Prelims
a) R12C7 = {18/27/36/45}, no 9
b) R23C4 = {39/48/57}, no 1,2,6
c) R34C7 = {89}
d) R45C5 = {29/38/47/56}, no 1
e) R4C89 = {29/38/47/56}, no 1
f) R5C67 = {19/28/37/46}, no 5
g) R5C89 = {49/58/67}, no 1,2,3
h) R6C78 = {17/26/35}, no 4,8,9
i) R8C34 = {19/28/37/46}, no 5
j) R9C45 = {49/58/67}, no 1,2,3
k) 11(3) cage at R1C4 = {128/137/146/236/245}, no 9
l) 10(3) cage at R2C9 = {127/136/145/235}, no 8,9
m) 42(7) disjoint cage at R1C1 = {3456789}, no 1,2
n) 39(8) cage at R6C9 = {12345789}, no 6
1a. 45 rule on N3 1 innie R3C7 = 9, placed for D/, R4C7 = 8, clean-up: no 3 in R2C4, no 1 in R23C7, no 2 in R4C5, no 3 in R4C89, no 3 in R5C5, no 1,2 in R5C6, no 5 in R5C89
1b. 10(3) cage at R2C9 = {127/136/145} (cannot be {235} which clashes with R12C7), 1 locked for N3
1c. R4C89 = {29/56} (cannot be {47} which clashes with R5C89), no 4,7
1d. Killer pair 6,9 in R4C89 and R5C89, locked for N6, clean-up: no 4 in R5C6, no 2 in R6C78
1e. R5C67 = {37}/[82/91] (cannot be [64] which clashes with R5C89), no 4,6
1f. 45 rule on N6 2 remaining innies R5C7 + R6C9 = 5 = [14]/{23}, clean-up: no 3 in R5C6
1g. 45 rule on N2 1 innie R1C5 = 1 outie R4C6 + 3, no 3 in R1C5, no 7 in R4C6
1h. 42(7) disjoint cage at R1C1 = {3456789}, 3 locked for N1
2a. 45 rule on N89 2 innies R78C4 = 1 outie R6C9 + 2
2b. Max R6C9 = 4 -> max R78C4 = 6, no 6,7,8,9 in R78C4, clean-up: no 1,2,3,4 in R8C3
2c. 45 rule on N9 3 outies R6C9 + R7C56 (all in same cage) = 16 = 2{59}/3{49/58}/4{39/57}, no 1,2 in R7C56
2d. 39(8) cage at R6C9 = {12345789}, 1 locked for N9
3. 45 rule on N2356 3 innies R1C5 + R4C4 + R6C9 = 17
[This may be a step which SudokuSolver isn’t programmed for.]
3a. Max R6C9 = 4 -> min R1C5 + R4C4 = 13, no 1,2,3 in R4C4
4. 45 rule on C12 3(2+1) outies R1C35 + R9C3 = 20
4a. Max R1C35 = 17 -> min R9C3 = 3
5. 45 rule on N5 3 innies R4C46 + R5C6 = 19 = {289/379/469/478/568}, no 1 in R4C6, clean-up: no 4 in R1C5 (step 1g)
5a. R4C46 + R5C6 = {289/379/469/478} (cannot be {568} = {56}8 because {56}+R5C67 = [82] clashes with R4C89), no 5, clean-up: no 8 in R1C5 (step 1g)
5b. Consider combinations for R4C46 + R5C6
R4C46 + R5C6 = {289/379/469}, 9 locked for N5
or R4C46 + R5C6 = {478} => R4C46 = {47}, R5C67 = [82], no 2 in R5C5
-> R45C5 = [38]/{47/56}, no 2,9
5c. Consider combinations for R45C5
R45C5 = [38]/{47} => R4C46 + R5C6 = {289/469} (cannot be {379/478} which clash with R45C5)
or R45C5 = {56} => R4C89 = {29} (cannot be {56} which clashes with R4C5), 2 locked for N6 => no 8 in R5C6 => R4C46 + R5C6 = {379/469}
-> R4C46 + R5C6 = {289/379/469}, 9 locked for N5
5d. R45C5 (step 5b) = [38]/{47/56}, R4C46 + R5C6 (step 5c) = {289/379/469}
Consider combinations for R1C5 + R4C6 (step 1g) = [52/63/74/96]
R1C5 + R4C6 = [52/63/96] => R45C5 = {38/47}
or R1C5 + R4C6 = [74], R4C46 + R5C6 = {469}, 6 locked for N5
-> R45C5 = [38]/{47}, no 5,6
5e. R4C46 + R5C6 (step 5c) = {289/469} (cannot be {379} which clashes with R45C5), no 3,7, clean-up: no 6 in R1C5 (step 1g), no 3 in R5C7, no 2 in R6C9 (step 1f)
5f. Killer pair 2,6 in R4C46 and R4C89, locked for R4
5g. 3 in N6 only in R6C789, locked for R6
5h. 42(7) disjoint cage at R1C1 = {3456789}, 4,6,8 locked for N1
5i. 39(8) cage at R6C9 = {12345789}, 2 locked for N9
5j. R4C46 + R5C6 = {289/469}, R45C5 = [38]/{47} -> combined cage R4C46 + R5C6 + R45C5 = {289}{47}/{469}[38], 4,8 locked for N5, 8 also locked for R5
5k. 15(4) cage at R5C4 = {1257} (cannot be {1356} = 3{156} which clashes with R6C78), locked for N5
[Cracked. A lot easier now.]
5l. R4C46 + R5C6 = {469} (only remaining combination) -> R4C46 = {46}, locked for R4 and N5, R5C6 = 9 -> R5C7 = 1, R6C9 = 4 (step 1f), R45C5 = [38], 8 placed for both diagonals, clean-up: no 5 in R1C5 (step 1g), no 5 in R4C89, no 7 in R6C78, no 5 in R9C4
5m. Naked pair {29} in R4C89, 9 locked for R4
5n. Naked pair {67} in R5C89, locked for R5
5o. Naked pair {35} in R6C78, 5 locked for R6
5p. Naked triple {127} in R6C456, locked for R6, 2 locked for N5 -> R5C4 = 5, clean-up: no 7 in R23C4
5q. R78C4 = R6C9 + 2 (step 2a), R9C6 = 4 -> R78C4 = 6 = {24}, locked for C4 and N8 -> R4C4 = 6, placed for D\, R4C6 = 4, placed for D/, clean-up: no 8 in R23C4, no 9 in R9C4, no 7,9 in R9C5
5r. R23C4 = [93], R1C5 = 7
5s. 42(7) disjoint cage at R1C1 = {3456789}, 5 locked for N1
5t. R6C9 + R7C56 (step 2c) = 16, R6C9 = 4 -> R7C56 = 12 = [93] (cannot be [57] which clashes with R9C56)
Further clean-up: no 2 in R2C7, no 7,9 in R8C3
5u. 4 in N2 only in R23C5 -> 11(3) cage at R1C4 = {146} (cannot be {245} because 2,5 only in R23C5) -> R1C4 = 1, R23C5 = {46}, 6 locked for C5 and N2, R6C4 = 7, placed for D/, R9C45 = [85], R68C5 = [21], R6C6 = 1, placed for D\
5v. 1 in R9 only in 14(3) cage at R9C1 = {149) (only possible combination, cannot be {167} which clashes with R9C6) -> R9C1 = 1, R9C23 = {49}, locked for R9 and N7
5w. R8C78 = [49] (hidden pair in N9), 9 placed for D\, R8C4 = 2 -> R8C3 = 8
5x. R9C78 = {36} (hidden pair in N9), 6 locked for R9 -> R89C6 = [67], R9C9 = 2, placed for D\, R3C3 = 7, placed for D\, R7C7 = 5, placed for D\, R6C78 = [35], R9C78 = [63], R12C7 = [27]
5y. R2C8 = 6 -> R1C89 = 11 = [83], 3,6 placed for D/
6a. R7C4 = 4 -> R567C3 = 11 = [362]
6b. R8C2 = 5 -> R78C1 = 9 = [63]
and the rest is naked singles.