This is my solve path for Whirlpool Sudoku by donut and chicken.
1. The killer cage in R2C8 and R2C9 sums to 4, and must be 1 and 3.
2. R2C7 must repeat in R3C6, as the former sees every other cell in its region. Neither square can be a 1 or 3.
3. 1 is now restricted to R5C7 in its region; other cells can see the 4 killer cage, or appear in a two-cell 11 cage, or cannot be a 1 thanks to step 2.
4. 3 must appear in R3C7 or R4C7 (and the other must be an 8 because of the 11 cage). All other cells in the region either see the 4 cage, or cannot be a 3 thanks to step 2.
5. 8 cannot be place in the 4 cage, and all other cells in R2 see the 11 cage. This places an 8 in R2C1.
6. R3C2 must repeat in R4C3, as it sees all other cells in its region. These cells cannot contain an 8, or the 11 cage would have no fill.
7. R9C2 must be an 8. All other cells in the region see an 8, or is ruled out by step 6.
8. R8C9 must be an 8. All other cells in the region see an 8, or is ruled out by a 7 cage.
9. R1C8 must be an 8. All other cells in the row see an 8.
10. There must be an 8 in the 13 cage. All other cells in the region see an 8, or is ruled out by step 6.
11. R3C7 must be a 3, and R4C7 must be an 8. The 13 cage is a 1/4/8 triple.
12. R7C8 must repeat in R6C7, as the former sees every other cell in its region.
13. R7C8 must also repeat in R8C9 or R9C9 – and since it sees an 8 in its column, it must repeat in R9C9.
14. R6C7, R7C8 and R9C9 now contain identical digits. Between them, they see 1, 3 and 8, and are orthogonally connected to a 1 and an 8 without a kropki dot. This restricts the cells to 4, 5 or 6.
15. There must be an 8 in the 14 cage. All other cells in its region see an 8, or is ruled out by step 14. The 14 cage must be a 1/5/8 triple or a 2/4/8 triple.
16. R7C7 cannot be a 1, 5 or 8. It sees 1 and 8 in its colum. It cannot be a 5, since R6C7/R7C8 are either a 5, or a 4/6 which cannot be adjacent to a 5 without a kropki dot. The 14 cage must therefore be a 2/4/8 triple.
17. R1C2 must be a 1. The rest of the column is ruled out by th 4 cage or the 13 cage.
18. R3C2 must repeat in R1C1, since it cannot be an 8, and sees the rest of C1 in its region.
19. R3C1 must be a 2. R3C2 cannot be a 2, as it is identical to R1C1, which is orthogonally connected to a 1 without a kropki dot. There’s no 2 in the 13 cage, and R3C6, R3C8 and R3C9 are orthognally connected to a 1 or 3 without a kropki dot.
20. 2 must appear in R2C5 or R2C6. It can’t be placed next to a 1 or 3 without a kropki dot, and it can’t be placed in R2C3 or R2C4, since the kropki dot would force the remaining cell to be a 1 or 3, contradicting the 4 cage.
21. R2C7 must repeat in R1C9, since it cannot be an 8, and sees every other cell in the row in its region. These cells can’t be a 9, as R1C9 is next to an 8 without a kropki dot.
22. 9 must appear in R2C5 or R2C6. It can’t be placed next to an 8, it can’t be placed in R2C3 or R2C4 without forcing an 8 on the kropki dot, and step 21 rules it out of R2C7. Between this and step 20, R2C5 and R2C6 are now a 2/9 pair.
23. 7 is ruled out of R2C2 since it’s next to an 8 without a kropki dot, and R2C7 since it’s the same digit as R1C9, which is next to an 8 without a kropki dot. 7 must be in R2C3 or R2C4. The kropki dot forces a 6 into the remaining cell, as there’s already an 8 in the row.
24. R1C9, R2C7 and R3C6 are identical digits. R2C7 sees an 8, a 1/3 pair, a 2/9 pair, and a 6/7 pair. It cannot be a 4, as it’s next to a 3 without a kropki dot. All three must be 5s.
25. R2C2 is the only cell in its row that can be a 4.
26. R1C1, R3C2 and R4C3 are identical digits. They see 1/2/3/4/5/8. R1C1 is next to an 8 without a kropki dot, ruling out 7 and 9. All three must be 6es.
27. R8C3 must appear in R9C1, as it sees an 8, and shares a region with all other cells in R9.
28. R8C2 sees 1/4/6/8. 7/9 are ruled out by the 7 cage. The 7 cage cannot be a 3/4 pair, as there’s no kropki dot between its cells. It can’t be a 5, as this would force a 2 into both R8C3 and R9C1 (see step 27), with two 2s appearing in C1. The only remaining candidate for R8C2 is 2. The 7 cage places a 5 into R8C3, as well as R9C1 thanks to step 27.
29. R7C4 must be a 5, as all other cells in its region see a 5.
30. R1C7 sees 1/3/5/6/8. It’s next to a 5 and an 8 with no kropki dot, ruling out 4, 7 and 9. Only 2 is possible.
31. R7C7 now sees a 2, and must be a 4.
32. R6C7 is next to a 4 without a kropki dot, ruling out 4 and 5. It must be a 6, as must the identical digits in R7C8 and R9C9.
33. R9C8 must be a 2. R8C8 sees a 2, and the remaining cells in the column share a region with the 14 cage, which contains a 2.
34. R8C8 sees 2/5/6/8. It’s next to a 2 and an 8 with no kropki dot, ruling out 1, 3, 7 and 9. It must be a 4.
35. The 9 in R9 must be in C6 or C7. R9C3 is next to an 8 with no kropki, and a 9 in R9C4 or R9C5 would place a second 8 in the row.
36. The 7 in R9 must be in C6 or C7. R9C3 is next to an 8 with no kropki, and a 7 in R9C4 or R9C5 would place a second 6 or 8 in the row. We now have a 7/9 pair in R9.
37. The 1 in R9 must be in C3. A 1 in R9C4 or R9C5 would force a second 2 in the row.
38. The 8 in C3 must be in R5 or R6, as they’re the only cells in their region that don’t see an 8 or the 14 cage (which contains an 8).
39. R3C3 is a 4. It sees a 1, and step 38 rules out an 8.
40. R8C5 is the only cell in its region that can be a 6. The cells in C3 and C7 see a 6, and the cell in C4 is next to a 5 with no kropki dot. The cell in C6 is on a kropki dot, but no 5 or 7 can be placed in the 14 cage.
41. R2C3 is a 7; it sees a 6 in its column. R2C4 is now a 6.
42. R8C7 is the only cell in its region that can be a 7. The cells in C3 see a 7, and the remaining cells are next to a 6 with no kropki dot.
43. R9C7 is a 9 to complete the column. This places a 7 in R9C6.
44. The 7 in R1 must be in C5. C3 and C6 see a 7, and C4 is ruled out as it’s next to a 6 with no kropki dot.
45. R8C1 is a 9. 1 and 3 are ruled out as it’s next to a 2 with no kropki dot.
46. R9C4 and R9C5 are a 3/4 pair to finish the row. R8C4 can’t be a 3, as it would rule out both candidates for R9C4 as there’s no kropki dot. The only remaining candidate for R8C4 is 1, and the 3 in this row must be in C6.
47. The kropki dot places a 2 in R7C6. The cage places an 8 in R7C5.
48. R2C6 is a 9, as it sees a 2. R2C5 is a 2 to complete the row. The kropki dot places a 1 in R3C5. The cage places an 8 in R3C4.
49. The 1 in C6 can only go in R4. The other cells are next to a 2 with no kropki, or see a 1. R1C6 is a 4 as it sees all other numbers. The 6 in C6 can only go in R5, with an 8 in R6 to complete the column.
50. The 9 in C5 must be in the 3x3 region; the only other cell sees a 9. The 9 in C4 must therefore be in R1. R1C3 must be a 3 to finish the row. R7C3 must be a 9, as it sees all other numbers.
51. R7C2 sees all numbers except 3 and 7. It’s next to a 2 with no kropki dot, so it’s a 7.
52. The 8 in C3 must be in R5, to avoid being next to a 9 with no kropki dot. R6C3 is a 2 to finish the column.
53. R6C4 sees all numbers except 3, 4 and 7. It’s next to a 2 and 5 with no kropki dot, so it’s a 7.
54. A 3 in R4C4 or R5C4 would break the puzzle by placing a 3 next to a 2 or 4 with no kropki dot. The 3 in C4 must be in R9. R9C5 is a 4 to finish the row.
55. Since the remaining cells in C4 are a 2/4 pair, the 3 in C5 must be in R6 to avoid placing it next to a consecutive digit with no kropki. R5C5 must now be a 9 to avoid placing a 5 next to a 6 with no kropki. R4C5 is a 5 to finish the column. R4C4 is a 2 to avoid placing a 4 next to a 5 with no kropki. R5C4 is a 4 to finish the region/column.
56. R4C8 sees every number except 3, 7 and 9. It’s next to an 8 with no kropki, so must be a 3.
57. R5C9 is a 2 – all other cells in the column see a 2. R6C9 is a 4 – the other cells in the column see a 4, or it’s next to a 3 with no kropki. R7C9 sees every number except 1 and 3, and must be a 1 since it’s next to a 4 with no kropki. R7C1 is a 3 to finish the row. R2C9 sees every number except 3. R2C8 is a 1 to finish the row. R6C8 sees every number except 5 and 9, and it’s next to a 6 with no kropki and must be 9. R6C1 sees every number except 1. R6C2 is 5 to finish the row. R3C8 sees every number except 7. R3C9 is 9 to finish the row. R4C9 is 7 to finish the column. R5C8 is a 5 to finish the column. R5C1 is a 7 as it sees every other number. R5C2 is a 3 to finish the row. R4C2 is a 9 to finish the column. R4C1 is a 4 to finish the puzzle.
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