Prelims
a) R23C6 = {16/25/34}, no 7,8,9
c) R45C4 = {15/24}
d) R45C6 = {19/28/37/46}, no 5
e) R45C7 = {39/48/57}, no 1,2,6
f) R6C12 = {16/25/34}, no 7,8,9
g) R9C89 = {15/24}
h) 11(3) cage at R7C4 = {128/137/146/236/245}, no 9
i) 12(4) cage at R2C5 = {1236/1245}, no 7,8,9
1a. 12(4) cage at R2C5 = {1236/1245}, 1,2 locked for C5
1b. 45 rule on R6789 1 outie R5C3 = 5, clean-up: no 1 in R4C4, no 7 in R4C7, no 2 in R6C12
1c. 45 rule on N36 3 innies R6C789 = 8 = {125} (cannot be {134} which clashes with R6C12), locked for R6 and N6, clean-up: no 7 in R5C7, no 6 in R6C12
1d. Naked pair {34} in R6C12, locked for R6 and N4
1e. 45 rule on R6 2 innies R6C39 = 8 = [62/71]
1f. R56C3 = 11,12 -> R78C3 = 12,13 = {39/48/49} (cannot be {67} which clashes with R6C3), no 1,2,6,7
1g. 8,9 in R6 only in R6C456, locked for N5, clean-up: no 1,2 in R45C6
1h. R23C6 = {16/25} (cannot be {34} which clashes with R45C6), no 3,4
1i. 18(3) cage at R4C1 = {189/279}, no 6, 9 locked for N4
1j. 45 rule on R1 2 innies R1C12 = 11 = {29/38/47/56}, no 1
1k. 45 rule on R1 3 outies R2C234 = 19 = {289/379/469/478/568}, no 1
1l. 45 rule on N3 1 innie R3C9 = 1 outie R4C8, no 1,2,5 in R3C9
2a. 45 rule on N7 2 remaining outies R6C3 + R9C4 = 13 = {67}, CPE no 6,7 in R6C4 + R9C3
2b. 45 rule on R9 1 innie R9C1 = 1 outie R8C2 + 2, no 8,9 in R8C2, no 1,2 in R9C1
2c. Hidden killer pair 8,9 in R9C123 and 15(3) cage at R9C5 for R9 -> R9C123 and 15(3) cage must each contain one of 8,9 (both of 8,9 in R9C123 would clash with R78C3)
2d. Killer pair 8,9 in R89C3 and R9C123, locked for N7
2e. 15(3) cage at R9C5 = {159/168/249/348} (cannot be {258} which clashes with R9C89, cannot be {267/357/456} which don't contain one of 8,9), no 7
2f. Killer pair 1,4 in 15(3) cage and R9C89, locked for R9, clean-up: no 2 in R8C2
2g. 7 in R9 only in R9C1234, CPE no 7 in R8C2, clean-up: no 9 in R9C1
2h. 22(4) cage at R8C2 = {1579/1678/2479/2569/2578/3478/3568} (cannot be {1489/2389} because R9C4 only contains 6,7, cannot be {4567} because R9C3 only contains 2,3,8,9, cannot be {3469} = 4{369} which clashes with R8C2 + R9C1 = [46])
2i. Killer pair 8,9 in R9C23 and 15(3) cage, locked for R9, clean-up: no 6 in R8C2
2j. 17(4) cage at R7C1 = {1367/1457/2357/2456}
2k. Killer pair 3,4 in 17(4) cage and R78C3, locked for N9, clean-up: no 5,6 in R9C1
2l. 17(4) cage = {1367/1457/2357} (cannot be {2456} because R9C1 only contains 3,7), 7 locked for N7
2m. 22(4) cage = {1678/2569} (cannot be {1579} = {159}7 which clashes with 17(4) cage, cannot be {2578} = 5{28}7 which clashes with R8C2 + R9C1 = [57]), 6 locked for R9
2n. {1678/2569} = [1687]/5{29}6, no 5,8 in R9C2
2o. 8 in N7 only in R789C3, locked for C3
3a. 45 rule on N124 1 remaining innie R6C3 = 2 outies R45C5 + 1
3b. R6C3 = {67} -> R45C5 = 5,6 = {23/24}/[51] (cannot be {14} which clashes with R45C4), no 1,6 in R4C5, no 6 in R5C5
3c. 12(4) cage at R2C5 = {1236/1245} -> R45C5 = {23}/[51] (cannot be {24} because 12(4) cage = {15}{24} clashes with R23C6), no 4 in R45C5, R23C5 = {16/24}, no 3,5
3d. Combined cage R23C5 + R23C6 = {16}{25}/{24}{16}, 1,2,6 locked for N2
3e. Variable hidden killer pair 8,9 in R1C456 and R23C4 for N2, R23C4 cannot both of 8,9 (which would clash with R6C4), 19(4) cage at R1C3 cannot contain both of 8,9 -> R1C456 and R23C4 must each contain one of 8,9
3f. Killer pair 8,9 in R23C4 and R6C4, locked for C4
3g. 19(4) cage at R1C3 = {1378/2359} (cannot be {1567/2467/3457} which don’t contain one of 8,9 for R1C456, cannot be {1279/1369/1468/2368} because 1,2,6 only in R1C3, cannot be {1459/2458} which clash with R23C5 + R23C6) -> R1C3 = {12}, R1C456 = {359/378}, no 4, 3 locked for R1 and N1, clean-up: no 8 in R1C12 (step 1j)
3h. Combined cage R1C12 + 19(4) cage = {29}1{378}/{47}2{359}/{56}1{378}, 7 locked for R1
3i. Combined cage R1C12 + 19(4) cage = {29}1{378}/{47}2{359}/{56}1{378}, CPE, no 7 in R2C4
3j. Consider combinations for 12(4) cage = {1236/1245}
12(4) cage = {1236} => 4 in N2 only in R23C4, R45C5 = {23} => R45C6 = {46}
or 12(4) cage = {1245} = {24}[51], R23C6 = {16}, R45C4 = {24}
-> 4 in R2345C4, locked for C4, 6 in R2345C6, locked for C6
3k. 1 in R4 only in R4C123, locked for N4
3l. 1 in R4 only in R4C123, CPE no 1 in R23C1
3m. 1 in N1 only in R1C3 + R3C23, CPE no 1 in R4C3
3n. 1 in C3 only in R13C3, locked for N1
3o. 45 rule on N4 3 remaining innies R4C23 + R6C3 = 15 = {267} (only remaining combination, cannot be {168} because 1,8 only in R4C2), 2 locked for R4 and 36(7) cage at R2C1, clean-up: no 4 in R5C4, no 3 in R5C5 (step 3c)
3p. R4C23 + R6C3 = {267}, CPE no 6,7 in R3C3
3q. R4C1 = 1 (hidden single in N4) -> R5C12 = 17 = {89}, locked for R5, clean-up: no 3,4 in R4C7
3r. 6 in C4 only in R789C4, locked for N8
3s. 45 rule on N14 2 outies R23C4 = 2 remaining innies R16C3 + 6
3t. R16C3 = [16/17/26/27] = 7,8,9 -> R23C4 = 13,14,15 = {49/59}/[87], no 8 in R3C4
3u. R16C3 = [16/17/27] (cannot be [26] because 19(4) cage = 2{359} which clashes with R23C4 = 14 = {59})
4a. 15(3) cage at R1C7 = {168/249/456} (cannot be {159/258} which clash with 19(4) cage at R1C3
4b. 14(3) cage at R2C8 = {158/167/239/257/347/356} (cannot be {149/248} which clash with 15(3) cage)
4c. 16(3) cage at R2C7 = {169/178/259/268/367/457} (cannot be {349/358} which clash with R45C7)
4d. R3C9 = R4C8 (step 1l) -> 16(3) cage = R23C7 + R3C9 = {178/259/367/457} (cannot be {169/268} which clash with 15(3) cage)
4e. R16C3 (step 3u) = [16/17/27], R6C39 (step 1e) = [62/71]
4f. Consider placements for R1C3 = {12}
R1C3 = 1 => 15(3) cage = {249/456} => R23C7 + R3C9 = {178/367} (cannot be {259/457} which clash with 15(3) cage)
or R1C3 = 2 => R6C3 = 7, R6C9 = 1, R6C7 = {25} => 16(3) cage = {178/367/457} (cannot be {259} which clashes with R6C7)
-> R23C7 + R3C9 = 16(3) cage = {178/367/457}, no 2,9, 7 locked for N3
5a. R16C3 (step 3u) = [16/17/27], R6C3 + R9C4 (step 2a) = {67}, 22(4) cage at R8C2 (step 2m) = {1678/2569}
5b. Consider permutations for R4C23 + R6C3 (step 3o) = {267}
R4C23 + R6C3 = {267} = {26}7 => R9C4 = 6 => 22(4) cage = {2569}, caged X-Wing for 2 in R4C23 and R9C23, no other 2 in C23
or R4C23 + R6C3 = {267} = {27}6 => R1C3 = 1
-> R1C3 = 1
[That step could have been done instead of step 4f, but was harder to spot. Both depended on the important step 3u.
Almost cracked; fairly straightforward from here.]
5c. R1C3 = 1 -> 19(4) cage at R1C3 (step 3g) = 1{378}, 7,8 locked for R1 and N2, clean-up: no 4 in R1C12 (step 1j)
5d. 9 in N2 only in R23C4, locked for C4 -> R6C4 = 8, placed for D/
5e. 9 in N2 only in R23C4, CPE no 9 in R2C1
5f. 4 in R1 only in R1C789, locked for N3, clean-up: no 4 in R4C8 (step 1l)
5g. 36(7) cage at R2C1 = {2345679}, no 8, 3 locked for N1
5h. R2C2 = 8 (hidden single in N1), placed for D\, R5C12 = [89], clean-up: no 2 in R1C1 (step 1j)
5i. R2C234 = 19 (step 1k) = {289/478/568} -> R2C34 = [29/65/74], no 4,9 in R2C3
5j. Naked triple {267} in R246C3, 2 locked for C3
5k. 9 in N7 only in R789C3, locked for C3
6a. 2 in C1 only in R78C1, locked for N7 -> R9C24 = [67] = 13 -> R8C2 + R9C3 = 9 = [18], 1 placed for D/, R9C1 = 3, placed for D/, R6C12 = [43], R1C4 = 3, naked pair {49} in R78C3, 4 locked for C3 and N7, R6C3 = 6 (cage sum), R6C9 = 2 (step 1e), R3C3 = 3, placed for D\
[No routine clean-ups from here]
6b. R5C5 = 2, placed for both diagonals, R5C4 = 1, R4C4 = 5, placed for D\ -> R4C5 = 3, R23C5 = 7 = {16}, locked for N2
6c. R3C2 = 4 (hidden single in N1), R3C4 = 9, R1C1 = 9 (hidden single in N1), placed for D\, R1C2 = 2 (step 1j), R2C3 = 7, R6C6 = 7, placed for D\, R6C5 = 9, R4C2 = 7, R7C2 = 5
6d. Naked triple {146} in R7C7 + R8C8 + R9C9, locked for N9
6e. Naked triple {456} in R1C789, 5,6 locked for N3, R2C8 = 9, placed for D/, R7C3 = 4, placed for D/, R4C6 = 6, placed for D/
6f. R3C7 = 7, R4C8 = 8 -> R2C7 = 1 (cage sum)
6g. R7C5 = 8 -> R7C46 = [21]
and the rest is naked singles, not using the diagonals.