Prelims
a) R1C12 = {39/48/57}, no 1,2,6
b) R1C34 = {17/26/35}, no 4,8,9
c) R1C56 = {15/24}
d) R34C1 = {17/26/35}, no 4,8,9
e) R4C78 = {49/58/67}, no 1,2,3
f) R78C6 = {14/23}
g) R9C67 = {19/28/37/46}, no 5
h) 21(3) cage at R1C8 = {489/579/678}, no 1,2,3
i) 9(3) cage at R3C2 = {126/135/234}, no 7,8,9
j) 24(3) cage at R3C4 = {789}
k) 11(3) cage at R9C2 = {128/137/146/236/245}, no 9
l) 14(4) cage at R1C7 = {1238/1247/1256/1346/2345}, no 9
1a. Naked triple {789} in 24(3) cage at R3C4, locked for R3 and N2, clean-up: no 1 in R1C3, no 1 in R4C1
1b. 45 rule on N3 2 innies R3C79 = 10 = {46}, locked for R3 and N3, clean-up: no 2 in R4C1
1c. 21(3) cage at R1C8 = {579} (only remaining combination), 5,7 locked for N3
1d. 45 rule on R12 1 outies R3C8 = 2, clean-up: no 6 in R4C1
1e. Naked triple {135} in R3C123, locked for N1
1f. R1C12 = {48} (only remaining combination), locked for R1 and N1
1g. R1C56 = {15} (only remaining combination), locked for N2, 5 locked for R1 -> R1C7 = 3, clean-up: no 7 in R9C6
1h. Naked pair {79} in R1C89, locked for N3, 7 locked for R1 -> R2C9 = 5
1i. 45 rule on N6 1 outie R3C9 = 1 innie R5C7 + 1 -> R3C9 = 6, R5C7 = 5, R3C7 = 4, placed for D/, clean-up: no 8 in R4C7, no 8,9 in R4C8, no 6 in R9C6
1j. R3C9 = 6 -> 17(4) cage at R3C9 = {1268/1367}, no 4,9, 1 locked for C9 and N6
1k. R1C6 = 5 (hidden single in C6) -> R1C5 = 1
1l. 4 in C9 only in R789C9, locked for N9
1m. 45 rule on N9 2 innies R79C7 = 7 = {16}, locked for C7 and N9 -> R2C7 = 8, R2C8 = 1, placed for D/, R9C6 = {49}, clean-up: no 7 in R4C8
1n. 45 rule on C1 3 innies R125C1 = 19 = {289/469/478} (cannot be {379} which clashes with R34C1), no 1,3
1o. 7 of {478} must be in R2C1 -> no 7 in R5C1
[And to simplify things a bit]
1p. 45 rule on C9 2 outies R17C8 = 16 = {79}, locked for C8
1q. 9 in N6 only in R46C7, locked for C7
2a. R35C7 = [45] = 9 -> R46C6 + R7C7 = 17 = {179/368} (cannot be {269} = {29}6 which clashes with R9C67, cannot be {278} because R7C7 only contains 1,6) -> R46C6 = {38/79}, no 1,2,6
2b. 45 rule on C789 3 outies R469C6 = 20 = {389/479}, 9 locked for C6
2c. Killer pair 7,8 in R3C6 and R469C6, locked for C6
2d. Killer pair 3,4 in R469C6 and R78C6, locked for C6
2e. 4 in C6 only in R789C6, locked for N8
2f. R789C6 = {14}9/{23}4
2g. Naked pair {26} in R1C3 + R2C6, locked for N2
3a. 45 rule on N8 2 innies R9C46 = 1 outie R6C5 + 9
3b. Max R9C46 = 17 -> max R6C5 = 8
3c. Min R6C5 = 2 -> min R9C46 = 11, no 1 in R9C4
3d. R9C46 cannot total 13 -> no 4 in R6C5
3e. 31(6) cage at R6C5 = {125689/135679/235678}
4a. 45 rule on N47 3(2+1) outies R3C12 + R9C4 = 1 innie R5C3 + 4
4b. Min R3C12 = 4 -> R5C3 cannot be lower than R9C4, no 1 in R5C3
[Steps 1p and 1q added to the early part of my Assassin 408 WT; now for new steps for this variant.]
5a. 18(4) cage at R4C5 = {1269/1368/1458/1467/2358/2457/3456} (cannot be {1278/1359/2349/2367} which clash with R46C6)
5b. Consider combinations for R46C6 + R7C7 (step 2a) = {38}6/{79}1
R46C6 + R7C7 = {38}6, 3,8 locked for N5 => 18(4) cage at R4C5 = {1269/1467/2457}
or R46C6 + R7C7 = {79}1, 7,9 locked for N5, 1 placed for D\ => 18(4) cage must contain 1 for N5 = {1368/1458}
-> 18(4) cage = {1269/1368/1458/1467/2457}
5c. Combined cages 18(4) cage + R46C6 = {1269/1467/2457}{38}/{1368/1458}{79}, 8 locked for N5
5d. R9C46 = R6C5 + 9 (step 3a)
5e. Consider placements for R6C5 = {23567}
R6C5 = {257} => 18(4) cage = {1269/1368/1458/1467} (cannot be {2457} which clashes with R6C5)
or R6C5 = 3 => R46C6 = {79}, locked for N5 => 18(4) cage = {1368/1458}
or R6C5 = 6 => R9C46 = 15 = [69], R9C7 = 1 => 11(3) cage at R9C2 = {23}6 => 7 in R9 only in R9C159, CPE no 7 in R5C5 using diagonals => 18(4) cage = {1269/1368/1458/1467} (cannot be {2457} because 4,5,7 only in R4C5 + R5C4)
-> 18(4) cage = {1269/1368/1458/1467}, 1 locked for R5 and N5
6a. 45 rule on N47 6(3+3) outies R3C123 + R469C4 = 25, R3C123 = {135} = 9 -> R469C4 = 16 = {259/358/367/457} (cannot be {268} which clashes with R1C4, cannot be {349} which clashes with R2C4)
6b. 6 of {367} must be in R46C4 (R46C4 cannot be {37} which clashes with R46C6), no 6 in R9C4
6c. 6 in N8 only in R78C4 + R789C5, locked for 31(6) cage at R6C5, no 6 in R6C5
6d. R9C46 = R6C5 + 9 (step 3a)
6e. R469C4 = {259/367/457} (cannot be {358} = {35}8 which clashes with R6C5 + R9C46 = [384]), no 8 in R9C4
6f. 8 in N8 only in 31(6) cage at R6C5 (step 3e) = {125689/235678}
6g. 45 rule on C6789 3 remaining innies R235C6 = 15 = {168/267}
6h. Consider combinations for R235C6
R235C6 = {168} = [681] => R1C4 = 2 => R469C4 = {367/457}, 7 locked for C4
or R236C6 = {267} => R3C6 = 7
-> no 7 in R3C4
7a. R46C6 + R7C7 (step 2a) = {179/368} = {38}6/{79}1, R469C4 (step 6e) = {259/367/457}
7b. Consider placement for 1 on D\
R3C3 = 1 => 21(4) cage at R3C3 = {1479/1569} (cannot be {1389} because R46C4 = {39} cannot contain both of 3,9, cannot be {1578} because no 4 in R9C4)
or R3C3 = 3 => 21(4) cage = {3459/3567} (cannot be {2379} which clashes with R46C6 + R7C7 = {79}1, cannot be {3468} because R469C4 cannot contain both of 4,6)
or R3C3 = 5 => 21(4) cage = {3567} (cannot be {2568} because R469C4 cannot contain both of 2,6, cannot be {3459} because R469C4 cannot contain two of 3,4,9)
-> 21(4) cage = {1479/1569/3459/3567}, no 2,8
7c. Consider placement for R5C6 = {126}
R5C6 = 1 => R78C6 = {23}, locked for N8 => R469C4 = {367/457} => 21(4) cage = {1479/3459/3567} (cannot be {1569} because R46C4 cannot contain both of 5,6)
or R5C6 = 2 => 2 in 31(6) cage at R6C5 (step 6f) in N8, locked for N8 => R469C4 = {367/457} => 21(4) cage = {1479/3459/3567} (same reason)
or R5C6 = 6 ‘sees’ R46C4 + R5C3 => 21(4) cage = {1479/3459}
-> 21(4) cage = {1479/3459/3567}
7d. Consider combinations for 21(4) cage
21(4) cage = {1479} => R469C4 = {457} (only way to include two of 4,7,9)
or 21(4) cage = {3459} => R46C6 + R7C7 = {79}1, locked for N5 => R46C4 = {45} => R469C4 = {457}
or 21(4) cage = {3567}, no 9 => R469C4 = {367}
-> R469C4 = {367/457}, no 2,9, 7 locked for C4
7e. Killer pair 3,4 in R2C4 and R469C4, locked for C4
7f. Hidden killer pair 8,9 in 18(4) cage at R4C5 and R46C6 for N5, R46C6 contains one of 8,9 -> 18(4) cage (step 5e) must contain one of 8,9 = {1269/1368/1458}, no 7
7g. 18(4) cage = {1269/1368} (cannot be {1458} because 4,5 only in R4C5), no 4,5
[After that combination analysis, it gets easier from here]
8a. R4C4 = 4 (hidden single in N5), placed for D\ -> R1C1 = 8, placed for D\, R1C2 = 4, R2C45 = [34]
8b. R4C4 = 4 -> R69C4 (step 7d) = {57}, 5 locked for C4
8c. 5 in N5 only in R6C45, 5 locked for R6
8d. R4C4 = 4 -> 21(4) cage at R3C3 (step 7c) = {1479/3459} -> R5C3 = 9, R3C3 = {13}
8e. R1C1 = 8 -> R25C1 (step 1n) = 11 = [74/92]
8f. R4C8 = 6 -> R4C7 = 7, clean-up: no 1 in R3C1
8g. R8C7 = 2 -> R89C8 = 13 = [58], R6C7 = 9
8h. R5C2 = 7 (hidden single in R5) -> 24(4) cage at R5C1 = {4578} (only remaining combination containing one of 2,4 for R5C1) -> R5C1 = 4, R67C3 = [85], 5 placed for D/, R2C1 = 7
8i. Naked pair {26} in R12C3, locked for C3 and N1 -> R2C2 = 9, placed for D\
8j. R6C4 = 7, placed for D/, R6C6 = 3, placed for D\ -> R3C3 = 1, placed for D\, R7C7 = 6, placed for D\ -> R5C5 = 2, placed for D/, R1C9 = 9, placed for D/, R4C6 = 8, placed for D/
8k. R78C6 = {14} (only remaining combination), locked for N8, 1 locked for C6
8l. R9C4 = 5 -> R9C24 = 6 = [24]
and the rest is naked singles, without using the diagonals.