Prelims
a) R1C45 = {59/68}
b) R2C23 = {19/28/37/46}, no 5
c) R2C45 = {12}
d) R34C9 = {13}
e) R45C2 = {29/38/47/56}, no 1
f) R56C8 = {89}
g) R56C9 = {29/38/47/56}, no 1
h) R78C8 = {14/23}
i) R8C56 = {15/24}
j) 43(8) cage at R2C6 = {13456789}, no 2
1a. Naked pair {12} in R2C45, locked for R2 and N2, no 8,9 in R2C23
1b. Naked pair {13} in R34C9, locked for C9, no 8 in R56C9
1c. Naked pair {89} in R56C8, locked for C8 and N6, clean-up: no 2 in R56C9
1d. 2 in N6 only in R56C7, locked for C7
1e. 15(3) cage at R5C7 contains 2 = {249/258/267), no 1,3
1f. 8,9 on {249/258} only in R7C7 -> no 4,5 in R7C7
1g. 45 rule on N3 2(1+1) outies R1C6 + R4C9 = 6 = [33/51]
1h. 45 rule on R12 2 outies R2C19 = 17 = {89}, locked for R2
1i. 19(4) cage at R1C1 cannot contain both on 8,9 -> no 8,9 in R1C123
1j. Hidden killer pair 8,9 in R1C45 and R1C789 for R1, R1C45 contains one of 4,5 -> R1C789 must contain one of 8,9 -> 29(5) cage at R1C6 must contain both of 8,9 in R1C789 + R2C9, locked for N3
1k. 29(5) cage = {23789/34589} (cannot be {14789/24689} because R1C6 only contains 3,5, cannot be {15689} which clashes with R1C45), no 1,6, 3 locked for R1
1l. 6 in N3 only in 18(4) cage at R2C7 = {1467/2367/3456}
1m. Killer pair 1,3 in 18(4) cage and R3C9, locked for N3
1n. R1C6 = 3 (hidden single in R1) -> R4C9 = 3, R3C9 = 1, clean-up: no 8 in R5C2
1o. Min R3C45 = 9 -> max R3C3 = 7
1p. 43(8) cage at R2C6 = {13456789} -> R5C5 = 3, clean-up: no 8 in R4C2
1q. 1 in R1 only in R1C123 -> 19(4) cage at R1C1 = {1279/1459/1468} (cannot be {1567} which clashes with R2C23 and doesn’t contain one of 8,9)
1r. Killer pair 4,7 in 19(3) cage and R2C23, locked for N1
1s. 8,9 in N1 only in R2C1 + R3C12, CPE no 8,9 in R45C1
1t. 45 rule on N9 3 innies R789C7 = 20 = {389/479/569/578}, no 1
1u. R4C7 = 1 (hidden single in C7)
2a. 45 rule on N9 1 innie R7C7 = 2 outies R9C56 + 2
2b. Max R9C56 = 7, no 7,8,9 in R9C56
2c. R9C56 cannot total 4 -> no 6 in R7C7
2d. R9C56 cannot total 5 = {14} which clashes with R8C56 -> no 7 in R7C7
2e. 15(3) cage at R5C7 (step 1e) = {249/258) (cannot be {267} because R7C7 only contains 8,9), no 6,7
2f. Killer pair 4,5 in R56C7 and R56C9, locked for N6
2g. R789C7 (step 1t) = {389/569} (cannot be {479} = 9{47} which clashes with 15(3) cage = {24}9, cannot be {578} = 8{57} which clashes with 15(3) cage = {25}8)
2h. R789C7 = {389} (only remaining combination, cannot be {569} = 9{56} because then R9C56 cannot total 7), locked for C7 and N9, clean-up: no 2 in R78C8
2i. Naked pair {14} in R78C8, locked for N9, 4 locked for C8
2j. R12C9 = {89} (hidden pair in C9)
2k. 4 in C9 only in R56C9 = {47}, locked for N6, 7 locked for C9 -> R4C8 = 6, R9C8 = 7 (hidden single in N9), clean-up: no 5 in R5C2
2l. Naked pair {25} in R56C7, 5 locked for C7, R7C7 = 8 (cage sum)
2m. R89C7 = {39} = 12 -> R9C56 = 6 = {15/24}, no 6
2n. Naked quad {1245} in R89C56, locked for N8
2o. 43(8) cage at R2C6 = {13456789}, CPE no 4,5,7,8,9 in R6C6
3a. 8 in N8 only in R89C4, locked for C4, clean-up: no 6 in R1C5
3b. 30(6) cage at R6C6 must contain 8 = {123789/135678/234678} (cannot be {124689} because 1,2,4 only in R6C6 + R9C3, cannot be {134589} because 4,5 only in R9C3)
3c. 1,2,4,5 only in R6C6 + R9C3 -> R6C6 = {12}, R9C3 = {1245}
3d. R7C6 = 6 (hidden single in C6)
3e. 30(6) cage = {135678/234678}, no 9 -> R7C5 = 7, R9C3 = {45}, R7C4 = 9 (hidden single in N8), clean-up: no 5 in R1C5
3f. Killer pair 4,5 in R9C3 and R9C56, locked for R9
3g. Hidden killer pair 1,2 in R6C6 and R89C6 for C6, R6C6 = {12} -> R89C6 must contain one of 1,2 and must contain one of 4,5
3h. Hidden killer pair 4,5 in R2345C6 and R89C6 for C6, R89C6 contains one of 4,5 -> R2345C6 must contain one of 4,5 -> R4C5 = {45} (only remaining uncompleted cell in 43(8) cage at R2C6)
3i. R136C5 = {689} (hidden triple in C6), 9 locked for N2
3j. 45 rule on N7 3 innies R7C13 + R9C3 = 12 = {345} (only possible combination), locked for N7
3k. Min R7C1 = 3 -> max R6C12 = 9, no 9
3l. R6C8 = 9 (hidden single in R6C) -> R5C8 = 8
3m. Killer pair 1,4 in R8C56 and R8C8, locked for R8
3n. 16(3) cage at R3C3 = {259/268/349/367} (cannot be {358} which clashes with R1C45, cannot be {457} because R3C5 only contains 6,8,9)
3o. 2,3 only in R3C3 -> R3C3 = {23}
3p. 45 rule on N1 3 innies R3C123 = 16 = {259/268/358}
3q. R3C3 = {23} -> no 2,3 in R3C12
3r. R3C38 = {23} (hidden pair in R3)
4a. 3 in R6 only in R6C123, 3 in R7 only in R7C13 -> 12(3) cage at R6C1 and 32(6) cage at R5C4 must both contain 3
4b. 12(3) cage at R6C1 = {138/237/345}, no 6
4c. 6 in R6 only in R6C345, locked for 32(6) cage, no 6 in R5C4
4d. 6 in N4 only in R5C123, locked for N4
4e. 32(6) cage must contain 3,6,9 = {135689/234689/235679}, 3 locked for C3
4f. R3C3 = 2 -> R23C8 = [53], R2C2 = 3 (hidden single in R2) -> R2C3 = 7, R1C78 = [72] (hidden pair in R1), R2C6 = 4, R4C5 = 5, clean-up: no 6 in R5C2
4g. R3C3 = 2 -> R3C45 = 14 = [59/68]
4h. R3C6 = 7 (hidden single in R3) -> R45C6 = [89], R6C5 = 6, clean-up: no 2 in R4C2
4i. 17(3) cage at R4C3 = {179/269/467} -> R4C4 = {27}, R5C3 = {16}
4j. 4 in C4 only in R56C4, locked for 32(6) cage, no 4 in R67C3
4k. 32(6) cage = {234689} (only remaining combination) -> R56C4 = {24}, 2 locked for C4 and N5, R67C3 = [83], R4C4 = 7, R6C6 = 1
4l. Naked pair {49} in R4C23, 4 locked for N4 -> R4C1 = 2, R45C2 = [47], R4C3 = 9, R4C4 = 7 -> R5C3 = 1 (cage sum)
4m. R6C2 = 5, R45C1 = [26] = 8 -> R3C12 = 14 = [59]
and the rest is naked singles.
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