Prelims
a) R1C12 = {59/68}
b) R12C7 = {19/28/37/46}, no 5
c) R23C9 = {39/48/57}, no 1,2,6
d) R3C34 = {69/78}
e) R78C1 = {16/25/34}, no 7,8,9
f) R7C67 = {17/26/35}, no 4,8,9
g) R89C3 = {89}
h) R9C89 = {15/24}
i) 11(3) cage at R2C1 = {128/137/146/236/245}, no 9
j) 19(3) cage at R8C4 = {289/379/469/478/568}, no 1
k) 14(4) cage at R8C6 = {1238/1247/1256/1346/2345}, no 9
1. 45 rule on N3 1 innie R3C7 = 2, placed for D/, clean-up: no 8 in R12C7, no 6 in R7C6
1a. R3C6 + R4C7 = 11 = {38/47/56}, no 1,9
1b. 30(7) cage at R4C3 must contain 2 in R4C3 + R5C3456, CPE no 2 in R5C12
2. 45 rule on N7 1 innie R7C3 = 4, placed for D/, clean-up: no 3 in R78C1
2a. R6C3 + R7C4 = 11 = {29/38/56}, no 1,7
2b. 30(7) cage must contain 4 in R5C4567 + R6C7, CPE no 4 in R5C89
3. Naked pair {89} in R89C3, locked for C3 and N7, clean-up: no 6,7 in R3C4, no 2,3 in R7C4 (step 2a)
4. 45 rule on R1234 3 innies R4C389 = 9 = {126/135/234}, no 7,8,9
5. 45 rule on N4 3 innies R456C3 = 1 outie R3C2 + 4
5a. Min R456C3 = 6 -> no 1 in R3C2
5b. R456C3 cannot total 7 -> no 3 in R3C2
6. 45 rule on N9 3 outies R789C6 = 1 innie R7C8 + 1
6a. Min R789C6 = 6 -> min R7C8 = 5
6b. Max R789C6 = 10, no 8 in R89C6
7. 45 rule on N12 4(1+3) innies R2C5 + R3C256 = 16
7a. Min R3C26 = 7 -> max R23C5 = 9, no 9 in R23C5
8. 45 rule on N1 4 innies R12C3 + R3C23 = 20 = {1379/2378/3467} (cannot be {1289/1469/1568/2369/2567/3458} which clash with R1C12, cannot be {1478/2459/2468} because 4,8,9 only in R3C2), no 5, 3 locked for C3, N1 and 17(4) cage at R1C3, clean-up: no 8 in R7C4 (step 2a)
8a. 4,8,9 only in R3C2 -> R3C2 = {489}
8b. R12C3 + R3C23 = {1379/2378/3467}, 7 locked for C3 and N1
8c. 5 in C3 only in R456C3, locked for N4
8d. 30(7) cage must contain 3 in R5C4567 + R6C7, CPE no 3 in R5C89
9. R12C3 + R3C23 (step 8) = {1379/3467} (cannot be {2378} which clashes with R3C34 = [78], overlap clash), no 2,8
[That’s how I originally saw this step.
With hindsight R3C34 = 15 -> R3C23 cannot be 15 (CCC) -> R12C3 cannot total 5 -> no 2 in R12C3 is more elegant.
Afmob and Ed would probably see that as
45 rule on N1 3 innies R12C3 + R3C2 = 1 outie R3C4 + 5, IOU R12C3 cannot total 5 -> no 2 in R12C3.]
9a. 2 in N1 only in R2C12, locked for R2
9b. 2 in C3 only in R456C3, locked for N4
10. R2C5 + R3C256 = 16 (step 7), min R2C5 + R3C56 = 8 -> no 9 in R3C2
10a. R3C2 = 4, clean-up: no 8 in R2C9, no 7 in R4C7 (step 1a)
10b. R3C2 = 4 -> R4C12 = 14 = {68}, locked for R4 and N4, clean-up: no 3,5 in R3C6 (step 1a)
10c. 11(3) cage at R2C1 = {128} (only remaining combination), locked for N1, clean-up: no 6 in R1C12
10d. Naked pair {59} in R1C12, locked for R1, clean-up: no 1 in R2C7
11. R4C389 (step 4) = {135/234}, 3 locked for R4 and N6, clean-up: no 8 in R3C6 (step 1a)
11a. Killer pair 4,5 in R4C389 and R4C7, locked for R4
11b. 7,9 in R4 only in R4C456 -> 23(5) cage at R2C5 = {12479} (only possible combination) -> R23C5 = [41], R4C456 = {279}, locked for R4 and N5, clean-up: no 6 in R1C7, no 8 in R3C9
11c. R4C389 = {135}, R4C7 = 4 (hidden single in R4) -> R3C6 = 7 (step 1a), R3C3 = 6, placed for D\, R3C4 = 9, R4C6 = 9, placed for D/, clean-up: no 6 in R2C7, no 3,5 in R2C9, no 2 in R6C3, no 5 in R7C4 (both step 2a), no 2 in R7C6, no 1 in R7C7
11d. R3C1 = 8, R4C12 = [68], clean-up: no 1 in R78C1
11e. Naked pair {25} in R78C1, locked for C1 and N7 -> R1C1 = 9, placed for D\, R2C1 = 1, R2C2 = 2, placed for D\, R4C4 = 7, placed for D\, R4C5 = 2, clean-up: no 1 in R7C6, no 4 in R9C8
11f. Naked pair {35} in R7C67, locked for R7 -> R78C1 = [25]
12. R6C3 = 5, R45C3 = [12], R7C4 = 6
12a. R4C89 = {35} -> 15(4) cage at R4C8 = {1356} (only possible combination), locked for N6, 6 also locked for R5
12b. 30(7) cage = {1234578} (only remaining combination) -> R56C7 = {78}, locked for C7 and N6, R5C456 = {345}, locked for R5 and N5 -> R5C12 = [79], R6C12 = [43], R9C1 = 3, placed for D/, R5C5 = 5, placed for both diagonals, R7C67 = [53], clean-up: no 1 in R9C8
13. R12C3 = {37} = 10 -> R12C4 = 7 = [25]
13a. R6C89 = {29} -> R7C8 = 7 (cage sum)
13b. R6C46 = {18}, R6C5 = 6, R7C5 = 9 -> R8C5 = 3 (cage sum)
14. Naked pair {48} in R89C4, locked for C4 and N8
14a. Naked pair {12} in R89C6, locked for 14(4) cage at R8C6 -> R89C7 = [65]
14b. R2C7 = 9, R2C9 = 7 -> R3C9 = 5
and the rest is naked singles, without using the diagonals.
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