This is a Killer-X.
Prelims
a) R12C6 = {89}
b) R2C12 = {19/28/37/46}, no 5
c) R45C7 = {18/27/36/45}, no 9
d) R45C8 = {19/28/37/46}, no 5
e) R67C1 = {19/28/37/46}, no 5
f) R6C23 = {18/27/36/45}, no 9
g) R78C5 = {39/48/57}, no 1,2,6
h) R78C7 = {39/48/57}, no 1,2,6
i) R9C56 = {19/28/37/46}, no 5
j) 10(3) cage at R1C1 = {127/136/145/235}, no 8,9
k) 20(3) cage at R3C1 = {389/479/569/578}, no 1,2
l) 9(3) cage at R3C6 = {126/135/234}, no 7,8,9
m) 10(3) cage at R6C7 = {127/136/145/235}, no 8,9
n) 7(3) cage at R8C1 = {124}
Steps resulting from Prelims
1a. Naked pair {89} in R12C6, locked for C6, clean-up: no 1,2 in R9C5
1b. Naked triple {124} in 7(3) cage at R8C1, locked for N7, clean-up: no 6,8,9 in R6C1
2. 45 rule on C6 4 innies R3459C6 = 11 = {1235}, locked for C6, clean-up: no 3,4,6 in R9C5
2a. 9(3) cage at R3C6 = {126/135/234}
2b. 4,6 of {126/235} must be in R3C7 -> no 2 in R3C7
3a. 45 rule on R6789 3 outies R4C4 + R5C34 = 21 = {489/579/678}, no 1,2,3
3b. 45 rule on R6789 3 innies R6C45 + R7C4 = 14 = {149/167/239/248/257/356} (cannot be {158/347} which clash with R4C4 + R5C34)
4. 45 rule on C1 4(3+1) outies R1C23 + R29C2 = 12
4a. Min R129C2 = 6 -> max R1C3 = 6
4b. Min R1C23 + R9C2 = 3+1 = 4 -> max R2C2 = 8, clean-up: no 1 in R2C1
5a. 45 rule on C9 2 innies R45C9 = 10 = {19/28/37/46}, no 5
5b. 45 rule on C9 3 outies R2C78 + R3C8 = 16
5c. 45 rule on C789 3 innies R1C78 + R3C7 = 16
5d. 45 rule on whole grid R1C78 + R2C3 = 16
5e. R1C78 + R3C7 = 16, R1C78 + R2C3 = 16 -> R2C3 = R3C7 = {13456}
[This can also be obtained from 45 rule on C123456, which I spotted later.
Note that whichever value is in R2C3 and R3C7 must be in R1C45 for N2.]
6. 45 rule on N1 4 innies R2C3 + R3C123 = 25 = {1789/2689/3589/3679/4579/4678}
6a. 1 of {1789} must be in R2C3 -> no 1 in R3C23
6b. 19(5) cage at R1C4 = {12349/12367/12457/13456} (cannot be {12358} which clashes with R3C6), no 8, 1 locked for N2
7. 45 rule on N9 1 outie R6C9 = 1 innie R7C8 + 6 -> R6C9 = {789}, R7C8 = {123}
8. 45 rule on N78 2 outies R6C16 = 1 innie R7C4 + 6
8a. Max R6C16 = 13 -> max R7C4 = 7
8b. Max R6C16 = 11 (cannot be [76] because R7C4 = 7 clashes with R78C6 = {47}) -> max R7C4 = 5
8c. 35(6) cage at R4C4 must contain 8,9 in R4C4 + R5C34 + R6C45, CPE no 8,9 in R5C5
9. 20(3) cage at R3C1 = {389/569/578} (cannot be {479} which clashes with R67C1 + R89C1), no 4
10. R45C9 = 10 (step 5a)
10a. Consider placement for 5 in N6
5 in R45C7 = {45}, 4 locked for N6 => no 6 in R56C89 => 6 in N6 only in 10(3) cage at R6C7 = {136}
or 5 in 10(3) cage = {145/235}
-> 10(3) cage = {136/145/235}, no 7
[Just spotted. Not sure how or if this can be used.]
11. 45 rule on N2 3 innies R23C5 + R3C6 = 1 outie R3C3 + 9 -> R23C5 cannot total 9 (IOU) -> R4C5 + R5C56 cannot total 12
[At this stage I can’t see how to use this to eliminate any of the combinations of 19(5) cage at R1C4 (step 6b) since R3C3 doesn’t ‘see’ R2C5 so, for three of the combinations, whichever value is in R3C3 must be in R2C5.]
12. Consider permutations for R6C9 + R7C8 (step 7) = [71/82/93]
R6C9 + R7C8 = [71]
or R6C9 + R7C8 = [82] => R6C78 = 8 = {35}, locked for R6 => R6C23 = {27}, locked for R6
or R6C9 + R7C8 = [93] => no 7 in R6C1
-> R6C1 = {1234}, clean-up: no 3 in R7C1
13. 9(3) cage at R3C6 = {126/135/234}, note that {126} can only be [261]
13a. Consider combinations for 19(5) cage at R1C4 (step 6b) = {12349/12367/12457/13456}
19(5) cage = {12349/12367/12457}, CPE no 2 in R3C6 => 9(3) cage = {135}/[342]
or 19(5) cage = {13456} => 7 in N2 must be in R23C5, locked for C5 => R9C56 = [82/91] => 9(3) cage = {135/234} (cannot be [261] which clashes with R9C6)
-> 9(3) cage = {135/234}, no 6
13b. R3C7 = {1345} -> R2C3 = {1345} (step 5e)
13c. R1C78 + R3C7 = 16 (step 5c), max R3C7 = 5 -> min R1C78 = 11, no 1 in R1C78
13d. R2C3 + R3C123 (step 6) = {1789/3589/3679/4579/4678} (cannot be {2689} because no 2,6 in R2C3), no 2
13e. R2C12 = {28/46}/[91] (cannot be {37} which clashes with R2C3 + R3C123), no 3,7
13f. R2C3 + R3C123 = {1789/3679/4579/4678} (cannot be {3589} which clashes with 9(3) cage = {35}1 using R2C3 = R3C7), 7 locked for R3 and N1
13g. 3 of {3679} must be in R2C3 -> no 3 in R3C123
13h. Consider again combinations for 19(5) cage = {12349/12367/12457/13456}
19(5) cage = {12349/12367}, 2,3 locked for N2
or 19(5) cage = {12457}, 2 locked for N2, CPE no 5 in R3C6 => R3C6 = 3 => no 2,3 in R23C5
or 19(5) cage = {13456}, 3 locked for N2, CPE no 5 in R3C6 => R3C6 = 2 => no 2,3 in R23C5
-> no 2,3 in R23C5
13i. 19(5) cage = {12349/12367/12457} (cannot be {13456} which clashes with R3C5), 2 locked for N2
13j. 3 in N1 only in R1C123 + R2C3 -> 3 in R1C123 + R3C7 (using R2C3 = R3C7), CPE no 3 in R1C789
14. Consider combinations for 9(3) cage at R3C6 (step 13a) = {135/234}
9(3) cage = {135}, 1 in R3C7 + R4C6, locked for D/
or 9(3) cage = {234} = [342], 2,4 locked for D/ => R9C1 = 1, placed for D/
-> 1 in R3C7 + R4C6 + R9C1, locked for D/
15. 45 rule on C1 2 outies R29C2 = 1 innie R1C1 + 2 -> no 2 in R9C2 (IOU)
15a. 2 in N7 only in R89C1, locked for C1, clean-up: no 8 in R2C2, no 8 in R7C1
15b. 45 rule on N7 3 innies R7C1 + R89C3 = 20 = {389/569/578}
15c. 7 of {578} must be in R7C1 -> no 7 in R89C3
16. R2C3 + R3C123 (step 13f) = {1789/3679/4579/4678}, 10(3) cage at R1C1 = {136/145/235}, R2C3 = R3C7 (step 5e), R1C78 + R2C3 = 16 (step 5d)
16a. Consider placement for 8 in N1
8 in R3C12 => R2C3 + R3C123 = {1789/4678} => R2C3 = {14}
or R2C12 = [82] => 10(3) cage = {136}, 3 locked for N1
or R2C12 = [82] => 10(3) cage = {145}, R12C6 = [89] => 9 in R1 in R1C789 so looking at those possibilities
9 in R1C78 => R1C78 + R2C3 = {29}5/{69}1 (cannot be {49}3 which clashes with 10(3) cage = {145}), no 3 in R3C7 => no 3 in R2C3
or 9 in R1C9 => 13(3) cage at R1C9 = 9{13}, locked for N3, no 3 in R3C7 => no 3 in R2C3
-> no 3 in R2C3, no 3 in R3C7
16b. 3 in N1 only in 10(3) cage = {136/235}, no 4, 3 locked for R1
16c. 9(3) cage at R3C6 (step 13a) = {135/234}, 3 locked for C6, clean-up: no 7 in R9C5
16d. Naked triple {124} in R9C126, locked for R9, 4 also locked for N7
16e. 2 in R9 only in R9C19, CPE no 2 in R4C6
16f. 9(3) cage at R3C6 (step 13a) = {135} (only remaining combination), no 4, 1 locked for D/, clean-up: no 4 in R2C3
16g. R2C3 + R3C123 = {1789/4579} (cannot be {4678} since R2C3 only contains 1,5), no 6, 9 locked for R3 and N1, clean-up: no 1 in R2C2
17. 19(5) cage at R1C4 (step 13i) = {12349/12367/12457} contains both of 1,2 in R123C4 + R1C5
17a. Hidden killer pair 1,2 in R789C4 and R9C6 for N8, R9C6 = {12} -> R789C4 contains one of 1,2
17b. Hidden killer pair 1,2 in R123C4 and R789C4 for C4, R789C4 contains one of 1,2 -> R123C4 cannot contain both of 1,2 -> R123C4 contains one of 1,2 -> R1C5 = {12}
17c. Killer pair 1,2 in R123C4 and R789C4, locked for C4
17d. 45 rule on C1234 2 outies R16C5 = 1 innie R2C3 + 4, R2C3 = {15} -> R16C5 = 5,9 = [14/18/23/27], R6C5 -> {3478}
17e. R6C45 + R7C4 (step 3b) = {149/167/239/248/257/356}
17f. 1,2 of {149/248} must be in R7C4 -> no 4 in R7C4
17g. 3 of {239/356} must be in R6C5 -> no 3 in R67C4
17h. 7 of {167/257} must be in R6C5 -> no 7 in R6C4
18. Min R23C5 = 10 (cannot total 9, step 11) -> max R4C5 + R5C56 = 11, no 9 in R4C5
18a. 9 in N5 only in R456C4, locked for C4 and 35(6) cage at R4C4
[I ought to have seen this step a bit earlier; it became available after step 15 but I was focussed on 19(5) cage whenever I could use it.]
19. 20(3) cage at R3C1 (step 9) = {569/578} (cannot be {389} which clashes with R2C1 + R67C1), no 3, 5 locked for C1
19a. Hidden killer pair 7,9 in 20(3) cage and R7C1 for C1, 20(3) cage contains one of 7,9 -> R7C1 = {79}, clean-up: no 4 in R6C1
19b. R1…9C1 = [18]{569}[3724]/[36]{578}[1924] -> R1C1 = {13}, R2C1 = {68}, R8C1 = 2, R9C1 = 4, placed for D/, R9C2 = 1, R9C6 = 2 -> R9C5 = 8, clean-up: no 8 in R6C3, no 4 in R78C5
19c. R6C16 = R7C4 + 6 (step 8)
19d. Max R6C16 = 10 -> no 5 in R7C4 -> R7C4 = 1, R6C16 = 7 = [16/34]
19e. 7 in C6 only in R78C6, locked for N8, clean-up: no 5 in R78C5
19f. R1C5 = 1 (hidden single in N2)
19g. R1C1 = 3, placed for D\, R6C1 = 1 -> R7C1 = 9, R78C5 = [39]
19h. 20(3) cage = {578} -> R2C1 = 6, R2C2 = 4, placed for D\
19i. R6C6 = 6, placed for D\, R78C6 = {47}, 4 locked for N8, R89C4 = {56}, locked for C4 and 22(4) cage at R8C3 -> R89C3 = [83]
19j. Naked pair {25} in R1C23, locked for R1, 5 locked for N1
19k. R2C3 = 1 -> R3C7 = 1 (step 5e)
19l R7C8 = 2 -> R6C78 = 8 = {35}, locked for R6 and N6, R6C9 = 8 (step 7)
190m. R6C23 = {27} (only remaining combination), locked for R6 and N4 -> R6C4 = 9, placed for D/, R6C5 = 4
19n. Naked pair {58} in R45C1, locked for N4, 8 locked for C1 -> R3C1 = 7, R3C3 = 9, placed for D\, R3C2 = 8
19o. R45C7 = {27} (only remaining combination), locked for C7 and N6
19p. R78C7 = [84] (only remaining permutation), 8 placed for D\, R4C4 = 7, placed for D\
19q. R9C4789 = [6975], R8C8 = 1, R78C9 = [63]
19r. R1C9 = 7, placed for D/, R23C9 = 6 = [24]
and the rest is naked singles, without using the diagonals.