Prelims
a) R4C78 = {39/48/57}, no 1,2,6
b) R78C9 = {17/26/35}, no 4,8,9
c) 9(3) cage at R1C8 = {126/135/234}, no 7,8,9
d) 19(3) cage at R1C9 = {289/379/469/478/568}, no 1
e) 12(4) cage at R3C4 = {1236/1245}, no 7,8,9
f) 35(5) cage at R7C2 = {56789}
1a. 35(5) cage at R7C2 = {56789}, locked for N7
1b. 45 rule on C9 1 innie R9C9 = 1, placed for D\, clean-up: no 7 in R78C9
1c. 45 rule on N9 2 innies R7C78 = 17 = {89}, locked for R7, N9 and 33(6) cage at R5C8
1d. 45 rule on N3 2 outies R34C6 = 8 = {17/26/35}, no 4,8,9
1e. R47C8 = {89} (hidden pair in C8) -> R4C7 = {34}
1f. 19(3) cage at R1C9 = {289/379/469/478} (cannot be {568} which clashes with R78C9), no 5
1g. 17(3) cage at R4C9 = {269/278/359/458/467} (cannot be {368} which clashes with R78C9)
2a. 45 rule on N47 1 outie R3C2 = 1 innie R7C3 +7 -> R3C2 = {89}, R7C3 = {12}
2b. 17(3) cage at R3C2 cannot contain both of 8,9, R3C2 = {89} -> no 8,9 in R4C23
2c. 3,4 in N7 only in R789C1, locked for C1 and 32(7) cage at R4C1
2d. 32(7) cage contains 3,4 = {1234589/1234679}, 9 locked for N4
2e. 45 rule on C123 3 innies R237C3 = 9 = {126/135/234}, no 7,8,9
3. 45 rule on R1234 2 innies R4C19 = 15 = {69/78}
4a. 45 rule on C123 3 outies R1C4 + R2C46 = 1 innie R7C3 + 19
4b. R7C3 = {12} -> R1C4 + R2C46 = 20,21, no 1,2
5. 8,9 in N8 only in 26(5) cage at R8C4 = {12689/13589/23489}, no 7
6. 45 rule on N689 2 innies R7C45 = 1 outie R5C6 + 7
6a. Max R7C45 = 13 -> max R5C6 = 6
7. 45 rule on N6 4 innies R56C78 = 16 must contain 1 for N6 = {1258/1267/1357/1456} (cannot be {1249/1348} which clash with R4C78), no 9
8. Hidden killer pair 3,4 in R4C23 and 13(3) cage at R5C3 for N4, R4C23 cannot contain both of 3,4 which would clash with R4C78 (alternatively 17(3) cage at R3C2 cannot contain both of 3,4) -> 13(3) cage must contain at least one of 3,4 -> 13(3) cage = {148/238/247/346}, no 5
9. 45 rule on N3 3 innies R123C7 = 17 = {269/278/359/458/467} (cannot be {179/368} which clash with 19(3) cage at R1C9), no 1
9a. 1 in N3 only in 9(3) cage at R1C8, locked for C8
9b. 9(3) cage = {126/135}, no 4
Rest of original step 9 deleted.
10. 1 in N6 only in R56C7, locked for 12(3) cage at R5C6, no 1 in R5C6
10a. 12(3) cage = {138/147/156}, no 2
10b. 3,4 of {138/147} must be in R5C6 -> no 3,4 in R56C7
10c. R7C45 = R5C6 + 7 (step 6)
10d. Min R5C6 = 3 -> min R7C45 = 10, no 1,2 in R7C45
10e. 18(3) cage at R6C5 = {279/369/378/459/468/567} (cannot be {189} because 1,8,9 only in R6C56), no 1
11. 45 rule on N69 3 outies R578C6 = 12 = {147/237/246/345} (cannot be {156} which clashes with R34C6)
11a. 1 in C6 only in R34C6 = {17} or R578C6 = {147}, 7 locked for C6 (locking chain)
11b. 1 in C6 only in R34C6 = {17} or R578C6 = {147} -> R578C6 = {147/246/345} (cannot be {237}, locking-out chain), 4 locked for C6
[Moving up my original step 15 and slightly modifying it.]
12. Consider placements for {17} in C6 (step 11)
R34C6 = {17}, locked for 25(5) cage at R1C7 => 7 in N3 only in 19(3) cage at R1C9
or R78C6 = {17} => R5C6 = 4 (hidden single in C6) => R56C7 = 8 contains 1 = {17}, locked for C7 => 7 in N3 only in 19(3) cage at R1C9
-> 19(3) cage at R1C9 (step 1f) = {379/478}, no 2,6, 7 locked for C9 and N3, clean-up: no 8 in R4C1 (step 3)
12a. 17(3) cage at R4C9 (step 1g) = {269/359/458}
13. 9(3) cage (step 9b) = {126/135}, 19(3) cage at R1C9 (step 12) = {289/379/478}, 17(3) cage at R4C9 (step 12a) = {269/359/458}
13a. Consider placements for 2 in N6
2 in R56C8, locked for C8 => 9(3) cage = {135} => 19(3) cage = {478}
or 2 in 17(3) cage = {269}, locked for C9 => 19(3) cage = {478}
-> 19(3) cage = {478}, 4,8 locked for C9 and N3, clean-up: no 7 in R4C1 (step 3)
13b. Naked pair {69} in R4C19, locked for R4, R4C8 = 8 -> R4C7 = 4, R7C78 = [89], 8 placed for D\, clean-up: no 2 in R3C6 (step 1d)
13c. R56C78 (step 7) = {1267/1357}
13d. Killer pair 2,3 in 9(3) cage at R1C8 and R56C8, locked for C8
13e. 12(3) cage at R5C6 (step 10a) = {147/156}, no 3
13f. R7C45 = R5C6 + 7 (step 6)
13g. Min R5C6 = 4 -> min R7C45 = 11, no 3
14. R1C4 + R2C46 = R7C3 + 19 (step 4a), R7C3 = {12} -> R1C4 + R2C46 = 20, 21 = {389/569/578}{489/579/678} (cannot be {479} because 4,7 only in R2C4)
14a. R237C3 (step 2e) = {126/234} (cannot be {135} = {35}1 which clashes with R1C4 + R2C46 = 20 = {389/569/578}), no 5, 2 locked for C3
14b. R1C4 + R2C46 = {389/578}{489/579/678} (cannot be {569} which clashes with R237C3 = {26}1)
14c. 7 of {678} must be in R2C4 -> no 6 in R2C4
15. Moved to become the start of new step 12.
16. 4 in N4 only in 13(3) cage at R5C3 = {148/247/346}
16a. Consider combinations for R237C3 (step 14a) = {126/234}
R237C3 = {126}, 6 locked for N1 => 6 in C1 only in R456C1, locked for N4 => 13(3) cage = {148/247}
or R237C3 = {234}, locked for C3 => 13(3) cage = {148/247} (cannot be {346} because 3,4 only then in R6C2)
-> 13(3) cage = {148/247}, no 3,6
16b. 6,9 in N4 only in 32(7) cage at R4C1 = {1234679}, no 5,8, 7 locked for N4
16c. 13(3) cage = {148} (only remaining combination), 1 locked for N4
16d. R4C23 = {35} (hidden pair in N4), locked for R4, R3C2 = 9 (cage sum) -> R7C3 = 2 (step 2a), placed for D/, clean-up: no 6 in R8C9
[Cracked at last, the rest is fairly straightforward.]
16e. R4C45 = [21], 2 placed for D\, R4C6 = 7, placed for D/ -> R3C6 = 1 (step 1d)
16f. R2C8 = 1 (hidden single on D/)
16g. R237C3 = {234} (only remaining combination) -> R23C3 = {34}, locked for C3, N1 and 28(5) disjoint cage at R1C6 -> R4C23 = [35]
16h. Naked pair {18} in R56C3, locked for C3 and N4 -> R6C2 = 4
17a. R1C2 = 1 (hidden single in N1) -> R1C13 = 12 = [57], 5 placed for D\
17b. R2C2 = 6, placed for D\, R5C2 = 2 (hidden single in C2)
17c. R3C9 = 7 (hidden single in R3)
17d. R3C1 = 8 (hidden single in R3) -> R2C1 = 2
17e. R3C8 = 2 (hidden single in R3) -> R1C8 = 6 (cage sum)
17f. 6 in R3 only in R3C45 -> 12(4) cage at R3C4 = {1236}, 3 locked for R3 and N2
17g. R3C3 = 4, placed for D\, R2C3 = 3
17h. R123C7 = [395], 5 placed for D/
17i. R8C2 = 8, placed for D/ -> R1C9 = 4, placed for D/ -> R9C1 = 3, placed for D/
18a. R5C5 = 9, R6C4 = 6, R6C6 = 3 -> R67C5 = 15 = [87], R7C2 = 5, R7C46 = [46], R7C9 = 3 -> R8C9 = 5
18b. R23C3 = {34} = 7 -> R1C6 + R2C46 = 21 = {579} (only remaining combination) -> R1C6 = 9, R2C46 = [75]
and the rest is naked singles, without using the diagonals.