Prelims
a) R1C67 = {29/38/47/56}, no 1
b) R23C3 = {89}
c) R34C1 = {17/26/35}, no 4,8,9
d) R4C56 = {29/38/47/56}, no 1
e) R5C56 = {17/26/35}, no 4,8,9
f) R7C89 = {59/68}
g) R89C9 = {19/28/37/46}, no 5
h) 11(3) cage at R6C2 = {128/137/146/236/245}, no 9
i) 43(8) cage at R8C1 = {13456789}, no 2
1a. Naked pair {89} in R23C3, locked for C3 and N1
1b. 45 rule on C1234 1 outie R9C5 = 3, clean-up: no 8 in R4C6, no 5 in R5C6, no 7 in R8C9
1c. 45 rule on R1234 2 outies R5C23 = 12 = [57/75/84/93]
1d. 45 rule on R1234 3 innies R234C2 = 9 = {126/135/234}, no 7,8,9
1e. 45 rule on R6789 2 outies R5C14 = 7 = {16/25/34}, no 7,8,9
1f. 45 rule on N36 2 outies R12C6 = 13 = {49/58/67}, no 1,2,3, clean-up: no 8,9 in R1C7
1g. 2,3 in N7 only in R7C123, locked for R7
1h. 45 rule on N6 2 outies R3C79 = 1 innie R4C7 + 10
1i. Min R3C79 = 11, no 1 in R3C79
1j. Max R3C79 = 17 -> max R4C7 = 7
1k. 18(3) cage at R5C1 = {189/279/369/378/459/468} (cannot be {567} which clashes with R34C1)
1l. Max R56C1 = 15 -> min R7C1 = 3
1m. Max R57C1 = 15 -> min R6C1 = 3
1n. 2 in N7 only in R7C23 -> 11(3) cage at R6C2 = {128/236/245}, no 7, no 2 in R6C2
2a. R234C2 (step 1d) = {126/135/234}, R5C23 (step 1c) = [57/75/84/93]
[Here I first found a forcing chain based on the placement for 8 in N4 followed by one for 3 in N7 but better is going directly to …
2b. Consider placement for 3 in N7
R7C1 = 3 => R56C1 = 15 = [69] => R5C23 = [84] (cannot be {57} which clashes with R5C56 = [17/53/71] when R5C1 = 6)
or 3 in R7C23 = {23} => R6C2 = 6 (cage sum), R234C2 = {135} (cannot be {234} which clashes with R7C2), 3,5 locked for 21(5) cage at R2C2 => R5C23 = [84]
-> R5C23 = [84], also 6 in R5C1 + R6C2, locked for N4, clean-up: no 2 in R3C1, no 3 in R5C14 (step 1e)
2c. R6C1 = 9 (hidden single in N4) -> R57C1 = 9 = [18/27/54/63], no 5,6 in R7C1
2d. 9 in R5 only in 18(3) cage at R5C7 = {279/369}, no 1,5, 9 locked for N6
2e. Killer pair 2,6 in R5C14 and 18(3) cage, locked for R5
2f. 11(3) cage at R6C2 (step 1n) = {236/245}, no 1
2g. 5 of {245} must be in R6C2 -> no 5 in R7C23
[At this stage I ought to have spotted Ed’s step 5, eliminating 3 from R6C2.]
2h. R234C2 = {126/135}, 1 locked for C2
2i. 1,5,9 in N7 only in R89C123, locked for 43(8) cage at R7C1, no 1,5,9 in R9C4
2j. 12(3) cage at R6C7 = {138/147/156/345} (cannot be {237/246} which clash with 18(3) cage at R5C7), no 2
2k. 45 rule on N6 3 innies R4C789 = 15 = {168/258/348/456} (cannot be {267} which clashes with 18(3) cage, cannot be {357} which clashes with 12(3) cage), no 7
2l. Combined half cage 9(3) cage + R6C2 = {126}3/{126}5/{135}6, 6 locked for C2
2m. 4 in N1 only in 13(3) cage at R1C1 = {247/346}, no 1,5
3a. R234C2 (step 2h) = {126/135}, 13(3) cage at R1C1 = {247/346}
3b. {126} must be {16}2 (cannot be {26}1 which clashes with 13(3) cage), no 2 in R23C2
3c. 45 rule on N1 4 innies R1C3 + R2C2 + R3C12 = 15 = {1257/1356}
3d. 2 of {1257} must be in R1C3 -> no 7 in R1C3
3e. Again consider placement for 3 in R7
R7C1 = 3 => R34C1 = [17/62/71] then with R1C3 + R2C2 + R3C12 = {1356} R23C2 must contain at least one of 3,5 while with R1C3 + R2C2 + R3C12 = {1257} R23C2 must be {15}
or 3 in R7C23 = {23} => R6C2 = 6 (cage sum) => R234C2 = {135}
-> R234C2 = {135}, 3,5 locked for C2
-> R6C2 = 6, R7C23 = [23], 3 placed for D/, clean-up: no 8 in R4C5, no 1 in R5C4 (step 1e)
3f. Consider placement for 2 in C1
2 in 13(3) locked for N1
or 2 in R4C1 => R3C1 = 6 => R1C3 + R2C2 + R3C12 = {1356}
or 2 in R5C1 => R67C1 = 16 = [97], no 7 in R3C1 => R1C3 + R2C2 + R3C12 = {1356}
-> R1C3 + R2C2 + R3C12 = {1356}, no 2,7, clean-up: no 1 in R4C1
3g. 2 in N1 only in 13(3) cage at R1C1 = {247}, 2 locked for C1, clean-up: no 6 in R3C1, no 5 in R5C4, no 7 in R7C1
3h. Killer pair 1,5 in R34C1 and R5C1, locked for C1
3i. R89C3 = {15} (hidden pair in N7), locked for C3 -> R1C3 = 6, clean-up: no 5 in R1C67
3j. Naked pair {27} in R46C3, locked for N4, clean-up: no 1 in R3C1
3k. R5C1 = 1 (hidden single in C1) -> R5C4 = 6, R6C1 = 9 -> R7C1 = 8 (cage sum), clean-up: no 7 in R5C56, no 6 in R7C89
3l. R5C56 = [53], 5 placed for both diagonals
3m. Naked pair {35} in R4C12, locked for R4
3n. Killer pair {27} in R4C3 and R4C56, locked for R4
3o. R4C789 (step 2k) = {168} (only remaining combination), 1,8 locked for R4 and N6, 8 locked for 25(4) cage at R3C7
3p. Naked triple {168} in R4C789, CPE no 6 in R3C7
3q. Naked triple {279} in 18(3) cage at R5C7, 7 locked for N6
3r. Naked triple {345} in 12(3) cage at R6C7, 4 locked for R6
3s. 43(8) cage at R8C1 = {13456789} -> R9C4 = 8, clean-up: no 2 in R8C9
3t. Naked pair {59} in R7C89, locked for R7 and N9, clean-up: no 1 in R9C89
3u. 30(6) cage at R6C5 = {124689/125679}, 9 locked for N8
3v. 21(5) cage at R5C4 = {12567} (only remaining combination), no 4 -> R8C4 = 5, 1 locked for C4, 2 locked for R6, R89C3 = [15]
3w. R1C67 = [83/92] (cannot be {47} which clashes with R1C2) -> R2C6 = {45} (step 1f)
3x. 31(6) cage at R1C3 = {234679} must have one of 2,7 and one of 4,9 in R123C4
3y. R12C6 = [85] (cannot be [94] which clashes with 31(6) cage) -> R1C7 = 3
4a. R6C5 = 8 (hidden single in R6) -> 30(6) cage at R6C5 (step 3u) = {124689}, no 7
4b. 7 in N8 only in R7C46, locked for R7
4c. 28(6) cage at R6C6 = {124678}, no 3, 8 locked for N9, clean-up: no 2 in R9C9
4d. R8C9 = 3 (hidden single in N9) -> R9C9 = 7, placed for D\ -> R6C6 = 1, placed for D\
4e. R2C2 = 3 -> R34C2 = [15], R34C1 = [53]
4f. Naked pair {27} in R6C34, locked for 21(5) cage at R5C4 -> R7C4 = 1
4g. R7C6 = 7 (hidden single in R7), clean-up: no 4 in R4C5
4h. R9C7 = 1 (hidden single in N9) -> R4C7 = 6, R7C7 = 4, placed for D\ -> R1C1 + R3C3 + R4C4 + R8C8 = [2896], R2C3 = 9, R9C8 = 2, R8C7 = 8, R6C789 = [534], clean-up: no 2 in R4C56
4i. R4C56 = [74], 4 placed for D/
4j. R4C89 = {18} = 9 -> R3C79 = 16 = [79], 7 placed for D/
4k. R1C9 = 1 -> R1C8 + R2C9 = 11 = [56]
and the rest is naked singles, without using the diagonals.