Ronnie has encouraged me to post my coloured cage pattern for this Christmas-themed puzzle so here it is.
I've mentioned previously in the forum that I use an Excel worksheet for solving sudokus. Here is my diagram for A187 after doing the Prelims. I normally use red for cage totals, green for candidates which I replace with blue when a cell is fixed; I've changed to black for this diagram because it gave a clearer image. I add notes, the result of applying 45s etc. in white cells below the diagram.
I've also posted another diagram in The Messier, The Merrier thread which has extra information that I used to keep track of the disjoint cages in that extremely messy cage pattern.
Here is my walkthrough for A187. It's fairly long because I didn't spot Afmob's step 1b.
Prelims
a) R78C3 = {15/24}
b) R78C7 = {18/27/36/45}, no 9
c) R89C5 = {14/23}
d) R9C12 = {49/58/67}, no 1,2,3
e) R9C89 = {18/27/36/45}, no 9
f) 8(3) cage in N1 = {125/134}
g) 22(3) cage in N3 = {589/679}
h) 10(3) cage at R1C9 = {127/136/145/235}, no 8,9
i) 6(3) cage at R4C4 = {123}
j) 21(3) cage at R8C4 = {489/579/678}, no 1,2,3
k) 40(8) cage at R6C3 = {12346789}, no 5
Steps resulting from Prelims
1a. 8(3) cage in N1 = {125/134}, 1 locked for N1
1b. 22(3) cage in N3 = {589/679}, 9 locked for N3
1c. 6(3) cage at R4C4 = {123}, CPE no 1,2,3 in R5C56
2. 45 rule on N7 2 innies R7C1 + R9C3 = 12 = [39]/{48/57}, no 1,2,6, no 9 in R7C1
3. 45 rule on N9 2 innies R7C9 + R9C7 = 12 = {39/48/57}, no 1,2,6
4. 45 rule on N1 3 innies R2C3 + R3C23 = 22 = {589/679}, 9 locked for N1, CPE no 9 in R3C4 + R4C3
5. 45 rule on N3 3 innies R2C7 + R3C78 = 13 = {148/238/247/346} (cannot be {157/256} which clash with 22(3) cage), no 5
6. 45 rule on R9 3 outies R8C456 = 20 = {389/479} (cannot be {569/578} because R8C5 only contains 1,2,3,4), no 1,2,5,6, 9 locked for R8 and N8, clean-up: no 3,4 in R9C5
6a. R8C5 = {34} -> no 3,4 in R8C46
[Here I missed 5 in N8 only in R9C46, locked for R9.]
7. 9 in 40(8) cage only in R6C34567, locked for R6
8. 45 rule on C12 2 innies R34C2 = 1 outie R1C3 + 11
8a. Min R34C2 = 12, no 1,2
9. Hidden killer pair 1,2 in 14(3) cage and R78C3 for N7, R78C3 has one of 1,2 -> 14(3) cage must have one of 1,2
9a. 14(3) cage = {158/167/239/248} (cannot be {149/257} which clash with R78C3, cannot be {347/356} which don’t contain one of 1,2)
9b. Hidden killer pair 6,7 in 14(3) cage and R9C12 for N7 (because 6 in N7 only in these cages) -> either 14(3) cage or R9C12 must contain both of 6,7
[Maybe this step is better called locking cages.]
9c. Killer pair 6,7 in 14(3) cage and R9C12, locked for N7, clean-up: no 5 in R7C1 + R9C3 (step 2)
10. 15(3) cage at R1C1 = {258/267} (cannot be {357/456} which clash with 8(3) cage, cannot be {348} which clashes with R7C1), no 3,4, 2 locked for C1 and N1, clean-up: no 5 in 8(3) cage in N1
11. 14(3) cage in N7 (step 9a) = {158/167/239/248}
11a. 3 of {239} must be in R8C1 -> no 3 in R78C2
11b. 3 in N7 only in R78C1, locked for C1
12. 21(3) cage at R8C4 = {489/579/678}
12a. 5,6 of {579/678} must be in R9C4 -> no 7 in R9C4
13. 17(3) cage at R8C6 = {179/278/359/368/458/467} (cannot be {269} because 2,6 only in R9C6)
13a. 1,2 of {179/278} must be in R9C6, 7,8 of {368/458/467} must be in R8C6 -> no 7,8 in R9C6
14. Hidden killer triple 1,2,3 in R9C5, 17(3) cage at R8C6 and R9C89 for R9, R9C5 contains one of 1,2, 17(3) cage at R8C6 and R9C89 cannot contain more than one of 1,2,3 -> 17(3) cage at R8C6 must contain one of 1,2,3 in R9C67 and R9C89 must contain one of 1,2,3
14a. 17(3) cage at R8C6 (step 13) = {179/278/359/368} (cannot be {458/467} which don’t contain any of 1,2,3), no 4, clean-up: no 8 in R7C9 (step 3)
14b. R9C89 = {18/27/36} (cannot be {45} which doesn’t contain any of 1,2,3), no 4,5
15. R9C12 = {58/67} (cannot be {49} which clashes with R7C1 + R9C3), no 4,9
[I ought to have spotted that after step 9c although it only becomes powerful after steps 14a and 14b.]
16. 4 in R9 only in R9C34 -> 21(3) cage at R8C4 = {489} (only remaining combination)
17. 9 in R89 only in R8C46 and R9C37 -> 21(3) cage at R8C4 and 17(3) cage at R8C6 must both contain 9 -> 17(3) cage (step 14a) = {179/359} (cannot be {278/368} which don’t contain 9), no 2,6,8, clean-up: no 4 in R7C9 (step 3)
18. 6 in N8 only in R7C456, locked for R7 and 40(8) cage at R6C3, no 6 in R6C34567, clean-up: no 3 in R8C7
[Even after that I still missed that R9C6 is hidden single 5 for N8.]
19. 6 in C3 only in R234C3, CPE no 6 in R3C24
20. 9 in C1 only in R45C1, locked for N4
20a. 14(3) cage in N4 = {149} (only remaining combination containing 9, cannot be {239} because 2,3 only in R5C2), locked for N4
21. 1 in 6(3) cage at R4C4 only in R45C4, locked for C4 and N5
22. Hidden killer pair 1,4 in R45C1 and R78C1 for C1, R45C1 must contain one of 1,4 -> R78C1 must contain one of 1,4
22a. Killer pair 1,4 in R78C1 and R78C3, locked for N7, clean-up: no 8 in R7C1 (step 2)
22b. Naked quint {25678} in R12369C1, locked for C1
23. 15(3) cage at R6C1 = {348/357/456} (cannot be {258/267} because R7C1 only contains 3,4), no 2
23a. 8 of {348} must be in R6C1 -> no 8 in R6C2
24. 2 in N4 only in R456C3, locked for C3, clean-up: no 4 in R78C3
25. Naked pair {15} in R78C3, locked for C3 and N7, clean-up: no 8 in R9C12
26. Naked pair {67} in R9C12, locked for R9 and N7, clean-up: no 5 in R7C9 (step 3), no 2,3 in R9C89
27. Naked pair {18} in R9C89, locked for R9 and N9 -> R9C34 = [94], R8C4 = 8, R89C5 = [32], R78C1 = [34], R78C2 = [82], R9C67 = [53], R8C6 = 9 (step 13), R7C9 = 9 (step 3), clean-up: no 5,7 in R7C7, no 6 in R8C7
28. Naked triple {167} in R7C456, locked for R7 and 40(8) cage at R6C3, no 1,7 in R6C34567 -> R78C3 = [51]
29. Naked quint {23489} in R6C34567, locked for R6
30. 15(3) cage at R6C1 (step 23) = {357} (only remaining combination), 5,7 locked in R6C12, locked for R6 and N4
31. Naked pair {16} in R6C89, locked for N6
32. 1 in C7 only in R23C7, locked for N3
33. 10(3) cage at R1C9 = {235} (only remaining combination), locked for C9 and N3
34. 22(3) cage in N3 = {679} (only remaining combination), locked for N3
35. 4 in C9 only in R45C9, locked for N6
35a. 17(3) cage in N6 = {458} (only remaining combination containing 4) -> R5C8 = 5, R45C9 = {48}, locked for C9 and N6 -> R9C89 = [81], R6C89 = [16], R8C89 = [67], R3C8 = 4, R7C8 = 2, R78C7 = [45]
36. Naked pair {79} in R12C8, locked for C8 and N3 -> R1C7 = 6, R4C8 = 3, R4C2 = 6, R9C12 = [67], R6C12 = [75], R3C2 = 9
37. Naked triple {238} in R456C3, locked for C3 -> R1C3 = 4, R23C3 = [67]
38. R5C2 = 4 (hidden single in C2), R45C9 = [48]
39. R2C3 + R3C2 = [69] = 15 -> R3C4 + R4C3 = 10 -> R4C3 = 8, R3C4 = 2, R45C4 = [13], R5C3 = 2, R6C4 = 9, R2C4 = 5
40. 35(7) cage at R2C4 = {1345679} (only combination without 2), no 8
and the rest is naked singles.
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