Prelims
a) R1C78 = {39/48/57}, no 1,2,6
b) 11(2) cage at R1C9 = {29/38/47/56}, no 1
c) R2C23 = {17/26/35}, no 4,8,9
d) R23C4 = {29/38/47/56}, no 1
e) R2C67 = {29/38/47/56}, no 1
f) R34C3 = {39/48/57}, no 1,2,6
g) R45C1 = {17/26/35}, no 4,8,9
h) R5C34 = {69/78}
i) R6C23 = {29/38/47/56}, no 1
j) R6C78 = {69/78}
k) R9C23 = {17/26/35}, no 4,8,9
l) 8(3) disjoint cage at R3C7 = {125/134}
m) 19(3) cage at R4C4 = {289/379/469/478/568}, no 1
1a. 45 rule on N1 2 innies R3C23 = 14 = {59}/[68], clean-up: no 5,8,9 in R4C3
1b. 45 rule on C123 2 innies R58C3 = 13 = {67}/[85/94] -> R8C3 = {4567}
1c. 45 rule on N7 1 outie R6C1 = 1 innie R8C3 -> R6C1 = {4567}
1d. 45 rule on N78 2 outies R6C15 = 9 = {45}/[63/72], R6C5 = {2345}
1e. 45 rule on R6 using R6C15 3 innies R6C469 = 10 = {127/136/145/235}, no 8,9
1f. Hidden killer pair 8,9 in R6C23 and R6C78 for R6, R6C78 contains one of 8,9 -> R6C23 must contain one of 8,9 = {29/38}
1g. R6C469 = {127/136/145} (cannot be {235} which clashes with R6C23, alternatively must contain 1 for R6)
2a. 45 rule on D/ 2 outies R4C4 + R6C6 = 10 = [64/73/82/91], R4C4 = {6789}, R6C6 = {1234}
2b. R4C4 + R6C6 = [64/82/91] (cannot be [73] because R5C5 + R6C4 = 12 = [84] clashes with 8(3) disjoint cage at R3C7 = {134}), no 7 in R4C4, no 3 in R6C6
2c. 17(3) cage at R7C3 = {179/269/278/368/458} (cannot be {359} which clashes with 8(3) disjoint cage, cannot be {467} which clashes with R8C3 + R9C23, killer ALS block)
2d. 17(3) cage at R7C3 = {179/269/278/368} (cannot be {458} because 11(2) cage at R1C9 + 19(3) cage at R4C4 cannot be {29}+6{67}), no 4,5
2e. 19(3) cage at R4C4 = {289/379/469/478/568}
2f. Consider placement for 1 on D/
1 in R3C7 + R4C6, locked for 8(3) disjoint cage => R4C4 + R6C6 = [64/82] => 19(3) cage = {478/568} (cannot be {289/469} = [892/694] which clash with R4C4 + R6C6, CCC)
or 1 in 17(3) cage = {179}, 7,9 locked for D/ => 19(3) cage = {289/469/568}
-> 19(3) cage = {289/469/478/568}, no 3
2g. {289/469} must be [982/946/964], no 2,9 in R5C5
2h. {478} must be [847] (cannot be [874] because R6C46 cannot be [42], step 1g), no 7 in R5C5
2i. {568} must be [685] (cannot be 8{65} which clashes with 8(3) disjoint cage = {15}2), no 5 in R5C5
2j. 9 on D/ only in 11(2) cage at R1C9 = {29}
or 17(3) cage = {179/269}
-> 17(3) cage = {179/269/368} (cannot be {278}, locking-out cages)
2k. 45 rule on N1478 2 outies R5C4 + R6C5 = 11 = [65/83/92] (cannot be [74] which clash with 19(3) cage = {469/478}, while R5C4 = 6 for 19(3) cage = {289} and R5C4 = 9 for 19(3) cage = {568}), no 7 in R5C4, no 4 in R6C5, clean-up: no 8 in R5C3, no 5 in R6C1 (step 1d), no 5 in R8C3 (step 1b)
2l. 19(3) cage = {469} must be [964] (cannot be [946] which clashes with R5C4 + R6C15 = [863], step 1d), no 6 in R6C4
2m. Combined cage 19(3) cage + R5C4 + R6C3 = {289}[65]/{469}[83]/{478}[65](because of R4C4 + R6C6)/{568}[92] -> 8 in R4C4 + R5C45, locked for N5
2n. Combined cage R34C3 + R58C3 = [57][94]/[84]{67}/[93]{67}, 7 locked for C3, clean-up: no 1 in R2C2, no 1 in R9C2
2o. R6C469 (step 1g) = {127/145} (cannot be {136} because only 2,4,5,7 in R6C4), no 3,6
3a. 45 rule on N2 1 innie R2C6 = 1 outie R4C5 -> no 8 in R2C6, no 1 in R4C5, clean-up: no 3 in R2C7
3b. 45 rule on N69 1 outie R5C6 = 1 innie R4C9 + 2, no 6,8,9 in R4C9, no 1,2 in R5C6
3c. 1 in N5 only in R46C6, locked for C6 and 8(3) disjoint cage, no 1 in R3C7
4a. R3C23 (step 1a) = {59}/[68], 19(3) cage at R4C4 (step 2f) = {289/469/478/568}, R4C4 + R6C6 (step 2b) = [64/82/91]
4b. Consider combinations for 8(3) disjoint cage at R2C7 = {125/134}
8(3) disjoint cage = 5{12} => R3C23 = [68], 8 placed for D\ => 19(3) cage = {469}
or 8(3) disjoint cage = [251] => R4C4 = 9 => 19(3) cage = {289/469}
or 8(3) disjoint cage = {134}, 4 locked for N5 using D/ => 19(3) cage = {289/568}
-> 19(3) cage = {289/469/568}, no 7
4c. 7 in N5 only in R4C5 + R5C6, CPE no 7 in R3C6
4d. 45 rule for N5 using R5C4 + R6C5 = 11 (step 2k), 4 remaining innies R4C56 + R56C6 = 15 containing 1,7 for N5 = {1257/1347}, no 6,9, clean-up: no 6,9 in R2C6 (step 3a), no 2,5 in R2C7, no 4,7 in R4C9 (step 3b)
4e. R2C6 = R4C5 (step 3a) -> R2456C6 = {1257/1347}, 7 locked for C6
4f. 9 in N5 only in R45C4, locked for C4, clean-up: no 2 in R23C4
4g. 19(3) cage = {289/469/568} = [982/964/685] -> R4C4 = {69}, R5C5 = {68}, clean-up: no 2 in R6C6 (step 2b)
4h. Killer pair 6,8 in R5C34 and R5C5, locked for R5, clean-up: no 2 in R4C1
4i. 17(3) cage at R7C3 (step 2j) = {179/269} (cannot be {368} which clashes with R5C5 on D/), no 3,8, 9 locked for N7 and D/, clean-up: no 2 in 11(2) cage at R1C9
5a. 8(3) disjoint cage at R2C7 = [314]/{25}1/{34}1, 1 on D/ only in R4C6 or 17(3) cage at R7C3 = {179}, 7 on D/ only in 11(2) cage at R1C9 = {47} or 17(3) cage at R7C3 = {179}
5b. Consider combinations for R1C78 = {39/48/57}
R1C78 = {39}, 3 locked for N3 => 11(2) cage at R1C9 = {47/56}, killer pair 4,5 in 11(2) cage and 8(3) disjoint cage => R6C4 = 2, placed for D/
or R1C78 = {48/57} => 11(2) cage at R1C9 = {38/56}, no 7
-> 17(3) cage at R7C3 (step 2j) = {179}, 1,7 locked for N7 and D/, clean-up: no 4 in 11(2) cage at R1C9, no 6 in R5C3 (step 1b), no 9 in R5C4, no 7 in R6C1 (step 1c), no 2 in R6C5 (step 1d)
5c. R4C4 + R6C6 = [91] (hidden pair in N5), placed for D\, clean-up: no 5 in R3C2 (step 1a), no 3 in R4C3
5d. R4C4 = 9 -> R5C5 + R6C4 = 10 = [64/82]
5e. 7 in C3 only in R45C3, locked for N4, clean-up: no 1 in R45C1
5f. 1 in N4 only in R45C2, locked for C2
5g. 15(3) cage at R3C2 = [681]/9{15}, no 2,3,4, no 6 in R4C2, no 9 in R5C2
5h. 6 in N4 only in R46C1, locked for C1
5i. R6C469 (step 2o) = {127/145} -> R6C9 = {57}
5j. 7 in R6 only in R6C789, locked for N6
5k. 12(3) cage at R7C7 = {138/147/156/237/246/345} (cannot be {129} because 1,9 only in R7C8), no 9
5l. 1 of {138} must be in R7C8 -> no 8 in R7C8
5m. 9 in N9 only in R7C9 + R8C79 + R9C78, locked for 45(9) cage at R4C8, no 9 in R5C9
6a. 45 rule on N23 3 remaining outies R4C569 = 12 = {147/237/345}
6b. 7 of {147/237} only in R4C5 -> no 2 in R4C5, clean-up: no 2 in R2C6 (step 3a), no 9 in R2C7
6c. 2 in N5 only in R4C6 + R6C4, locked for D/
6d. 1,2 in N3 only in R2C9 + R3C89, locked for 16(4) cage at R2C9, no 1,2 in R4C9, clean-up: no 3,4 in R5C6 (step 3b)
6e. Combined cage R1C78 + 11(2) cage at R1C9 = {39}{56}/{48}{56}/{57}{38}, 5 locked for N3
6f. 8(3) disjoint cage at R2C7 = {34}1 (only remaining combination), 3,4 locked for D/, clean-up: no 8 in 11(2) cage
6g. Naked pair {34} in R3C7 + R4C6, CPE no 3,4 in R3C6 + R4C7
6h. Naked pair {56} in 11(2) cage, locked for N3 and D/, R5C5 = 8, placed for D\, clean-up: no 7 in R1C78, no 5 in R2C6, no 5 in R4C5 (step 3a)
6i. R4C569 = 12 = {345} -> R4C9 = 5, R4C56 = {34}, locked for R4, 3 locked for N5, R34C3 = [57], 5 placed for D\, R3C2 = 9 (step 1a), R4C1 = 6 -> R5C1 = 2, R5C34 = [96], naked pair {38} in R6C23, 8 locked for R6 and N4, R6C9 = 7, R45C2 = [15], R6C5 = 5, R5C6 = 7, R6C1 = 4 -> R8C3 = 4 (step 1c), R7C3 = 1, R8C2 = 7, R9C1 = 9, clean-up: no 3 in R2C23, no 6 in R2C4, no 4 in R2C7, no 3 in R9C23
6j. R1C2 = 4 (hidden single in C2), clean-up: no 8 in R1C78
6k. Naked pair {39} in R1C78, locked for R1 and N3 -> R3C7 = 4 -> R4C45 = [43], R2C6 = 4, R2C7 = 7, R1C9 = 6, R2C8 = 5, clean-up: no 7 in R3C4
6l. R4C5 = 4 -> R3C56 = 13 = [76]
6m. Naked pair {38} in R23C4, locked for C4 and N2
6n. R7C8 = 7 (hidden single in N9) -> R7C7 + R8C8 = 5 = {23}, locked for N9, 2 placed for D\, R2C23 = [62], R9C23 = [26]
6o. R4C8 + R5C9 = [23] (hidden singles in 45(9) cage at R4C8) -> R8C8 = 3, R7C7 = 2, R89C7 = [65] (hidden singles in 45(9) cage at R4C8), R9C6 = 8
6p. R6C5 = 5, R7C46 = [49] -> R78C5 = 8 = [62]
and the rest is naked singles, without using the diagonals.