This is a Killer-X
Prelims
a) 13(2) cage at R1C9 = {49/58/67}, no 1,2,3
b) R34C4 = {69/78|
c) 12(2) cage at R4C5 = {39/48/57}, no 1,2,6
d) 7(2) cage at R4C6 = {16/25/34}, no 7,8,9
e) 11(2) cage at R5C4 = {29/38/47/56}, no 1
f) 6(2) cage at R5C5 = {15/24}
g) R6C67 = {18/27/36/45}, no 9
h) R6C89 = {79}
i) 11(3) cage at R1C7 = {128/137/146/236/245}, no 9
j) 19(3) cage at R2C9 = {289/379/469/478/568}, no 1
k) 17(5) cage at R3C5 = {12347/12356}, no 8,9
1. Naked pair {79} in R6C89, locked for R6 and N6, clean-up: no 2,4 in R5C4, no 2 in R6C67
1a. 19(3) cage at R2C9 = {289/469/478/568} (cannot be {379} which clashes with R6C9), no 3
2. 45 rule on N23 3 outies R4C479 = 14
2a. Min R4C47 = 7 -> no 8 in R4C9
2b. 19(3) cage at R2C9 (step 1a) = {289/469/478/568}
2c. 2 of {289} must be in R4C9 -> no 2 in R23C9
3. 45 rule on N6 4 innies R4C79 + R56C7 = 14 = {1238/1256/1346/2345}
3a. R4C479 = 14 (step 2) = {149/167/239/257/347/356} (cannot be {158} = [815] which clashes with R4C6 + R5C7 = [52] using R4C79 + R56C7, cannot be {248} = 8{24} which clashes with R4C6 + R5C7 = [25/43] using R4C79 + R56C7), no 8 in R4C4, clean-up: no 7 in R3C3
3b. R4C479 = {149/167/239/257/347} (cannot be {356} = [635] which clashes with R4C6 + R5C7 = [34/52] using R4C79 + R56C7)
3c. R4C479 = {167/239/257/347} (cannot be {149} = [914] which clashes with R4C6 + R5C7 = [16/43] using R4C79 + R56C7)
3d. 7 of {167} must be in R4C4 -> no 6 in R4C4, clean-up: no 9 in R3C4
4. 45 rule on N2 3 innies R3C456 = 16 = 6{37}/8{17}/8{26}/8{35}, no 4
4a. 17(5) cage at R3C5 = {12347/12356}, R3C56 = {17/37}, 7 locked for R3
or R3C56 = {26/35} are only in {12356}
-> no 7 in R3C78
4b. R4C479 (step 3c) = {167/257/347} (cannot be {239} = [932] which clashes with R3C456 = 6{37} using R34C4 = 15), no 9
4c. R4C4 = 7 -> R3C4 = 8, 7 placed for D\, clean-up: no 5 in 12(2) cage at R4C5, no 3,4 in R6C5
4d. R4C4 = 7 -> R4C79 = 7 = [16/25/34/52], no 4,6 in R4C7
4e. 9 in N5 only in 12(2) cage at R4C5 = {39} or 11(2) cage at R5C4 = [92] -> 11(2) cage = [56/65/92] (cannot be [38], locking-out cages), no 3,8
4f. Killer pair 2,5 in 11(2) cage and 6(2) cage at R5C5, locked for N5, clean-up: no 2,5 in R5C7, no 4 in R6C7
5. 45 rule on N5 2 remaining outies R56C7 = 7 = [16/43/61], no 3 in R5C7, no 5,8 in R6C7, clean-up: no 4 in R4C6, no 1,4 in R6C6
5a. 1 in N5 only in R4C6 + R5C5 + R6C5, locked for D/
6. 45 rule on N2 3 outies R3C78 + R4C7 = 9 = {126/135/234}
6a. 19(3) cage at R2C9 (step 1a) = {289/469/478/568}
6b. Consider placements for 9 in N3
9 in 13(2) cage at R1C9 = {49}, locked for N3 and D/ => 6(2) cage at R5C5 = {15}, 5 locked for D/ => R3C7 = {236} => R3C78 + R4C7 = {126/135} with 3 of {135} in R3C7, no 3 in R4C7 => no 4 in R4C9 (step 4d) => 19(3) cage = {568}
or 9 in 19(3) cage = {289/469}
-> 19(3) cage = {289/469/568}, no 7
6c. Taking that first path further, 19(3) cage = {568} must be [856] (cannot be [865] which because R3C78 + R4C7 = {135} is inconsistent with R4C79 (step 4d) = [25]) -> no 5 in R24C9, clean-up: no 2 in R4C7 (step 4d)
6d. 17(5) cage at R3C5 = {12347/12356}, 2 locked for R3
6e. Consider permutations for R4C79 (step 4d) = [16/34/52]
R4C79 = [16] => R3C56 (step 4a) = {26/35} => 17(5) cage = {12356}, 5 locked for R3 => 19(3) cage = {49}6
or R4C79 = [34] => 19(3) cage = {469}
or R4C79 = [52] => 19(3) cage = {289}
-> 19(3) cage = {289/469}, no 5, 9 locked for C9 and N3, clean-up: no 4 in 13(2) cage at R1C9
6f. R6C89 = [97], clean-up: no 6 in R2C8
7. 19(3) cage at R2C9 (step 6e) = {289/469}
7a. Consider combinations for 11(2) cage at R5C4 = {56}/[92]
11(2) cage = {56} => 6(2) cage at R5C5 = {24}, R4C6 = 1 (hidden single in N5) -> R5C7 = 6
or 11(2) cage = [92] => 6(2) cage = {15}, locked for D/ => 13(2) cage at R1C9 = [67]
-> no 6 in R4C9, clean-up: no 1 in R4C7 (step 4d)
7b. 4 of 19(3) cage = {469} must be in R4C9 -> no 4 in R23C9
7c. Killer pair 6,8 in 13(2) cage at R1C9 and R23C9, locked for N3
7d. 17(5) cage at R3C5 = {12347/12356}, 1 locked for R3
7e. R3C78 + R4C7 (step 6) = {135/234}, 3 locked for 17(5) cage at R3C5, clean-up: no 5 in R3C56 (step 4a)
7f. R3C78 + R4C7 (step 6) = {135/234}, CPE no 3 in R12C7
7g. 1 of {135} must be in R3C8, 3 of {234} must be in R4C7 -> no 3,5 in R3C8
7h. 11(3) cage at R1C7 = {137/245}
7i. 3 of {137} must be in R1C8 -> no 1,7 in R1C8
7j. Consider placements for R4C7 = {35}
R4C7 = 3 => R56C7 (step 5) = {16}, locked for C7
or R4C7 = 5 => R3C8 = 1
-> 11(3) cage at R1C7 = {245} (only remaining combination), locked for N3, clean-up: no 8 in 13(2) cage at R1C9
7k. Naked triple [673] in R1C9 + R2C8 + R3C7, placed for D/
7l. R23C9 = [89], R3C8 = 1, R4C7 = 5 -> R4C9 = 2 (step 4d), R4C6 = 1 -> R5C7 = 6, R6C7 = 1 -> R6C6 = 8, placed for D\
7m. 12(2) cage at R4C5 = {39} (only remaining combination), locked for N5
7n. 6(2) cage at R5C5 = {24}, (only remaining combination), locked for N5 and D/
7o. 11(2) cage at R5C4 = [56]
7p. 17(5) cage at R3C5 = {12356} (only remaining combination) -> R3C56 = [26] -> R5C5 = 4, placed for D\, R6C6 = 2, R3C3 = 5, placed for D\, R5C89 = [83], R4C8 = 4, R9C9 = 1, placed for D\, R5C6 = 9, R4C5 = 3
7q. Naked pair {24} in R12C7, locked for C7 and N3 -> R1C8 = 5, R7C7 = 9, placed for D\, R7C3 = 8
8. 12(3) cage at R1C4 = {147} (only remaining combination) -> R1C5 = 7, R12C4 = {14}, locked for C4 and N2
8a. R12C6 = [35], R2C5 = 9
8b. R1C1 = 2, placed for D\
8c. R12C7 = [42], R12C4 = [14], R1C23 = [89], R4C123 = [896], R8C2 = 5, R78C9 = [54], R78C5 = [18], R8C67 = [27]
8d. Naked pair {13} in R28C3, locked for C3 -> R6C23 = [34]
8e. R2C2 = 6, placed for D\
and the rest is naked singles, without using the diagonals.
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