Wow! I’ve never tried a killer like this before. The first hard work was setting up the worksheet (fortunately Copy and Paste was very helpful) and colouring the cages. Then I had to decide how to describe the cells. I could have labelled them A to U and 1 to 15. However since some analysis will almost certainly be needed in each grid, I’ll label the grids G1 to G5 and use the normal rows and columns for each grid; then some cells in the overlapping areas will have different descriptions depending on which grid is being analysed; for example G1R7C7 is also G3R1C1.
If I've made any errors, including typos (I often typed R instead of G, I think I've corrected most of those typos), or anything needs clarification, please let me know by PM. I think I missed some clean-ups; no need to comment on them.
When you make any placements in the cross-over areas, remember to make all the appropriate candidate eliminations. I overlooked a few and had to go back and add more clean-ups. When I've used naked pairs in the cross-over areas, I've tried to state which areas they apply to.
Prelims (grouped because there are so many)
a) 4(2) cages = {13}
b) 5(2) cages = {14/23}
c) 6(2) cage at G5R9C4 = {15/24}
d) 7(2) cages = {16/25/34}, no 7,8,9
e) 8(2) cages = {17/26/35}, no 4,8,9
f) 9(2) cages = {18/27/36/45}, no 9
g) 10(2) cages = {19/28/37/46}, no 5
h) 11(2) cages = {29/38/47/56}, no 1
i) 13(2) cages = {49/58/67}, no 1,2,3
j) 14(2) cages = {59/68}
k) 15(2) cages = {69/78}
l) 17(2) cage at G1R7C9 = {89}
m) 8(3) cage at G4R4C5 = {125/134}
n) 10(3) cages = {127/136/145/235}, no 8,9
o) 11(3) cages = {128/137/146/236/245}, no 9
p) 19(3) cages = {289/379/469/478/568}, no 1
q) 20(3) cages = {389/479/569/578}, no 1,2
r) 21(3) cage at G4R1C3 = {489/579/678}, no 1,2,3
s) 22(3) cage at G4R4C8 = {589/679}
t) 24(4) cages = {789}
u) 14(4) cage at G2R1C5 = {1238/1247/1256/1346/2345}, no 9
v) 26(4) cage at G2R8C3 = {2789/3689/4589/4679/5678}, no 1
w) 28(4) cage at G4R6C3 = {4789/5689}, no 1,2,3
Steps resulting from Prelims
1a. Naked pair {13} in G2R8C67, locked for G2R8
1b. Naked pair {13} in G5R23C9, locked for G5C9 and G5N3, clean-up: no 5,7 in G5R4C8, no 6,8 in G5C45C9
1c. Naked pair {13} in G5R5C67, locked for G5R6
1d. Naked pair {89} in G3R1C34, locked for G3R1
1e. 8(3) cage at G4R4C5 = {125/134}, 1 locked for G4N5, clean-up: no 9 in G4R5C7
1f. 22(3) cage at G4R4C8 = {589/679}, 9 locked for G4N6
1g. Naked triple {789} in 24(3) cage at G2R1C1, locked for G2N1, clean-up: no 1,2,3 in G2R2C4, no 2,3,4 in G2R4C2
1h. Naked triple {789} in 24(3) cage at G5R2C1, locked for G5N1 (which is also G3N9)
2. 45 rule on G1N7, 1 innie G1R7C3 = 3, clean-up: no 8 in G1C78C1
2a. 1 in G1N7 only in 12(3) cage at G1R9C1, locked for G1R9
2b. 12(3) cage = {129/147/156}, no 8
3. 45 rule on G5C9, 1 innie G5R1C9 = 8, clean-up: no 1 in G5R1C56, no 1 in G5R2C4
4. 45 rule on G4R9, 1 outie G4R8C6 = 7, G4R9C67 = 3 = {12}, locked for G4R9, clean-up: no 3 in G4R5C7, no 3 in G4R7C9, no 4 in G4R8C78, no 9 in G4R9C12, no 9 in G4R9C89
5. 45 rule on G1N12345678 1 outie G1R7C7 = 1
5a. 12(3) cage at G1R7C8 = {237/246/345}, no 8,9
[I found steps 5, 7, 8 and 9 easy to spot because I’d noticed these outies when I was colouring the cages.
]
6. G2R9C1 = 1 (hidden single in G2N7), clean-up: no 4 in G2R6C2
7. 45 rule on G2N12345689 1 outie G2R7C3 = 5
8. 45 rule on G4N12456789 1 outie G4R3C7 = 6, clean-up: no 3 in G3R8C5, no 7 in G4R4C2, no 4 in G4R5C6, no 5 in G4R8C8
9. 45 rule on G5N23456789 1 outie G5R3C3 = 1, G5R23C9 = [13], clean-up: no 8 in G3R8C5, no 8 in G5R8C2
10. G5R1C4 = 1 (hidden single in G5R1), G5R2C4 = 8, clean-up: no 6 in G5R4C5, no 5 in G5R9C5
11. Naked pair {79} in G5R2C12, locked for G5R2, G5N1 and G3R8 -> G5R3C2 = 8, clean-up: no 1 in G3R8C5, no 2 in G3R9C5
12. 8,9 in G5R1 only in 23(4) cage at G5R1C7 = {2489} (only remaining combination), locked for G5N3, clean-up: no 6 in G5R4C8
13. 5 in G5R2 only in 14(3) cage at G5R2C5 = {356} (only remaining combination), locked for G5R2, 3 also locked for G5N2, clean-up: no 6 in G5R1C56
14. Killer pair 2,4 in G5R1C56 and 23(4) cage at G5R1C7, locked for G5R1
15. Naked triple {356} in G5R1C123, locked for G5R1, G5N1 and G3R7, clean-up: no 4 in G5R1C56
16. Naked pair {27} in G5R1C56, locked for G5R1 and G5N2
17. G5R2C8 = 2 (hidden single in G5N3), G5R2C3 = 4, G5R3C1 = 2, clean-up: no 5 in G3R9C5, no 6 in G5R3C8, no 5 in G5R8C2, no 3 in G5R8C7
17a. Naked pair {13} in G5R4C8 + G5R5C7, locked for G5N6
17b. 6 in G5N3 only in G5R23C7, locked for G5C7, clean-up: no 8 in G5R9C8
18. G3R9C7 = 2 -> G3R89C6 = 9 = [54/63] (cannot be {18} because 1,8 only in G3R8C6)
19. 45 rule on G1N3 2 innies G3R3C78 = 5 = [23/32/41], G3R4C8 = {789}
19a. G1R23C9 = {16/25} (cannot be {34} which clashes with G3R3C78), no 3,4
19b. Killer pair 1,2 in G1C23C9 and G1R3C78, locked for G1N3
19c. Killer pair 5,6 in G1C2C78 and G1R23C9, locked for G1N3
19d. 7 in G1N3 only in 19(3) cage at G1R1C7, locked for G1R1
20. 15(3) cage at G3R1C5 = {267} (only remaining combination), locked for G3R1, 2 also locked for G3N2 -> G3R1C2 = 4, G3R1C8 = 3, clean-up: no 7 in G1R8C1, no 8 in G2R4C2, no 2 in G2R6C1
20a. G3R1C8 = 3 -> G3R2C78 = 10 = [46/64/82], no 7,9
20b. G3R1C2 = 4 -> G3R2C23 = 8 = {35} (cannot be {26} which clashes with G3R2C78), locked for G3R2, G3N1 and G1R8, clean-up: no 6 in G1R7C1
21. 11(3) cage at G3R2C4 = {146} (only remaining combination), locked for G3R2 and G3N2 -> G3R2C78 = [82], G2R6C2 = 1, G2R6C1 = 4, clean-up: no 9 in G2R4C2
21a. Naked pair {27} in G3R1C56, locked for G3R1 and G3N2 -> G3R1C7 = 6
22. 45 rule for G2C1 1 remaining innie G2R1C1 = 9, clean-up: no 5 in G2R1C89
22a. Naked pair {68} in G2R1C89, locked for G2R1 and G2N3 -> G2R12C2 = [78], clean-up: no 2 in G2R2C3, no 5,7 in G2R4C8
23. Naked pair {79} in G2R89C3, locked for G2C3, G2N7 and G3C9 -> G2R9C2 = 4, G3R4C8 = 6 (cage sum), G3R7C8 = 5, G3R7C7 = 3, G3R7C9 = 6, G3R6C8 = 1 (cage sum) , clean-up: no 3 in G5R8C2
24. G2R5C2 = 9 (hidden single in G2C2), G2R5C34 = 10 = [28/37/64/82], no 3,5,6 in G2R5C4
25. 45 rule on G4C1 3 innies G4R159C1 = 8 = {125/134}, 1 locked for G4C1, clean-up: no 1,2 in G4R1C2, no 3,4,5 in G4C9C2
26. 45 rule on G1N1 3 innies G1R3C123 = 21 = {489/579/678}, no 1,2,3
27. 2,6 in G1N9 only in G1R9C789, locked for G1R9
28. 12(3) cage at G1R9C1 = {147} (only remaining combination), locked for G1R9 and G1N7
28a. 5 in G1N7 only in G1R7C12, locked for G1R7
29. 3,5 in G1R9 only in 22(5) cage at G1R8C4 = {13459/23458} (cannot be {13567} because 1,6,7 only in G1R8C46), no 6,7
29a. 1,2,4 only in G1R8C46 = {14/24}, 4 locked for G1N8
30. 45 rule on G5N8 2 innies G5R7C46 = 12 = {39/57}/[48], no 1,2,6, no 4 in G5C7C6
31. 12(3) cage at G5R7C5 = {138/147/156/237/246} (cannot be {129/345} which clash with G5R9C45), no 9
31a. 1 in G5N8 only in G5R789C5, locked for G5C5
32. 12(3) cage at G5R9C1 = {138/147/156/237/246} (cannot be {129/345} which clash with G5R9C45), no 9
33. 24(4) cage at G5R6C9 contains both of 6,9, cannot both be in G5R789C9 which would clash with G5C9C78 -> G5R6C9 = {69}
33a. Killer pair 6,9 in G5C789C9 and G5R9C78, locked for G5N9
34. Hidden killer pair 1,3 in G5R7C78 and G5R8C78 for G5N9, G5R8C78 contains one of 1,3 -> G5R7C78 must contain one of 1,3
34a. 45 rule on G5N9 2 innies G5R7C78 = 1 outie G5R6C9 + 2
34b. G5R6C9 = {69} -> G5R7C78 = 8,11 = {17/35/38} (other combinations don’t contain either of 1,3), no 2,4
35. 8 in G5C8 only in 17(3) cage at G5R5C8 = {368/458}, no 1,7,9
36. G5R3C8 = 7 (hidden single in G5C8), G5R4C8 = 1, G5R5C67 = [13], clean-up: no 4 in G5R8C7
37. Killer pair 3,4 in 17(3) cage at G5R5C8 and G5R8C8, locked for G5C8 -> G5R1C78 = [49], clean-up: no 5 in G5R9C7
38. Naked pair {56} in G5R23C7, locked for G5C7
39. G5R7C78 (step 35) = {38} (only remaining combination, cannot be {17} because 1,7 only in G5R7C7, cannot be {35} because 3,5 only in G5R7C8) -> G5R7C8 = 3, G5R7C7 = 8, G5R8C8 = 4, G5R8C7 = 1, G5R9C7 = 9, G5R9C8 = 5, clean-up: no 5,8 in G5R8C3, no 6 in G5R8C6, no 1 in G5R9C5
39a. Naked pair {24} in G5R9C45, locked for G5R9 and G5N8
40. G5R7C46 (step 30) = {57} (only remaining combination), locked for G5R7 and G5N8, clean-up: no 8 in G5R89C6
40a. G5R89C6 = [96], G5R7C5 = 1, G5R8C45 = [38], clean-up: no 6 in G5R3C5, no 6 in G5R8C2
41. Naked pair {27} in G5R8C23, locked for G5R8 and G5N7 -> G5R7C3 = 9, 24(4) cage at G5R6C9 = [9267]
42. G5R8C1 = 5 -> G5R67C1 = 12 = [84], G5R56C8 = [86], 12(3) cage at G5R9C1 = [138], G5R7C2 = 6, G5R56C2 = 5 = [41], G5R45C9 = [45]
43. 17(3) cage at G5R4C1 = {269} (only remaining combination) -> G5R4C2 = 2, G5R8C23 = [72], G5R2C12 = [79], G5R46C7 = [72], G5R5C3 = 7
44. G5R67C7 = [28] = 10 -> G5R67C6 = 12 = {57} (only remaining combination), locked for G5C6 -> G5R2C6 = 3, G5R34C6 = [48], G5R3C7 = 6 (cage sum), G5C2C57 = [65]
45. Naked pair {59} in G5R34C5, locked for G5C5 -> G5R5C5 = 2, G5R1C56 = [72], G5R9C45 = [24], G5R6C5 = 3, G5R5C4 = 9 (cage sum), G5R34C5 = [95], G5R34C4 = [56], G5R46C3 = [35], G5R45C1 = [96], G5R67C4 = [47], G5R67C6 = [75]
[That’s finished G5. It had become “isolated” so I focussed on it.]
46. G3R5C8 = 7 -> G3R5C67 = 9 = {45} (only remaining combination because 1,3,6,8 only in G3C5C6), locked for G3R5
47. 45 rule on G3R5 3 innies G3R5C159 = 12 = {129/138} -> G3R5C5 = 1
47a. 9 of {129} must be in G3R5C1 -> no 2 in G3R5C1
48. G3R89C6 (step 18) = [63] (cannot be [54] which clashes with G3R5C6)
49. G3C89C5 = [54] (cannot be [27] which clashes with G3C1C5)
50. G3R2C5 = 6
50a. 45 rule on G3C5 1 remaining innie G3R1C5 = 2, G3R1C6 = 7
51. G3R7C7 = 3 -> 22(4) cage at G3R6C6 = {2389} (only remaining combination) -> G3R6C7 = 9, G3R67C6 = {28}, locked for G3C6
52. G3R2C6 = 1 (hidden single in G3C6), G3R2C4 = 4
53. 15(3) cage at G3R8C4 = {159} (only remaining combination, cannot be {258} because 2,8 only in G3R8C4, cannot be {348/357} because 3,4,5 only in G3R9C3) -> G3R8C4 = 1, G3R9C34 = [59], G3R1C34 = [98], G3R2C23 = [53], clean-up: no 9 in G1R2C7, no 2 in G1R8C1, no 6 in G4R9C8
54. G3R9C2 = 7 -> G3R8C23 = 10 = {28}, locked for G3R8, G3N7 and G4R2 -> G3R8C1 = 3, clean-up: no 8 in G4R8C8, no 4 in G4R9C9
55. G3R2C1 = 7
56. 17(3) cage at G3R4C1 = {458} (only remaining combination) -> G3R5C1 = 8, G3R46 = {45}, locked for G3C1 and G3N4, G3R3C1 = 2, G3R7C1 = 9, clean-up: no 3 in G1R3C8 (step 19), no 7 in G1R4C8
57. G3R78C1 = [93] = 12 -> G3R67C2 = 7 = [61], G3R3C23 = [86], G3R8C23 = [28], G3R5C3 = 2, G3R5C9 = 3, G3R5C24 = [96], G3R4C2 = 3, clean-up: no 1 in G1R23C9, no 7 in G4R1C2, no 2 in G4R78C9, no 9 in G4R8C7, no 3 in G4R9C8
58. G3R6C1 = 4 (hidden single in G3R6), G3R4C1 = 5, G3R4C67 = [94], G3R3C6 = 5, G3R5C67 = [45], G3R3C45 = [39], G3R23C9 = [97], clean-up: no 8 in G2R9C45
59. G3R46C3 = [17], G3R7C3 = 4, G3C67C4 = [52], G3R4C45 = [78], G3R46C9 = [28], G3R67C5 = [37], G3R67C6 = [28], clean-up: no 6 in G4R78C9, no 7 in G4R9C8
[Now G3 is finished, so the three remaining grids are all “isolated”. I’ll work on each grid separately and will revert to normal RmCn descriptions for the cages and cells. It will make the remaining steps easier to read, and save me some typing
]
Grid 160. Naked pair {25} in R23C9, locked for C9 and N3 -> R3C8 = 1, R4C8 = 9, R3C7 = 4 (step 19)
61. R2C78 = [86], 19(3) cage at R1C7 = [937]
62. Naked triple {148} in 13(3) cage at R4C9, locked for N6
63. R56C8 = {27} = 9 -> R5C7 = 3
64. Naked triple {359} in R9C456, locked for N8
64a. {359} = 17 -> R8C46 = 5 = {14}, 1 locked for R8
65. R3C123 (step 26) = {579/678}, 7 locked for R3 and N1
66. 10(3) cage at R1C3 = {136/145/235}
66a. Killer pair 5,6 in 10(3) cage and R3C123, locked for N1
67. 14(3) cage at R1C1 = {149/248} (cannot be {239} because 3,9 only in R2C1), no 3
68. R2C2 = 3 (hidden single in N1) -> R12C3 = 7 = [25/52/61], no 4, no 1 in R1C3
69. 45 rule on N1 1 innie R3C3 = 1 outie R4C2 + 4, no 7 in R3C3, no 6,7,8 in R4C2
70. 17(3) cage at R3C1 contains 7 for R3 = {179/278/467}, no 5, clean-up: no 9 in R3C3 (step 69)
70a. 5 in N1 only in R123C3, locked for C3
71. 45 rule on N2 2 outies R4C5 = 1 innie R3C46 + 3
71a. Min R3C46 = 5 -> R4C5 = 8, R3C46 = 5 = {23}, locked for R3 and N2 -> R23C9 = [25]
71b. R4C5 = 8 -> R23C5 = 10 = [19/46]
72. 8 in R3 only in R3C123 (step 65) = {678}, locked for R3 and N1 -> R3C5 = 9, R2C5 = 1 (step 71b), R2C3 = 5, R1C3 = 2
73. Naked pair {14} in R1C12, locked for R1 and N1 -> R2C1 = 9, R8C1 = 6, R7C1 = 5, R8C5 = 2, R67C5 = 12 = [57], R1C5 = 6, R5C5 = 4, R6C7 = 6, R4C7 = 5, R9C5 = 3
74. R34C7 = [45] = 9 -> R34C6 = 9 = [27/36]
75. R8C6 = 1 (hidden single in C6), R8C4 = 4, R2C46 = [74]
76. R5C5 = 4 -> R5C46 = 15 = {69}, locked for R5 and N5 -> R4C6 = 7, R3C6 = 2 (step 74), R3C4 = 3, R67C6 = [38], R1C46 = [85], R9C46 = [59], R5C46 = [96], R7C4 = 6
77. R7C34 = [36] = 9 -> R6C34 = 8 = [71], R56C8 = [72]
78. R4C1 = 3 (hidden single in R4), R56C1 = 10 = [28], 13(3) cage at R4C9 = [184], R4C234 = [462], R3C123 = [768], R5C23 = [51], R6C2 = 9, R8C23 = [89], R7C2 = 2, R9C3 = 4, R9C12 = [17], R1C12 = [41]
Grid 279. Naked pair {69} in R9C45, locked for R9 and N8
80. 14(4) cage at G2R1C5 contains 5 for R1 = {2345} (cannot be {1256} which clashes with R1C34), no 5 in R2C6
80a. 1 in R1 only in R1C34 = {14}, locked for R1
80b. 4 in {2345} must be in R2C6 -> R2C6 = 4, R1C34 = [41], clean-up: no 6 in R2C34, no 7 in R23C5
81. 15(3) cage at R2C7 = {159} (only remaining combination), locked for R2 and N3 -> R2C34 = [37], R23C1 = [25], R34C2 = [65], R2C5 = 6, R3C5 = 2, R3C3 = 1, R9C45 = [69], clean-up: no 4,8 in R4C8
82. Naked pair {35} in R1C56, locked for R1 and N2 -> R1C7 = 2
83. 16(4) cage at R3C3 contains 1 = {1249} (cannot be {1348} because 3,4 only in R4C4) -> R3C4 = 9, R4C34 = [24]
84. R5C2 = 9 -> R5C34 = 10 = [82], R6C3 = 6, R67C4 = [38]
85. R8C4 = 5 -> R678C5 = 19 = {478} (only remaining combination) -> R6C5 = 8, R78C5 = {47}, locked for C5 and N8
86. R45C5 = [15] = 6 -> R5C67 = 13 = {67}, locked for R5 -> R45C1 = [73]
86a. R1C56 = [35]
87. 10(3) cage at R5C8 = {127/145}, 1 locked for C8
87a. Killer pair 4,7 in R3C8 and 10(3) cage, locked for C8 -> R8C8 = 6, R1C89 = [86], R4C8 = 9, R3C8 = 4
88. R34C6 = [86], R34C7 = [73], R5C67 = [76], R5C8 = 1, 15(3) cage at R3C9 = [384]
89. R9C8 = 3 (hidden single in C8), R9C679 = [285], R6C67 = [95], R7C67 = [14], R8C67 = [31], R78C5 = [74], 15(3) cage at R2C7 = [951], R67C8 = [72], R678C9 = [297]
And finally Grid 490. 45 rule on R1 1 remaining innie R1C6 = 2, R9C67 = [12], clean-up: no 6 in R1C2, no 8 in R5C67, no 9 in R8C8
90a. Naked pair {35} in R1C12, locked for R1 and N1, clean-up: no 8 in R4C2
91. 10(3) cage at R2C2 = {145} (only remaining combination) -> R2C4 = 5, R2C23 = {14}, locked for R2 and N1, clean-up: no 9 in R4C2
92. Naked quad {6789} in R1C45 and R2C56, locked for N2, 8 also locked for R1, 9 also locked for R2
93. 45 rule on N9 2 remaining innies R7C78 = 11 = [56/74/83], R7C7 = {578}, R7C8 = {346}
93a. R78C9 = {19} (hidden pair in N9), locked for C9
94. 22(3) cage at R4C8 = {679} (only remaining combination, cannot be {589} because 5,8,9 only in R45C8) -> R4C9 = 7, R45C8 = {69}, locked for C8 and N6 -> R8C8 = 3, R8C7 = 8, R9C9 = 6, R9C8 = 5, R7C7 = 7, R67C8 = [84], clean-up: no 3 in R5C6, no 1 in R6C2, no 4 in R8C23
95. R7C7 = 7 -> R6C67 + R7C6 = 10 = {136/145} -> R6C7 = 1, R5C7 = 4, R5C6 = 6, R67C6 = [45], R23C6 = [93], R4C67 = [85], R4C2 = 4, R3C2 = 9, R45C8 = [69], R2C23 = [14], clean-up: no 6 in R8C3
96a. Naked pair {23} in R67C2, locked for C2 -> R1C12 = [35], R8C2 = 6, R8C3 = 1, R9C1 = 4, R9C2 = 7
97. R5C1 = 1 (hidden single in C1), R5C2 = 8, R5C3 = 7 (cage sum), R1C3 = 6, R2C1 = 7, R2C5 = 6, R3C5 = 4 (cage sum), R3C4 = 1
98. 8(3) cage at R4C5 = {125} (only remaining combination) -> R4C5 = 1, R5C45 = [25], R56C9 = [32], R67C2 = [32], R78C9 = [19], R8C1 = 5, R8C45 = [42]
99. R2C1 = 7 -> R34C1 = 10 = [82], R34C3 = [29], R4C4 = 3, R67C1 = [69], R67C3 = [58], R7C4 = 6, R6C4 = 9 (cage sum), 20(3) cage at R9C3 = [389], R1C45 = [78], R67C5 = [73]