Prelims
a) R1C78 = {18/27/36/45}, no 9
b) R34C5 = {49/58/67}, no 1,2,3
c) R56C8 = {16/25/34}, no 7,8,9
d) R89C4 = {19/28/37/46}, no 5
e) 22(3) cage at R1C4 = {589/679}
f) 10(3) cage at R1C6 = {127/136/145/235}, no 8,9
g) 11(3) cage at R7C3 = {128/137/146/236/245}, no 9
h) 26(4) cage at R2C7 = {2789/3689/4589/4679/5678}, no 1
1a. 45 rule on C6789 1 outie R2C5 = 3 -> R12C6 = 7 = {16/25}
1b. 22(3) cage at R1C4 = {589/679}, 9 locked for N2, clean-up: no 4 in R4C5
1c. Killer pair 5,6 in 22(3) cage at R12C6, locked for N2, clean-up: no 7,8 in R4C5
1d. 4 in N2 only in R3C456, locked for R3
1e. 45 rule on N3 2 outies R4C89 = 17 = {89}, locked for R4 and N6, clean-up: no 4 in R3C5
1f. Naked pair {89} in R4C89, CPE no 8,9 in R2C8
1g. Killer pair 7,8 in 22(3) cage and R3C5, locked for N2
1h. 45 rule on N36 2 innies R56C9 = 9 = {27/36/45}, no 1
1i. 45 rule on N36 2 outies R78C9 = 10 = {19/28/37/46}, no 5
2a. 45 rule on C1234 2 outies R15C5 = 11 = [74/92] (cannot be {56} which clashes with R4C5)
2b. 45 rule on C789 4 outies R6789C6 = 26 = {2789/3689/4589/4679} (cannot be {5678} which clashes with R12C6), no 1, 9 locked for C6
2c. 45 rule on C789 1 outie R6C6 = 1 innie R9C7 + 2, no 2 in R6C6, no 8,9 in R9C7
2d. 45 rule on C9 1 outie R2C8 = 1 innie R9C9 + 1, no 1 in R2C8, no 2,7,8,9 in R9C9
2e. 12(3) cage at R3C6 = {138/147/237/345} (cannot be {156/246} which clash with R12C6), no 6
2f. 12(3) cage at R4C7 = {147/156/237/345} (cannot be {246} which clashes with R56C8)
3. 37(7) cage at R6C6 = {1246789/1345789/2345689}, R6C6 = R9C7 + 2 (step 2c)
3a. Consider placement for 4 in 37(7) cage
R6C6 = 4
or 4 in R78C78 + R9C89, locked for N9, no 4 in R9C7 => no 6 in R6C6
-> no 6 in R6C6, clean-up: no 4 in R9C7
3b. Consider placement for 5 in N9
5 in R78C78 + R9C89 => no 5 in R6C6
or R9C7 = 5 => R6C6 = 7
-> no 5 in R6C6, clean-up: no 3 in R9C7
[Alternatively 37(7) cage must contain 4 -> R6C6 + R9C7 cannot be [64], 37(7) cage must contain both or neither of 3,5 -> R6C6 + R9C7 cannot be [53].]
4. 22(3) cage at R1C4 = {589/679}, R15C5 (step 2a) = [74/92]
4a. Consider combinations for R12C6 (step 1a) = {16/25}
R12C6 = {16} => R12C4 = {58}, 5 locked for C4, 8 locked for N2, R15C5= [92], R34C5 = [76]
or R12C6 = {25}, locked for C6 and N1, 22(3) cage = {679}, locked for N1, 6 locked for C4 => R34C5 = [85], R6C5 = 6 (hidden single in N5)
-> 6 in R46C5, locked for C5 and N5, no 5 in R456C4, no 2 in R45C6
4b. 1 in C5 only in 18(4) cage at R6C5 = {1269/1458/1467} (cannot be {1278} which clashes with R3C5)
4c. 6 of {1269/1467} must be in R6C5 -> no 2,7,9 in R6C5
5a. 45 rule on N7 2 innies R7C12 = 1 outie R7C4 + 6, IOU no 6 in R7C12
5b. 39(7) cage at R5C1 = {1356789/2346789}, 6 locked for N4
5c. 2 in N5 only in R456C4 + R5C5, locked for 21(5) cage at R4C4
5d. 21(5) cage = {12378/12459/23457}
6. 45 rule on R1234 2 innies R4C47 = 1 outie R5C6 + 1, IOU no 1 in R4C7
7. 45 rule on N1 2(1+1) outies R3C4 + R4C1 = 1 innie R3C2 + 1, IOU no 1 in R4C1
7a. Min R3C4 + R4C1 = 3 -> min R3C2 = 2
7b. R3C4 + R4C1 cannot total 10 -> no 9 in R3C2
8. 45 rule on C123 2 outies R37C4 = 1 innie R5C3 + 3
8a. R7C12 = R7C4 + 6 (step 5a)
8b. Consider placement of 8 in N5
8 in R5C12 + R6C123, locked for 39(7) cage at R5C1 => R7C12 cannot total 11 = {29/47/56} which clash with R78C3 + R7C4 = {24}5 => no 5 in R7C4
or R5C3 = 8 => R37C4 = 11 = [47]
-> no 5 in R7C4
8c. 5 in C4 only in R12C4 -> R12C4 = {58}, locked for N2, 8 locked for C4 -> R13C5 = [97], R4C5 = 6, clean-up: no 2 in R12C6 (step 1a), no 2 in R89C4
8d. Naked pair {16} in R12C6, locked for C6, 1 locked for N2
8e. Naked pair {24} in R3C46, 2 locked for R3
8f. R1C5 = 9 -> R5C5 = 2 (step 2a), placed for both diagonals, clean-up: no 5 in R6C8, no 7 in R6C9 (step 1h), no 1 in R9C9 (step 2d)
8g. 12(3) cage at R3C6 (step 2e) = {237/345}, no 8, 3 locked for C6 and N5, clean-up: no 1 in R9C7 (step 2c)
8h. 4 of {345} must be in R3C6 -> no 4 in R45C6
8i. 8 in N5 only in R6C56, locked for R6
9a. 21(5) cage (step 5d) = {12459} (only remaining combination, cannot be {12378/23457} because 3,5,8 only in R5C3) -> R5C3 = 5, R456C4 = {149}, locked for C4 and N5 -> R3C4 = 2, clean-up: no 2 in R6C8, no 4 in R6C9 (step 1h), no 6 in R89C4
9b. R3C6 = 4 -> R45C6 = 8 = [53], 5 placed for D/, R6C5 = 8, R6C6 = 7, placed for D\, R9C7 = 5 (step 2c), clean-up: no 4 in R1C8, no 4 in R6C8, no 6 in R6C9 (step 1h), no 6 in R2C8, no 4 in R9C9 (both step 2d)
9c. R7C4 = 6 (hidden single in N8) -> R78C3 = 5 = [14/32/41]
9d. 7 in N9 only in R78C9 = 10 (step 1i) = {37}, locked for C9, 3 locked for N9, R9C9 = 6, placed for D\, R2C8 = 7 (step 2d), clean-up: no 2 in R1C78
9e. R56C9 (step 1h) = 9 = [45], clean-up: no 3 in R6C8
9f. Naked pair {16} in R56C8, locked for C8 and N6 -> R5C7 = 7, R46C7 = {23}, locked for C7, clean-up: no 8 in R1C7
9g. R2C9 = 2 (hidden single in N3)
9h. 8 in R5 only in R5C12, locked for 39(7) cage at R5C1
10a. R4C47 (step 6) = R5C6 + 1, R5C6 = 3 -> R4C47 = 4 = [13], 1 placed for D\, R56C4 = [94], 4 placed for D/, R6C7 = 2
10b. R8C7 = 1 (hidden single in N9), clean-up: no 8 in R1C8
10c. 39(7) cage at R5C1 = {1356789} (cannot be {2346789} because 2,4,7 only in R7C12), no 2,4, 7 locked for R7 and N7 -> R78C9 = [37], R89C4 = [37], R7C3 = 1, placed for D/, R8C3 = 4 (step 9c), R1C9 = 8, placed for D/, R12C4 = [58], R1C8 = 3 -> R1C7 = 6, R3C7 = 9, placed for D/
and the rest is naked singles, without using the diagonals (although quicker if they are used).