Prelims
a) R1C56 = {29/38/47/56}, no 1
b) R23C5 = {19/28/37/46}, no 5
c) R2C67 = {29/38/47/56}, no 1
d) R23C8 = {49/58/67}, no 1,2,3
e) R23C9 = {59/68}
f) R78C1 = {69/78}
g) R78C2 = {49/58/67}, no 1,2,3
h) R78C5 = {15/24}
i) R8C34 = {29/38/47/56}, no 1
j) R9C45 = {19/28/37/46}, no 5
k) R1C789 = {123}
l) 21(3) cage at R3C6 = {489/579/678}, no 1,2,3
m) R9C123 = {127/136/145/235}, no 8,9
n) 12(4) cage at R2C3 = {1236/1245}, no 7,8,9
Steps resulting from Prelims
1a. Naked triple {123} in R1C789, locked for R1 and N3, clean-up: no 8,9 in R1C56 + R2C6
1b. R23C8 = {49/67} (cannot be {58} which clashes with R23C9), no 5,8
1c. Killer pair 6,9 in R23C8 and R23C9, locked for N3, clean-up: no 2,5 in R2C6
1d. R78C2 = {49/58} (cannot be {67} which clashes with R78C1), no 6,7
1e. Killer pair 8,9 in R78C1 and R78C1, locked for N7, clean-up: no 2,3 in R8C4
1f. R23C5 = {19/28/37} (cannot be {46} which clashes with R1C56, no 4,6
2a. 45 rule on R1 2 outies R2C24 = 4 = {13}, locked for R2, clean-up: no 8 in R2C7, no 7,9 in R3C5
2b. 45 rule on N3 2 innies R23C7 = 12 = [48/57/75], no 4 in R3C7
2c. R23C7 = 12 -> R34C7 cannot total 12 (CCC) -> no 9 in R3C6
2d. Hidden killer triple 1,2,3 in R2C4, R23C5 and R3C4 for N2, R2C4 = {13}, R23C5 must contain one of 1,2,3 -> R3C4 = {123}
2e. 45 rule on N7 2 innies R78C3 = 7 = [16]/{25/34}, no 6,7 in R7C3, no 7 in R8C3, clean-up: no 4 in R8C4
2f. Max R7C3 = 5 -> min R6C3 + R7C4 = 11, no 1 in R6C3 + R7C4
2g. R78C3 = 7 -> R67C3 cannot total 7 (CCC) -> no 9 in R7C4
2h. 45 rule on R9 2 outies R8C68 = 8 = {17/26/35}, no 4,8,9
3a. 45 rule on C1234 2 innies R69C4 = 10 = {19/28/37/46}, no 5
3b. 45 rule on C6789 2 innies R14C6 = 11 = {47/56}
3c. Combined half-cage R14C6 + R2C6 = {47}6/{56}4/{56}7, 6 locked for C6, clean-up: no 2 in R8C8 (step 2h)
4. R1C56 = {47/56}, R2C67 = {47}/[65] -> combined cage R1C56 + R2C67 = {47}[65]/{56}{47}, CPE no 7 in R2C5, clean-up: no 3 in R3C5
4a. 3 in N2 only in R23C4, locked for C4, clean-up: no 7 in R69C4 (step 3a), no 3,7 in R9C5
4b. Killer pair 1,2 in R23C5 and R78C5, locked for C5, clean-up: no 8,9 in R9C4, no 1,2 in R6C4 (step 3a)
4c. 3 in C5 only in R456C5, locked for N5
[Step 5 probably isn’t needed, but I saw it before I saw step 6.]
5. 45 rule on C1234 1 outie R9C5 = 1 innie R6C4, 45 rule on C6789 1 outie R1C5 = 1 innie R4C6 -> 29(5) cage at R4C5 must contain the same numbers as R14569C5
5a. R14569C5 = 29(5) = {34679/35678} (cannot be {34589} which clashes with R78C5)
6. R23C5 = {28}[91], R78C5 = {15/24} -> combined cage R2378C5 = {28}{15}/[91]{24} -> R9C45 = {46} (cannot be [19/28] which clash with combined cage), locked for R9 and N8, clean-up: no 8,9 in R6C4 (step 3b), no 2 in R78C5, no 5 in R8C3, no 2 in R7C3 (step 2e)
[Cracked. The rest is straightforward.]
6a. Naked pair {15} in R78C5, locked for C5 and N8, clean-up: no 6 in R1C6, no 9 in R2C5, no 5 in R4C6 (step 3b), no 6 in R8C3, no 1 in R7C3 (step 2e), no 3,7 in R8C8 (step 2h)
6b. Naked pair {28} in R23C5, locked for C5 and N2
6c. Naked pair {13} in R23C4, locked for C4
6d. Naked pair {46} in R69C4, locked for C4
6e. R1C4 = 9 (hidden single in N2), clean-up: no 2 in R8C3
6f. 8 in R1 only in R1C123, locked for N1
7. 1 in N7 only in 10(3) cage at R9C1 = {127}, locked for R9 and N7, clean-up: no 8 in R78C1
7a. Naked pair {69} in R78C1, locked for C1 and N7, clean-up: no 4 in R78C2
7b. Naked pair {58} in R78C2, locked for C2 and N7
7c. Naked pair {34} in R78C3, locked for C3
7d. 12(4) cage at R2C3 = {1236} (only remaining combination) -> R3C4 = 3, R2C24 = [31], 3 placed for D\
7e. Naked triple {126} in R234C3, locked for C3 -> R9C3 = 7
7f. 9 in C3 only in R56C3, locked for N4
7g. R3C2 = 9 (hidden single in N1), clean-up: no 4 in R2C8, no 5 in R2C9
7h. R3C2 = 9 -> R23C1 + R4C2 = 11 = {146/245}, no 7, CPE no 4 in R456C1
7i. 6 of {146} must be in R4C2 -> no 1 in R4C2
7j. 7 in N1 only in R1C12, locked for R1, clean-up: no 4 in R1C56, no 4,7 in R4C6 (step 3b)
7k. R1C56 = [65], R1C3 = 8, R9C45 = [64], R4C6 = 6, R6C4 = 4, both placed for D/ -> R7C3 = 3, placed for D/, R8C3 = 4 -> R8C4 = 7
7l. Naked quad {3589} in R9C6789, locked for 33(6) cage at R8C6 -> R8C6 = 2 -> R8C8 = 6 (step 2h), placed for D\, R78C1 = [69], R7C4 = 8, R7C3 = 3 -> R6C3 = 5 (cage sum), R7C2 = 5, R8C2 = 8, placed for D/, R79C6 = [93]
7m. R45C4 = {25}, R5C3 = 9 -> R5C2 = 6 (cage sum)
7n. R5C5 = 7, placed for both diagonals, R1C1 = 4, placed for D\, R1C2 = 7
7o. R2C8 = 9 -> R3C8 = 4
7p. R3C67 = [75] -> R4C7 = 9 (cage sum), R2C67 = [47], R9C789 = [859]
7q. R7C5 = 1 -> R7C7 = 2, placed for D\
7r. R6C7 = 6 (hidden single in C7), R7C67 = [92] -> R8C7 = 1 (cage sum), R1C7 = 3
7s. R56C6 = {18}, R5C7 = 4 -> R5C8 = 3 (cage sum)
7t. R7C89 = [74], R8C9 = 3 -> R6C8 = 2 (cage sum)
7u. R1C8 = 1 -> R1C9 = 2, placed for D/
and the rest is naked singles, without using the diagonals.