C23 = {19/28/37/46}, no 5
k) R9C45 = {69/78}
l) 20(3) cage at R3C8 = {389/479/569/578}, no 1,2
m) 11(3) cage at R6C5 = {128/137/146/236/245}, no 9
n) 10(4) cage at R2C1 = {1234}
o) 26(4) cage at R6C9 = {2789/3689/4589/4679/5678}, no 1
p) 14(4) cage at R7C7 = {1238/1247/1256/1346/2345}, no 9
Steps resulting from Prelims
1a. Naked pair {89} in R45C2, locked for C2 and N4, clean-up: no 1,2 in R9C3
1b. Naked quad {1234} in 10(4) cage at R2C1, no 1,2,3,4 in R1C1
[Ed wanted interesting steps, so here’s one …]
2. 45 rule on N14 4(3+1) outies R125C4 + R7C2 = 21
2a. Max R7C2 = 7 -> min R125C4 = 14
2b. All 3-cell combinations from 13 upward must contain at least one of 6,7,8,9
2c. Killer quad 6,7,8,9 in R125C4, R67C4 and R9C4, locked for C4
2d. Hidden killer quad 6,7,8,9 in R125C4, R67C4 and R9C4 for C4, R67C4 and R9C4 contain three of 6,7,8,9 -> R125C4 must contain one of 6,7,8,9
2e. Max R125C4 = 18 (all 3-cell combinations from 19 upward contain more than one of 6,7,8,9) -> min R7C2 = 3
2f. Max R4C4 = 5 -> min R5C5 + R6C6 = 12, no 1,2 in R5C5 + R6C6
3. 45 rule on D\ 2(1+1) outies R2C4 + R8C6 = 8 = {17/26/35}/[44], no 8,9
4. 45 rule on N1 3(2+1) outies R12C4 + R4C1 = 10
4a. Max R12C4 = 9, no 9 in R1C4
5. 45 rule on N9 3(1+2) outies R6C9 + R89C6 = 11
5a. Min R89C6 = 3 -> max R6C9 = 8
5b. Min R6C9 = 2 -> max R89C6 = 9, no 9 in R9C6
6. 9 in N6 only in R4C789, locked for R4 -> R45C2 = [89], clean-up: no 3 in R4C6, no 2,3 in R4C7
7. 45 rule on N3 2 innies R2C7 + R3C8 = 12 = [39]/{48/57}, no 1,2,6, no 3 in R3C8, clean-up: no 3,7,8 in R2C6
8. 45 rule on N7 2 innies R7C2 + R8C3 = 9 = {36/45}/[72], no 1,7,8,9 in R8C3
9. 45 rule on R1234 2 remaining innies R4C34 = 10 = [64/73]
9a. 17(3) cage at R4C4 = {359/368/458/467}
9b. R4C4 = {34} -> no 3,4 in R5C5 + R6C6
9c. R4C67 = [29/56/65] (cannot be {47} which clashes with R4C34), no 4,7
10. 45 rule on N4 2(1+1) outies R5C4 + R7C2 = 1 innie R4C1 + 11
10a. Min R5C4 + R7C2 = 12 -> min R5C4 = 5
11. 45 rule on N12 3(1+2) outies R2C7 + R4C15 = 8
11a. Min R4C15 = 3 -> max R2C7 = 5, clean-up: no 1,2 in R2C6, no 4,5 in R3C8 (step 7)
11b. Min R2C7 = 3 -> max R4C15 = 5, no 5,6,7 in R4C5
12. 45 rule on C1234 2 outies R89C5 = 2 innies R34C4 + 9
12a. Min R34C4 = 4 -> min R89C5 = 13, no 1,2,3 in R8C5
13. 45 rule on R1 2 innies R1C19 = 1 outie R2C3 + 7, IOU no 7 in R1C9
14. 9 in C6 only in R36C6
14a. 45 rule on C6789 4 innies R1367C6 = 26 = {2789/3689/4589/4679}, no 1, clean-up: no 6 in R1C5
14b. 2 of {2789} must be in R1C6 -> no 2 in R37C6
14c. 11(3) cage at R6C5 = {128/137/146/236/245}
14d. 8 of {128} must be in R7C6 -> no 8 in R67C5
15. 9 in C4 only in R67C4 = {69} or R9C45 = [96] (locking cages) -> no 6 in R9C4, clean-up: no 9 in R9C5
15a. Min R89C5 = 13 (step 12a) -> min R8C5 = 5
15b. Min R8C5 = 5 -> max R8C34 = 7 -> max R8C4 = 4 (12(3) cage at R8C3 cannot be [255])
16. Hidden killer pair 5,9 in R4C67 and 20(3) cage at R3C8 for R4, R4C67 contains one of 5,9 -> 20(3) cage must contain one of 5,9 in R4C89
16a. 20(3) cage at R3C8 = {479/569/578} (cannot be {389} because 8{39} plus R4C67 = {56} clashes with R4C34, blocking cages), no 3
17. R125C4 + R7C2 = 21 (step 2)
17a. Max R125C4 containing one of 6,7,8 (step 2d) = 17 -> min R7C2 = 4, clean-up: no 6 in R8C3 (step 8)
18. 45 rule on R6789 2 innies R6C36 = 1 outie R5C1 + 8, IOU no 8 in R6C6
19. 45 rule on R89 3 outies R7C137 = 1 innie R8C9 + 3
19a. Min R7C137 = 6 -> min R8C9 = 3
20. 45 rule on R9 2 innies R9C19 = 1 outie R8C7 + 4, IOU no 4 in R9C1
[I thought that Ed had managed to “Assassinate” me until I found this step which cracks the puzzle.]
21. Min R34C4 = [13] = 4 -> min R89C5 = 13 = {67} (cannot be [58] which clashes with 17(3) cage at R4C4 = [359/386]) -> no 5 in R8C5
21a. Naked quad {6789} in R7C4 + R8C5 + R9C45, locked for N8, clean-up: no 1,2 in R2C4 (step 3)
21b. Max R7C56 = 9 -> min R6C5 = 2
22. R1367C6 (step 14a) = {3689/4589/4679} (cannot be {2789} because R7C6 only contains 3,4,5), no 2, clean-up: no 5 in R1C5
22a. 7,8,9 only in R36C6 -> R3C6 = {789}, R6C6 = {79}
22b. 3 of {3689} must be in R7C6 -> no 3 in R1C6, clean-up: no 4 in R1C5
23. 17(3) cage at R4C4 (step 9a) = {359/467} (cannot be {368/458} because R6C6 only contains 7,9)
23a. 5,6 only in R5C5 -> R5C5 = {56}
24. R356C6 = {789} (hidden triple in C6) -> R5C6 = {78}, R5C7 = {12}
25. 1 in C6 only in R89C6, locked for N8
25a. 1 in C6 only in R89C6, CPE no 1 in R8C7 + R9C9
26. 11(3) cage at R6C5 = {236/245}, no 7, 2 locked for C5, clean-up: no 5 in R1C6
26a. 2 in N2 only in R13C4, locked for C4
26b. Naked pair {34} in R48C4, locked for C4, clean-up: no 4,5 in R8C6 (step 3)
27. 12(3) cage at R8C3 = {237/246} (cannot be {345} because 3,4,5 only in R8C34), no 5,8,9 -> R8C3 = 2, R7C2 = 7 (step 8)
27a. Killer pair 6,7 in R8C5 and R9C45, locked for N8
27b. Clean-up: no 6 in R2C4 (step 3), no 8,9 in R6C4, no 3 in R9C2, no 3,8 in R9C3
28. 17(3) cage at R4C4 (step 23) = {359} (only remaining combination, cannot be {467} which clashes with R6C4) -> R4C4 = 3, R5C5 = 5, R6C6 = 9, all placed for D\, 5 also placed for D/, R8C4 = 4, R8C5 = 6 (step 27), clean-up: no 6 in R4C7, no 2 in R5C89, no 9 in R9C4
29. Naked pair {78} in R9C45, locked for R9 and N8 -> R7C4 = 9, R6C4 = 6, R4C6 = 2, both placed for D/, R4C7 = 9, R6C5 = 4, R4C5 = 1 (hidden single in N5), R1C5 = 3, R1C6 = 4, R7C5 = 2, R7C6 = 5 (step 26), R2C6 = 6, R2C7 = 3, R3C8 = 9 (step 7), R4C1 = 4, clean-up: no 5 in R1C78, no 5 in R6C7, no 3,5 in R6C8
30. Naked pair {78} in R3C56, locked for R3 and N2 -> R2C45 = [59], R13C4 = [12], R8C6 = 3 (step 3), R9C6 = 1, R1C9 = 8, R8C2 = 1, both placed for D/, R3C7 = 4, placed for D/, R2C8 = 7, R3C12 = [13], R2C1 = 2, R2C2 = 4, R3C3 = 6, both placed for D\
and the rest is naked singles, without using the diagonals.
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