Prelims
a) R34C3 = {17/26/35}, no 4,8,9
b) R34C4 = {16/25/34}, no 7,8,9
c) R34C5 = {39/48/57}, no 1,2,6
d) R34C6 = {29/38/47/56}, no 1
e) R34C7 = {69/78}
f) R67C5 = {19/28/37/46}, no 5
g) R89C1 = {18/27/36/45}, no 1
h) R89C4 = {59/68}
i) R89C5 = {29/38/47/56}, no 1
j) R89C6 = {29/38/47/56}, no 1
k) R89C9 = {17/26/35}, no 4,8,9
l) 11(3) cage at R4C1 = {128/137/146/236/245}, no 9
m) 21(3) cage at R4C8 = {489/579/678}, no 1,2,3
n) 10(3) cage at R5C7 = {127/136/145/235}, no 8,9
1. 1 in N8 only in R7C456, locked for R7
1a. 45 rule on N8 3 innies R7C456 = 9 = {126/135}, no 4,7,8,9, clean-up: no 1,2,3,6 in R6C5
1b. Killer pair 5,6 in R7C456 and R89C4, locked for N8
2. 45 rule on R12 2 innies R2C19 = 15 = {69/78}
2a. Min R2C9 = 6 -> max R3C89 = 6, no 6,7,8,9 in R3C89
3. 45 rule on R1234 2 outies R5C19 = 10 = [19/28/37]/{46}, no 5, no 7,8 in R5C1
4. 45 rule on R6789 2 innies R6C28 = 9 = {27/36/45}/[81], no 1,9 in R6C2
5. 45 rule on R89 2 innies R8C28 = 7 = {16/25/34}, no 7,8,9
6. 45 rule on N1 1 outie R1C4 = 1 innie R3C3 + 2, no 1,2,6 in R1C4
7. 45 rule on N3 1 innie R3C7 = 1 outie R1C6 + 6, R1C6 = {123}, R3C7 = {789}, clean-up: no 9 in R4C7
7a. 21(3) cage at R4C8 = {489/579} (cannot be {678} which clashes with R4C7), no 6, 9 locked for N6, clean-up: no 4 in R5C1 (step 3)
8. 45 rule on N6 3 innies R4C7 + R6C79 = 14
8a. Min R4C7 = 6 -> max R6C79 = 8, no 8 in R6C79
9. 45 rule on N7 1 outie R6C1 = 1 innie R7C3 + 4, R6C1 = {6789}, R7C3 = {2345}
10. 45 rule on N9 1 innie R7C7 = 1 outie R6C9 + 4, R6C9 = {12345}, R7C7 = {56789}
11. 45 rule on C1234 2 innies R25C4 = 13 = {49/58/67}, no 1,2,3
11a. Killer triple 4,5,6 in R25C4, R34C4 and R89C4, locked for C4, clean-up: no 2,3 in R3C3 (step 6), clean-up: no 5,6 in R4C3
[Ed commented “Andrew will be relieved there is no killer quad in c4 this time! (see comment at the end of his WT for A219)”. Only a killer triple this time!
]
[Oops! After going through Ed’s walkthrough, I noted that I’d missed the clash with R89C4 eliminating {58} from R25C4.]
12. 45 rule on C6789 2 innies R25C6 = 12 = {39/48/57}, no 1,2,6
13. 45 rule on C89 1 innie R9C8 = 1 outie R5C7 + 4, R5C7 = {12345}, R9C8 = {56789}
14. 12(3) cage at R8C7 = {129/138/147/237/246/345} (cannot be {156} which clashes with R89C9)
14a. R9C8 = {56789} -> no 5,6,7,8,9 in R89C7
15. 45 rule on N3 3 innies R123C7 = 19 = {289/379/568} (cannot be {469/478} which clashes with R34C7, CCC), no 1,4
[With hindsight, this 45 is good to eliminate the 1 but 45 rule on N3 2 innies R12C7 = 1 outie R4C7, IOU no 4 in R12C7 is a simpler way to eliminate the 4.]
16. 45 rule on N1 3 innies R123C3 = 13 = {139/148/157/247/256/346} (cannot be {238} because no 2,3,8 in R3C3)
16a. R12C3 cannot contain 5 because R13C3/R23C3 would clash with R34C3, CCC, no 5 in R12C3
[Similarly, with hindsight, 45 rule on N1 2 innies R12C3 = 1 outie R4C3 + 5, IOU no 5 in R12C3.]
16b. 15(3) cage at R1C3 = {168/249/267/348}
16c. 7,9 of {249/267} must be in R1C4 -> no 7,9 in R12C3
16d. R123C3 = {148/247/256/346} (cannot be {157} because 5,7 only in R3C3)
16e. 1 of {148} must be in R3C3 -> no 1 in R12C3
17. 45 rule on C123 3 outies R167C4 = 11 = {128/137}, no 9, 1 locked for C4, clean-up: no 7 in R3C3 (step 6), no 6 in R34C4, no 1 in R4C3
17a. 1 in C4 only in R67C4, locked for 15(4) cage at R6C3, no 1 in R6C3
18. 1 in C6 only in R167C6
18a. 45 rule on C789 3 outies R167C6 = 11 = {128/137/146}, no 5,9
18b. 4,7,8 of {128/137/146} must be in R6C6 -> no 1 in R6C6
19. R7C456 (step 1a) = {126} (only remaining combination), locked for R7 and N8, clean-up: no 7 in R7C5, no 8 in R89C4, no 9 in R89C5, no 9 in R89C6
20. Naked pair {59} in R89C4, locked for C4, clean-up: no 4,8 in R25C4 (step 11), no 2 in R34C4
21. R67C4 = {12} (hidden pair in C4), locked for 15(4) cage at R6C3, no 2 in R6C3
21a. 15(4) cage at R6C3 = {1239/1248/1257}
21b. 7,8,9 only in R6C3 -> R6C3 = {789}
22. R1C4 = 8 (hidden single in C4), R12C3 = 7 = {34}, locked for C3 and N1 -> R7C3 = 5, R6C3 = 7 (step 21a), R4C3 = 2, R3C3 = 6, clean-up: no 9 in R2C9 (step 2), no 9 in R3C6, no 4 in R4C5, no 3,5 in R4C6, no 4 in R5C6 (step 12), no 8 in R5C9 (step 3), no 2 in R6C8 (step 4), no 4 in R89C1, no 3 in R8C8 (step 5)
23. 45 rule on N4 1 remaining innie R6C1 = 9, clean-up: no 6 in R2C9 (step 2), no 1 in R7C5
24. Naked pair {78} in R2C19, locked for R2 -> R2C4 = 6, R5C4 = 7, clean-up: no 5 in R2C6 (step 12), no 5 in R3C5, no 4 in R3C6, no 3 in R5C1 (step 3), no 5 in R5C6 (step 12)
25. R5C4 = 7 -> R5C56 = 11 = [29/38/83], no 1,4,5,6,9 in R5C5
26. R6C4 = 1 (hidden single in N5), R7C4 = 2, R7C5 = 6, R6C5 = 4, R7C6 = 1, R34C4 = [43], clean-up: no 9 in R2C6 (step 12), no 9 in R3C5, no 7 in R3C6, no 8 in R4C5, no 8 in R5C56 (step 25), no 5,8 in R6C2, no 5 in R6C8 (both step 4), no 7 in R89C5
27. R25C6 = [39], R5C5 = 2, R12C3 = [34], R1C6 = 2, R3C7 = 8 (step 7), R4C7 = 7, R2C19 = [87], R3C5 = 7, R4C5 = 5, R3C6 = 5, R4C6 = 6, R6C6 = 8, R7C7 = 9, R6C7 = 2 (cage sum), R5C9 = 4, R5C1 = 6 (step 3), R6C2 = 3, R6C8 = 6, R6C9 = 5, clean-up: no 1,3 in R89C1, no 1,3 in R89C9
28. R5C23 = [58] (hidden pair in N4)
29. Naked pair {19} in R89C3, locked for N7, R9C2 = 8 (cage sum)
30. Naked pair {26} in R89C9, locked for C9 and N9
31. R2C9 = 7 -> R3C89 = 5 = [23], R3C12 = {19], R4C12 = [41]
32. Naked pair {27} in R89C1, locked for C1 and N7 -> R7C1 = 3, R7C9 = 8, R7C2 = 4, R7C8 = 7, R8C8 = 1 (cage sum)
and the rest is naked singles.