Prelims
a) R1C34 = {19/28/37/46}, no 5
b) R34C1 = {49/58/67}, no 1,2,3
c) R67C9 = {39/48/57}, no 1,2,6
d) R9C67 = {16/25/34}, no 7,8,9
e) 11(3) cage at R2C3 = {128/137/146/236/245}, no 9
f) 6(3) cage at R2C4 = {123}
g) 6(3) cage at R4C2 = {123}
h) 21(3) cage at R4C4 = {489/579/678}, no 1,2,3
i) 22(3) cage at R5C7 = {589/679}
j) 11(3) cage at R7C5 = {128/137/146/236/245}, no 9
k) 20(3) cage at R8C4 = {389/479/569/578}, no 1,2
Steps resulting from Prelims
1a. Naked triple {123} in 6(3) cage at R2C4, locked for N2, clean-up: no 7,8,9 in R1C3
1b. Naked triple {123} in 6(3) cage at R4C2, locked for N4
1c. 22(3) cage at R5C7 = {589/679}, 9 locked for N6, clean-up: no 3 in R7C9
2. 15(3) cage at R5C1 = {456} (only remaining combination), locked for N4, clean-up: no 7,8,9 in R3C1
3. 45 rule on N1 3 innies R1C13 + R3C1 = 18 = {369/459/468/567} (cannot be {189/279/378} because 7,8,9 only in R1C1), no 1,2, clean-up: no 8,9 in R1C4
3a. 7,8,9 only in R1C1 -> R1C1 = {789}
3b. Naked triple {789} in R146C1, locked for C1
4. 45 rule on N6 3 innies R4C79 + R6C9 = 9 = {135/234} (cannot be {126} because no 1,2,6 in R6C9), no 6,7,8, 3 locked for N6, clean-up: no 4,5 in R7C9
4a. 3 of 6(3) cage at R4C2 = {123} must be in R4C23 (R4C23 cannot be {12} which clashes with R4C79), no 3 in R5C3
4b. 3 in N4 only in R4C23, locked for R4
4c. R6C9 = 3 (hidden single in N6) -> R7C9 = 9
4d. Killer pair 1,2 in R4C23 and R4C79, locked for R4
5. 45 rule on N9 2 remaining innies R9C79 = 5 = [14/32/41], clean-up: no 1,2,5 in R9C6
6. 22(3) cage at R5C7 = {589/679}
6a. 5,6 must be in R6C78 (R6C78 cannot be {79/89} which clash with R6C13, ALS block) -> no 5,6 in R5C7
6b. Killer triple 7,8,9 in R6C13 and R6C78, locked for R6
7. 14(3) cage at R5C6 = {149/158/167/248/257} (cannot be {239/347} because 3,7,9 only in R5C6, cannot be {356} = 3{56} which clashes with R6C78), no 3
7a. 7,8,9 only in R5C6 -> R5C6 = {789}
7b. Killer triple 7,8,9 in 21(3) cage at R4C4 and R5C6, locked for N5
8. R5C5 = 3 (hidden single in N5), placed for both diagonals
8a. 45 rule on N5 2 remaining innies R4C6 + R6C4 = 7 = [52/61]
8b. Naked triple {123} in R236C4, locked for C4
9. 45 rule on N8 3 innies R7C4 + R9C46 = 14 = {347/356} -> R9C6 = 3, R9C7 = 4, R9C9 = 1 (step 5), placed for D\
9a. R79C4 = [47/56/65]
10. 1,2 in N8 only in 11(3) cage at R7C5 = {128}, 8 locked for N8
11. 3 in N9 only in 15(3) cage at R7C7 = {357}, locked for N9
12. 8 in C4 only in R45C4, locked for N5
12a. 21(3) cage at R4C4 contains 8 = {489/678}, no 5
12b. 5 in C4 only in R789C4, locked for N8
13. 11(3) cage at R2C3 = {128/137/236/245} (cannot be {146} which clashes with R1C13 + R3C1)
13a. 7 of {137} must be in R3C3 -> no 7 in R2C3 + R3C2
13b. 8 of {128} must be in R3C23 (R3C23 cannot be {12} which clashes with R3C5) -> no 8 in R2C3
13c. 6 of {236} must be in R3C23 (R3C23 cannot be {23} which clashes with R3C45, ALS block) -> no 6 in R2C3
14. 16(3) cage at R1C2 = {178/259/268/349/367/457} (cannot be {169/358} which clash with R1C13 + R3C1)
14a. 1 of {178} must be in R2C1 -> no 1 in R1C2
15. R1C4 = {467}, R79C4 (step 9a) = [47/56/65] -> combined half cage R179C4 = 4{56}/6{47}/7{56}, 6 locked for C4
16. 45 rule on N2 3 innies R1C46 + R3C6 = 21 = {489/579/678}
16a. 4 of {489} must be in R1C4 -> no 4 in R13C6
16b. Consider combinations for 21(3) cage at R4C4 (step 12a) = {489/678}
21(3) cage = {489}, locked for N5 => R2C6 = 4 (hidden single in C6)
or 21(3) cage = {678}, locked for N5 => R5C6 = 9 => R1C46 + R3C6 = {678}
-> no 4 in R1C4, clean-up: no 6 in R1C3
16c. R1C46 + R3C6 = {579/678}, 7 locked for N2
17. Killer pair 6,7 in R1C4 and R79C4, locked for C4
17a. 21(3) cage at R4C4 (step 12a) = {489} (only remaining combination, cannot be {678} because 6,7 only in R4C5), locked for N5 -> R5C6 = 7
18. R1C4 = 7 (hidden single in N2) -> R1C3 = 3
18a. R1C13 + R3C1 (step 3) contains 3 = {369} -> R3C1 = 6, R4C1 = 7, R1C1 = 9, placed for D\, R6C1 = 8, R6C3 = 9
19. R5C7 = 9 (hidden single in N6) -> R6C78 = 13 = {67}, locked for R6 and N6
19a. R5C6 = 7 -> R6C56 = 7 = {25}, locked for R6 -> R4C6 = 6, R6C4 = 1, both placed for D/, R6C2 = 4
20. 11(3) cage at R2C3 (step 11) = {128/245}, no 7, 2 locked for N1
20a. R2C2 = 7 (hidden single in N1), placed for D\ -> R7C7 = 5, placed for D\, R6C6 = 2, placed for D\
20b. R8C8 = 6 (hidden single on D\) -> R6C78 = [67], R7C8 = 3, R8C7 = 7
20c. R9C5 = 7 (hidden single in N8) -> R8C45 = 13 = {49}, locked for R8 and N8
21. Naked pair {18} in R78C6, locked for C6 and N8 -> R13C6 = [59], R1C2 = 8 -> R2C1 = 1 (cage sum), R3C3 = 4, placed for D\
22. Naked pair {12} in R45C3, locked for C3 and N4 -> R4C2 = 3
23. Naked pair {12} in R14C7, locked for C7 -> R3C7 = 8, placed for D/
23a. Naked pair {25} in R8C2 + R9C1, locked for N7 and D/
24. R8C3 = 8, R8C9 = 2, R1C9 = 4, R4C9 = 5, R5C9 = 8, R4C8 = 4, R5C8 = 2 (cage sum)
and the rest is naked singles, without using the diagonals.