Prelims
a) 34(5) cage at R1C5 = {46789}
b) 17(5) cage at R1C9 = {12347/12356}, no 8,9
c) 33(5) cage at R5C4 = {36789/45789}, no 1,2
d) 16(5) cage at R6C1 = {12346}
e) 35(5) cage at R8C4 = {56789}
f) 15(5) cage at R8C9 = {12345}
[I overlooked 32(5) cage at R3C5 = {26789/35789/45689}, no 1 so didn’t use it.]
1a. R5C5 = 4, placed for both diagonals
1b. 34(5) cage at R1C5 = {46789}, CPE -> R1C4 = {1235}
1c. 16(5) cage at R6C1 = {12346}, 4 locked for C1
1d. 35(5) cage at R8C4 = {56789}, CPE -> R9C6 = {1234}
1e. 15(5) cage at R8C9 = {12345}, 5 locked for N9
1f. 4 in R9 only in R9C6789, locked for 15(5) cage, no 4 in R8C9
1g. 8,9 in C9 only in R567C9, locked for 31(5) cage at R5C9, no 8,9 in R7C78
1h. 7,8,9 in R9 only in R9C2345 -> R8C4 = {56}
1i. Caged X-Wing for 5 in 35(5) cage and 15(5) cage, no other 5 in R8
2a. 17(5) cage at R1C9 = {12347} (cannot be {12356} which clashes with 15(5) cage at R8C9, ALS block), 4 locked for C9
2b. R567C9 = {689} (hidden triple in C9) = 23 -> R7C78 = 8 = {17}, locked for R7 and N9
2c. Naked quad {2345} in R8C9 + R9C789, 2,3,4 locked for N9 and 15(5) cage -> R9C6 = 1
2d. Naked triple {689} in R7C9 + R8C78, CPE no 6,8,9 in R7C6
2e. 5 in R1 only in R1C1234, locked for 19(5) cage at R1C1, no 5 in R2C1
2f. 19(5) cage = {12358/12457/13456}, no 9
2g. 6,7 of {12457/13456} must be in R2C1 (R1C123 cannot contain {46/47} which clash with 34(5) cage at R1C5, ALS block), no 6,7 in R1C123
2h. 6,9 in R1 only in R1C5678, locked for 34(5) cage, no 6,9 in R2C6
2i. 9 in C1 only in R345C1, locked for 23(5) cage at R3C1, no 9 in R3C23
2j. 1,7 in C9 only in R1234C9, locked for 17(5) cage, no 1,7 in R2C8
2k. 5 in C9 only in R89C9, locked for N9
2l. 1 in R8 only in R8C12, locked for 16(5) cage at R6C1, no 1 in R6C1
2m. 9 in N1 only in R2C23 + R3C1, CPE no 9 in R3C4
3a. 27(5) cage at R7C6 = {23589/23679/24678/34569} (cannot be {24579/34578} because R8C78 must contain two of 6,8,9)
3b. R8C78 = {689} -> no 6,8,9 in R8C56 (or R7C6 but already eliminated there by CPE)
3c. Variable killer pair 7,8 in R8C3 and R8C5678 for R8, R8C3 cannot contain both of 7,8 -> 27(5) cage must contain at least one of 7,8 = {23589/23679/24678}, 2 locked for N8
4a. 19(5) cage (step 2f) = {12358/12457/13456}
4b. Hidden killer triple for 7,8,9 in 19(5) cage and 23(5) cage at R3C1 for C1, 23 (5) cage can only contain two of 7,8,9 -> 19(5) cage must contain one of 7,8 in R12C1 = {12358/12457}, no 6, no 8 in R1C23
4c. 23(5) cage contains 9 and one of 7,8 = {12389/12479}, no 5,6
4d. Two of 7,8,9 must be in R345C1 -> no 7,8 in R3C23
4e. R1C1 = 5 (hidden single in C1), placed for D\
4f. Naked triple {234} in R9C789, 2,3 locked for R9 and N9 -> R9C1 = 6, placed for D/, R8C49 = [65]
4g. Naked pair {89} in R8C78, locked for R8 and N9 -> R7C9 = 6
4h. Naked pair {89} in R56C9, locked for N6
4i. R8C78 = {89} = 17 -> R7C6 + R8C56 = 10 = {235} (only remaining combination) -> R7C6 = 5, R8C78 = {23}, locked for R8 and N8
4j. R8C123 = [417], 1 placed for D/ -> R67C1 = {23}, locked for C1
4k. 1 in R1 only in R1C34, locked for 19(5) cage, no 1 in R2C1
4l. 1 in C1 only in R345C1, locked for 23(5) cage, no 1 in R3C3
4m. 23(5) cage = {12389/12479}, 2 locked for R3 and N1
4n. 19(5) cage = {12358/12457} -> R1C34 = [12]
4o. Naked triple {234} in R1C2 + R3C23, 3,4 locked for N1, 4 locked for C2
4p. R7C4 = 4 (hidden single in N8)
4q. Naked pair {23} in R3C3 + R9C9, locked for D\
4r. Naked pair {23} in R3C3 + R9C9, CPE no 3 in R3C9
4s. 8 in R1 only in R1C5678, locked for 34(5) cage, no 8 in R2C6
4t. 33(5) cage at R5C4 = {36789/45789} -> R6C3 = {46}
5a. 45 rule on R1 2 outies R2C16 = 1 innie R1C9 + 8
5b. R1C9 = {37} -> R2C16 = 11,15 = [74/87], 7 locked for R2
5c. 24(5) cage at R2C2 = {13569} (only possible combination, cannot be {13578} because R2C23 must contain two of 6,8,9) -> R2C23 = {69}, locked for R2, 9 locked for N1, R2C45 + R3C4 = {135}, locked for N2
5d. R45C1 = {19} (hidden pair in C1), 9 locked for N4
5e. 26(5) cage at R4C2 = {23678} (only possible combination, cannot be {23579} = {2357}9 which clashes with R6C1), no 5,9
5f. R46C3 = [54] (hidden pair in N4) -> R9C2 = 5 (hidden single in N7)
5g. 33(5) cage at R5C4 (step 4t) = {45789}, no 3,6, 5 locked for C4 and N5
5h. Naked pair {13} in R23C4, locked for N2, 1 locked for C4 -> R2C5 = 5
5i. R7C7 = 1 (hidden single on D\) -> R7C8 = 7
5j. 7 on D\ only in R4C4 + R6C6, locked for N5
5k. Naked pair {89} in R79C3, locked for C3 and N7
5l. R2C23 = [96], 9 placed for D\ -> R8C78 = [98], 8 placed for D\
5m. R4C34 = [57] = 12 -> R3C56 + R4C5 = 20 = {389} -> R3C56 = {89}, locked for R3 and N2, R4C5 = 3
6a. 17(5) cage at R1C9 = {12347/12356}, 3 locked for N3
6b. R3C1 = 7 -> R3C7 = 5, placed for D/
6c. Naked pair {89} in R6C4 + R7C3, locked for D/ and 33(5) cage at R5C4 -> R5C4 = 5, R4C6 = 2, placed for D/
6d. R3C7 = 5, R4C6 = 2 -> 26(5) cage at R2C7 = {24569} (only remaining combination) -> R2C7 = 4, R4C7 = 6, R5C6 = 9
and the rest is naked singles, without using the diagonals.