Prelims
a) R1C12 = {01}
b) R12C8 = {49/58/67}, no 0,1,2,3
c) R12C9 = {29/38/47/56}, no 0,1
d) R2C12 = {06/15/24}, no 3,7,8,9
e) R34C5 = {05/14/23}, no 6,7,8,9
f) R34C6 = {07/16/25/34}, no 8,9
g) R34C7 = {01}
h) R6C34 = {04/13}
i) R67C5 = {49/58/67}, no 0,1,2,3
j) R7C34 = {07/16/25/34}, no 8,9
k) R89C1 = {79}
l) R89C2 = {05/14/23}, no 6,7,8,9
m) R89C8 = {06/15/24}, no 3,7,8,9
n) R89C9 = {06/15/24}, no 3,7,8,9
o) 25(4) cage at R3C1 = {1789/2689/3589/3679/4579/4678}, no 0
1a. Naked pair {01} in R1C12, locked for R1 and N1, clean-up: no 5,6 in R2C12
1b. Naked pair {24} in R2C12, locked for R2 and N1, clean-up: no 9 in R1C8, no 7,9 in R1C9
1c. Naked pair {01} in R34C7, locked for C7
1d. Naked pair {79} in R89C1, locked for C1 and N7, clean-up: no 0 in R7C4
1e. 0 in N3 only in R3C789, locked for R3, clean-up: no 5 in R4C5, no 7 in R4C6
2a. 45 rule on R5 total = 44 -> no 1 in R5
2b. Using the property of Rainbow SS puzzles which HATMAN states, R5C5 = 0, which is paired with 1, the missing number in R5, so no 1 in C5 and N5, 1 in every other row, column and nonet, clean-up: no 4,5 in R3C5, no 6,7 in R3C6, no 4 in R4C5, no 3,4 in R6C3
2c. R5C5 = 0 -> R5C46 = 17 = {89}, locked for R5 and N5; 8 and 9 must be paired, clean-up: no 4,5 in R7C5
2d. Naked pair {23} in R34C5, locked for C5
2e. 10(3) cage at R5C1 = {235} (only remaining combination), locked for R5 and N4
2f. Naked triple {467} in 17(3) cage at R5C7, locked for N6
3a. R1C12 = {01} correspond with R9C89 and 0,1 paired -> R9C89 = {01}, locked for R9 and N9, clean-up: no 4,5 in R8C2
3b. R9C89 = {01} -> R8C89 = {56}, locked for R8 and N9
3c. R2C12 = {24} correspond with R8C89 = {56} -> 2,4 paired with 5,6 -> 3 and 7 must be paired
3d. R34C5 = {23} correspond with R67C5 -> R67C5 = {67}, locked for C5, 2 paired with 6 -> 4 paired with 5
3e. R34C7 correspond with R67C3 -> R67C3 = {01}, locked for C3, R7C4 = {67}
3f. Naked pair {67} in R7C45, locked for R7 and N8
3g. R12C9 = [29/38/47/83] (cannot be {56} which clashes with R8C9), no 5,6
3h. 0 in R4 only in R4C789, locked for N6
3i. R2C46 = {01} (hidden pair in R2), 1 locked for N2, clean-up: no 6 in R4C6
3j. 12(4) cage at R8C3 = {0246/0345/1236/1245} (cannot be {0129/0138} because 0,1 only in R8C4), no 8,9
3k. 0,1 only in R8C4 -> R8C4 = {01}
3l. R4C6 corresponds to R6C4, no 7 in either -> R4C6 = 5, R6C4 = 4, R3C6 = 2, R34C5 = [32], R6C3 = 0, R7C34 = [16], R67C5 = [67], clean-up: no 4 in R9C2
3m. R12C9 correspond with R89C1, R89C1 = {79} -> R12C9 = {38}, locked for C9 and N3, clean-up: no 5 in R12C8
3n. R12C7 correspond with R89C3, no 8,9 in R89C3 -> no 9 in R12C7
3o. R2C4 corresponds with R8C6, R2C4 = {01} -> R8C6 = {01}
3p. Naked pair {01) in R8C46, 0 locked for R8 and N8, clean-up: no 5 in R9C2
3q. Naked pair {23} in R89C2, locked for C2 and N7 -> R2C12 = [24], R8C3 = 4
3r. 10(3) cage at R5C1 = [352] -> 17(3) cage at R5C7 = [647], clean-up: no 9 in R2C8
3s. Naked pair {67} in R12C8, locked for N3, 6 locked for C8 -> R2C7 = 5, R8C8 = 5, R9C8 = 1, R89C9 = [60]
3t. 12(4) cage at R8C3 = {0246/0345/1236/1245}
3u. 2,3 only in R9C4 -> R9C4 = {23}
3v. R9C4 = {23} corresponds with R1C6 -> R1C6 = {67}
3w. Naked pair {67} in R1C68, locked for R1
3x. Naked pair {89} in R28C5, locked for C5
3y. Naked pair {23} in R9C24, locked for R9
4a. R4C2 corresponds with R6C8, no 0,1 in R6C8 -> no 1 in R4C2
4b. 25(4) cage at R3C1 = {4579/4678} (cannot be {1789} which clashes with R6C1) -> R4C1 = 4, 7 locked for C2
4c. R4C1 corresponds with R6C9 -> R6C9 = 5
4d. 20(4) cage at R1C3 = {0389/0569/0578/1379/1568}
4e. Consider placements for R9C3 = {56}
R9C3 = 5 => R19C5 = [54] => 20(4) cage = {0389/1379}
or R9C3 = 6 => R8C3 => R89C4 = 2 = [02] => 20(4) cage = {1379}
-> 20(4) cage = {0389/1379}, no 5,6
4f. Naked pair {89} in R1C4 + R2C5, locked for N2
4g. R1C4 = {89} corresponds with R9C6 -> R9C6 = {89}
4h. Naked pair {89} in R8C5 + R9C6, locked for N8
4i. Consider placements for R7C6 = {34}
R7C6 = 3 => R9C4 = 2
or R7C6 = 4, R9C5 = 5, R9C3 = 6, R8C3 = 4 => R89C4 = 2 = [02]
-> R9C4 = 2, R89C2 = [23]
4j. R1C6 corresponds with R9C4, R9C4 = 2 -> R1C6 = 6, R12C8 = [76]
4k. R3C8 corresponds with R7C2, R4C9 corresponds with R6C1
4l. Consider combinations for 25(4) cage = {4579/4678}
25(4) cage = {4579} => R3C8 = 0 and/or R4C9 = 1 => R34C7 = [10]
or 25(4) cage = {4678} => R6C1 = 1 and/or R7C2 = 0 => R3C8 = 0 and/or R4C9 = 1 => R34C7 = [10]
-> R34C7 = [10]
4m. R3C8 = 0 (hidden single in R3) -> R7C2 = 0, R1C12 = [01], R6C1 = 1 (hidden single in R6), R4C9 = 1 (hidden single in R4)
4n. R4C8 corresponds with R6C2 = {89} -> R4C8 = {89}
4o. R3C9 corresponds with R7C1
4p. Consider placements for R7C1 = {58}
R7C1 = 5 => 25(4) cage = {4678}
or R7C1 = 8, R3C9 = 9 => 25(4) cage = {4678} (cannot be {4579} = [5749] which clashes with R3C4)
-> 25(4) cage = {4678}, no 5,9
[Took me a while to spot this key step]
5a. Consider permutations for R3C4 = {57}
R3C4 = 5 => R19C5 = [45], R9C3 = 6
or R3C4 = 7, no 5 in C4 => all other columns must contain 5, R7C1 = 5 (then hidden single in C1) => R9C3 = 6
-> R9C3 = 6, R8C3 = 4, R9C4 = 2 -> R8C4 = 0 (cage sum)
[Cracked, straightforward from here]
5b. R2C4 = 1 -> 20(4) cage at R1C3 (step 4d) = {1379} -> R1C34 = [39], R2C3 = 7
5c. R1C3 = 3 corresponds with R9C7 -> R9C7 = 7
5d. R2C3 = 7 corresponds with R8C7 -> R8C7 = 3
5e. Naked pair {68} in R3C12, locked for 25(4) cage at R3C1, 8 locked for R3
5f, R4C2 = 7 corresponds with R6C8 -> R6C8 = 3
5g. All other columns contain 7 -> no 7 in C4 -> R3C4 = 5, R3C3 = 9
5h. R3C4 = 5 corresponds with R7C6 -> R7C6 = 4, R9C5 = 5
5i. R1C57 = [42], R4C38 = [89], R6C27 = [98], R7C789 = [982]
5j. R7C9 = 2 corresponds with R3C1 -> R3C1 = 6
and the rest is naked singles.