Prelims
a) R1C12 = {16/25/34}, no 7,8,9
b) R1C34 = {16/25/34}, no 7,8,9
c) R1C67 = {18/27/36/45}, no 9
d) R2C12 = {69/78}
e) R34C1 = {18/27/36/45}, no 9
f) R34C2 = {15/24}
g) R34C8 = {49/58/67}, no 1,2,3
h) R34C9 = {19/28/37/46}, no 5
i) R45C6 = {19/28/37/46}, no 5
j) R6C67 = {49/58/67}, no 1,2,3
k) R8C34 = {13}
l) R9C67 = {18/27/36/45}, no 9
m) 19(3) cage at R1C8 = {289/379/469/478/568}, no 1
n) 9(3) cage at R5C7 = {126/135/234}, no 7,8,9
o) 10(4) cage at R2C7 = {1234}
Steps resulting from Prelims
1a. Naked pair {13} in R8C34, locked for R8
1b. 10(4) cage at R2C7 = {1234}, CPE no 1,2,3,4 in R1C7, clean-up: no 5,6,7,8 in R1C6
2. R1C67 = [18/27] (cannot be [36/45] which clash with the pair of 7(2) cages at R1C1 and R1C34
2a. Killer triple 1,2,3 in R1C12, R1C34 and R1C6, locked for R1
2b. 3 in R1 only in R1C12 and R1C34 -> one of the 7(2) cages at R1C1 and R1C34 must be {34}, 4 locked for R1 (locking cages)
[Alternatively 45 rule on R1 3 innies R1C589 = 22 = {589/679}
Hidden killer pair 7,8 in R1C589 and R1C7 -> R1C7 = {78}, R1C6 = {12}…]
3. 45 rule on R1 1 innie R1C5 = 1 outie R2C9 + 3, no 7,8,9 in R2C9
4. 45 rule on C6789 3 outies R169C6 = 13 = {139/148/157/238/247/256} (cannot be {346} because R1C6 only contains one of 1,2)
4a. R1C6 = {12} -> no 1,2 in R9C6, clean-up: no 7,8 in R9C7
5. 45 rule on N9 2 outies R6C89 = 1 innie R9C7 + 11, min R6C89 = 12, no 1,2 in R6C89
6. 45 rule on R1234 2 innies R4C56 = 9 = {18/27/36}/[54], no 4,9 in R4C5, no 9 in R4C6, clean-up: no 1 in R5C6
7. 45 rule on R6789 2 innies R6C15 = 4 = {13}, locked for R6
8. 18(3) cage at R5C1 = {189/369/378} (cannot be {279/459/468/567} because R6C1 only contains one of 1,3), no 2,4,5
8a. R6C1 = {13} -> no 1,3 in R5C12
9. 45 rule on R1 3 innies R1C589 = 22 = {589/679}
9a. 8 of {589} must be in R1C89 (cannot be 8{59} because 19(3) cage at R1C8 cannot be {59}5), no 8 in R1C5, clean-up: no 5 in R2C9 (step 3)
9b. 8 in R1 only in R1C789, locked for N3, clean-up: no 5 in R4C8, no 2 in R4C9
10. 45 rule on C89 2 innies R28C8 = 1 outie R5C7 + 1
10a. Min R28C8 = 3 -> min R5C7 = 2
10b. Max R28C8 = 7 -> max R8C8 = 6
11. 18(3) cage at R7C7 = {279/369/459/468/567} (cannot be {189/378} because R8C8 only contains 2,4,5,6), no 1
11a. 2 of {279} must be in R8C8 -> no 2 in R78C7
12. 45 rule on N2 1 outie R4C4 = 2 innies R1C46 + 3
12a. Min R1C46 = 3 -> min R4C4 = 6
12b. Max R1C46 = 6 -> max R1C4 = 5, clean-up: no 1 in R1C3
13. Max R4C7 + 9(3) cage at R5C7 = 13(4) must contain 1, locked for N6, clean-up: no 9 in R3C9
14. 45 rule on C89 4(3+1) innies R258C8 + R5C9 = 10
14a. Min R258C8 = 6 -> max R5C9 = 4
15. 22(5) cage at R6C4 = {12469/12478/12568/23458/23467} (cannot be {12379/13459/13468/13567} which clash with R8C4)
15a. Killer pair 1,3 in 22(5) cage and R8C4, locked for N8, clean-up: no 6 in R9C7
16. R169C6 (step 4) = {148/157/247/256}, no 9, clean-up: no 4 in R6C7
17. 45 rule on C789 3 innies R169C7 = 18 = {189/279/378/468/567} (cannot be {369/459} because R1C7 only contains 7,8)
17a. 5 of {567} must be in R9C7 -> no 5 in R6C7, clean-up: no 8 in R6C6
[Can “chain” down C7 to eliminate 3,4 from R78C7 but I’ll leave that for now.]
18. 45 rule on R12 4 innies R2C3678 = 15 = {1239/1248/1257/1347/1356} (cannot be {2346} which clashes with R2C9), 1 locked for R2
19. 34(6) cage at R8C5 = {145789/235789/245689/345679} (cannot be {136789} which clashes with R8C3), CPE no 5 in R9C6, clean-up: no 4 in R9C7
19a. R169C6 (step 16) = {148/157/247/256}
19b. 6 of {256} must be in R9C6 -> no 6 in R6C6, clean-up: no 7 in R6C7
20. 45 rule on N36 4(1+3) innies R1C7 + R6C789 = 29
20a. R1C7 = {78} -> R6C789 = 21,22 = {579/589/679} (cannot be {489} because 8{49} clashes with R1C7 and 9{48} clashes with R6C67, CCC, cannot be {678} because no {468} in R169C7), no 4 in R6C89, 9 locked for R6 and N6, clean-up: no 4 in R3C8, no 1 in R3C9
20b. 6 of {679} must be in R6C89 (R6C789 cannot be 6{79} which clashes with R6C67, CCC), no 6 in R6C7, clean-up: no 7 in R6C6
21. R169C7 (step 17) = {189/279/378}, no 5, clean-up: no 4 in R9C6
21a. Naked quad {1234} in 10(4) cage at R2C7 and R9C7, locked for C7, 4 also locked for 10(4) cage, no 4 in R2C8
22. 9(3) cage at R5C7 = {126/135} (cannot be {234} because R5C7 only contains 5,6), no 4, 1 locked for R5 and N6
22a. R5C7 = {56} -> no 5,6 in R5C8
22b. 4 in N6 only in R4C789, locked for R4, clean-up: no 5 in R3C1, no 2 in R3C2, no 6 in R5C6
23. R28C8 = R5C7 + 1 (step 10)
23a. Min R5C7 = 5 -> min R28C8 = 6, max R2C8 = 3 -> no 2 in R8C8
[Alternatively 38(7) cage at R6C8 must contain two of 1,2,3 -> killer triple 1,2,3 in 38(7) cage and R9C7, locked for N9]
24. Killer pair 5,6 in R5C7 and R6C89, locked for N6, clean-up: no 7 in R3C8, no 4 in R3C9
[In feedback to one of my walkthroughs about a couple of years ago udosuk commented “Andrew sometimes needs to look deeper to get more out of his steps”. Excellent advice for all of us. With hindsight this applies to step 25a which I could have done immediately after step 20b.]
25. R6C789 (step 20a) = {579/589/679}
25a. 9 of {579/679} must be in R6C7, 9 of {589} must be in R6C7 (R6C789 cannot be 8{59} which clashes with R6C67, CCC) -> R6C7 = 9, R6C6 = 4, clean-up: no 6 in R4C6
25b. R169C7 (step 21) = {189/279}, no 3, clean-up: no 6 in R9C6
26. R5C3 = 4 (hidden single in R5), clean-up: no 3 in R1C4
27. 3 in N9 only in 38(7) cage at R6C8 = {1346789/2345789}, 4 locked for N9
27a. 18(3) cage at R7C7 (step 11) = {567} (only remaining combination), locked for N9, 7 also locked for C7 -> R1C7 = 8, R1C6 = 1, clean-up: no 6 in R1C123, no 9 in R5C6
27b. R169C7 (step 25b) = {189} (only remaining combination) -> R9C7 = 1, R9C6 = 8
[Oops! I forgot to manually eliminate 8 from R45C6 and the resulting clean-up for R45C6, which would have made my solving path a bit shorter.]
28. Naked quad {2345} in R1C1234, locked for R1, clean-up: no 2 in R2C9 (step 3)
28a. R2C8 = 1 (hidden single in N3)
29. 38(7) cage at R6C8 (step 27) = {2345789} (only remaining combination), no 6
30. R5C7 = 6 (hidden single in N6), R8C8 = 6 (hidden single in N9), clean-up: no 7 in R4C8
30a. 9(3) cage at R5C7 (step 22) = {126} (only remaining combination) -> R5C89 = [21]
30b. 2 in N3 only in 10(4) cage at R2C7, locked for N3, clean-up: no 8 in R4C9
30c. 3 in N6 only in R4C79, locked for R4, clean-up: no 6 in R3C1, no 7 in R5C6
31. 18(3) cage at R5C1 (step 8) = {189/378}, 8 locked for R5 and N4 -> R5C6 = 3, R4C6 = 7, R6C5 = 1, R6C1 = 3, clean-up: no 4 in R1C2, no 1,2 in R3C1, no 3 in R3C9, no 6 in R4C1
31a. Naked pair {59} in R5C45, locked for R5 and N5
31b. Naked pair {78} in R5C12, locked for N4
31c. Naked triple {348} in R4C789, locked for R4 and N6 -> R4C4 = 6, R4C5 = 2, R6C4 = 8, clean-up: no 7 in R3C1, no 4 in R3C2
32. Naked pair {15} in R4C12, locked for R4 and N4 -> R4C3 = 9
32a. Naked pair {15} in R34C2, locked for C2, clean-up: no 2 in R1C1
33. R6C23 = {26} = 8 -> R7C23 = 12 = [48/93] (cannot be {57} which clashes with R7C7)
34. 18(3) cage at R7C1 = {279/369/468/567} (cannot be {189/378/459} which clash with R7C23), no 1
35. R8C3 = 1 (hidden single in N7), R8C4 = 3
36. R7C6 = 6 (hidden single in C6), R7C4 = 1 (hidden single in N8)
36a. R6C4 + R7C46 = [816] = 15 -> R7C5 + R8C6 = 7 = [52], R5C45 = [59], R78C7 = [75], clean-up: no 2 in R1C3
36b. Naked pair {59} in R23C6, locked for N2
36c. Naked pair {47} in R89C5, locked for C5 and 34(6) cage in R8C5 -> R1C5 = 6, R9C4 = 9, R2C9 = 3 (step 3), R4C9 = 4, R3C9 = 6, R4C7 = 3, R4C8 = 8, R3C8 = 5, R34C2 = [15], R4C1 = 1, R3C1 = 8, R2C5 = 8, R2C4 = 4 (cage sum)
and the rest is naked singles.
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We'd driven across Canada in our younger daughter's car from Lethbridge, Alberta to St. John's, Newfoundland.