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SOLO-008 · Irregular Sudoku

EXTREME

The Nine Territories

Complete the grid completely. Only one solution respects all constraints.

This page contains the solution.

The answer

486753129 / 924875631 / 531962748 / 613294857 / 759381264 / 847126593 / 298547316 / 165438972 / 372619485

Coordinates: lines from top to bottom, columns from left to right.
L / C123456789
1486753129
2924875631
3531962748
4613294857
5759381264
6847126593
7298547316
8165438972
9372619485

The reasoning

  1. Note the candidates in each box by crossing the line, column and region.
  2. In the certificate below, units 1 to 9 are lines, 10 to 18 columns, 19 to 27 regions. Units 28 and 29, if present, are diagonals.
  3. A nude subset of two or three cells reserves as many numbers: these figures are excluded from the other cells of the unit. An interaction limits one digit in the intersection of two units and excludes from the rest of the second.
  4. Each hypothesis opens a separate branch. Never keep in the neighbouring branch a value found under an abandoned hypothesis. The contradictions and all the figures deduced appear in the tree of evidence.
  5. The search finds exactly a complete grid. It runs through 27 states; the 13 contradictory branches are closed. Finally check each unit and each starting point.

Common mistakes and false leads

Show the full search proof

Each branch is independent. The tree records the deductions and contradictions found with the method used here.

  1. L9C1: only place for 3 in unit 10 → 3
  2. L7C5: only place for 4 in unit 26 → 4
  3. Units 3 and 21 overlap. In unit 3, 7 must lie in the overlap. Remove it from L2C6.
  4. Units 8 and 27 overlap. In unit 8, 2 must lie in the overlap. Remove it from L9C8, L9C9.
  5. Units 13 and 23 overlap. In unit 13, 3 must lie in the overlap. Remove it from L6C6, L6C7.
  6. Units 23 and 5 overlap. In unit 23, 8 must lie in the overlap. Remove it from L5C8, L5C9.
  7. L3C9: only place for 8 in unit 24 → 8
  8. Units 27 and 17 overlap. In unit 27, 8 must lie in the overlap. Remove it from L1C8.
L4C1 = 5

Assumption: L4C1 = 5

  1. Units 3 and 21 overlap. In unit 3, 5 must lie in the overlap. Remove it from L1C9, L2C6, L2C9.
  2. Units 3 and 21 overlap. In unit 3, 7 must lie in the overlap. Remove it from L2C6.
  3. Units 8 and 27 overlap. In unit 8, 2 must lie in the overlap. Remove it from L9C8, L9C9.
  4. Units 13 and 23 overlap. In unit 13, 3 must lie in the overlap. Remove it from L6C6, L6C7.
  5. Units 27 and 17 overlap. In unit 27, 8 must lie in the overlap. Remove it from L1C8.
L2C6 = 1

Assumption: L2C6 = 1

  1. Units 3 and 21 overlap. In unit 3, 5 must lie in the overlap. Remove it from L1C9, L2C9.
  2. Units 8 and 27 overlap. In unit 8, 2 must lie in the overlap. Remove it from L9C8, L9C9.
  3. Units 13 and 23 overlap. In unit 13, 3 must lie in the overlap. Remove it from L6C6, L6C7.
  4. Units 20 and 1 overlap. In unit 20, 1 must lie in the overlap. Remove it from L1C1, L1C2.
  5. L8C1: only place for 1 in unit 10 → 1
  6. L5C1: only place for 7 in unit 10 → 7
  7. L4C2: only place for 1 in unit 11 → 1
  8. Nude subset in unit 19: L1C1, L3C1 reserve [4, 6]; remove these numbers from L1C2, L1C3, L2C2.
  9. Units 11 and 25 overlap. In unit 11, 7 must lie in the overlap. Remove it from L7C3.
  10. Units 13 and 23 overlap. In unit 13, 1 must lie in the overlap. Remove it from L6C7.
  11. Units 27 and 17 overlap. In unit 27, 8 must lie in the overlap. Remove it from L1C8.
L1C1 = 4

Assumption: L1C1 = 4

  1. L3C1: only candidate → 6
  2. L1C9: only place for 6 in unit 1 → 6
  3. Units 1 and 20 overlap. In unit 1, 9 must lie in the overlap. Remove it from L3C4.
  4. Units 3 and 21 overlap. In unit 3, 5 must lie in the overlap. Remove it from L2C9.
  5. Units 8 and 27 overlap. In unit 8, 2 must lie in the overlap. Remove it from L9C8, L9C9.
  6. L9C9: only candidate → 5
  7. Units 11 and 25 overlap. In unit 11, 7 must lie in the overlap. Remove it from L7C3.
  8. Units 13 and 23 overlap. In unit 13, 1 must lie in the overlap. Remove it from L6C7.
  9. Units 13 and 23 overlap. In unit 13, 3 must lie in the overlap. Remove it from L6C6, L6C7.
  10. Units 14 and 23 overlap. In unit 14, 6 must lie in the overlap. Remove it from L5C4, L6C3, L6C4, L6C6.
  11. Nude subset in Unit 6: L6C3, L6C6, L6C7 reserve [5, 7, 9]; remove these numbers from L6C2, L6C4, L6C8, L6C9.
  12. Nude subset in Unit 23: L6C3, L6C6, L6C7 reserve [5, 7, 9]; remove these numbers from L4C5, L5C4, L5C5.
  13. L4C5: only candidate → 6
  14. L5C5: only candidate → 8
  15. L2C4: only place for 8 in unit 13 → 8
  16. Units 27 and 17 overlap. In unit 27, 6 must lie in the overlap. Remove it from L5C8, L6C8.
  17. L6C2: only place for 6 in unit 6 → 6
  18. L5C6: only place for 6 in unit 5 → 6
  19. L7C6: only candidate → 7
  20. L6C6: only candidate → 5
  21. L3C6: only candidate → 2
  22. L1C6: only candidate → 3
  23. L2C9: only candidate → 4
  24. L3C4: only candidate → 4
  25. L6C8: only place for 4 in unit 6 → 4
  26. L8C2: only place for 4 in unit 8 → 4
  27. L5C3: only place for 4 in unit 5 → 4
  28. L9C2: only place for 7 in unit 11 → 7
  29. L9C8: only place for 8 in unit 9 → 8
L1C3 = 2

Assumption: L1C3 = 2

  1. L2C2: only candidate → 5
  2. L1C2: only candidate → 8
  3. L2C3: only candidate → 7

contradiction: a box no longer has no candidate

L1C3 = 8

Assumption: L1C3 = 8

  1. L7C2: only place for 8 in unit 7 → 8
  2. L5C2: only place for 9 in unit 11 → 9
  3. L4C4: only candidate → 2
  4. L4C8: only candidate → 9
  5. L9C4: only candidate → 6
  6. L8C4: only candidate → 9
  7. L7C3: only candidate → 6
  8. L7C8: only candidate → 1
  9. L8C9: only candidate → 2
  10. L8C7: only candidate → 7
  11. L8C8: only candidate → 6
  12. L9C3: only candidate → 2
  13. L2C3: only candidate → 7
  14. L2C5: only candidate → 5
  15. L1C5: only candidate → 9
  16. L1C8: only candidate → 2
  17. L1C2: only candidate → 5
  18. L1C7: only candidate → 1
  19. L2C2: only candidate → 2
  20. L3C5: only candidate → 7
  21. L3C8: only candidate → 5

contradiction: a box no longer has no candidate

all the possibilities of this bifurcation have been examined

L1C1 = 6

Assumption: L1C1 = 6

  1. L3C1: only candidate → 4
  2. Nude subset in Unit 13: L3C4, L4C4, L9C4 reserve [2, 6, 9]; remove these numbers from L2C4, L5C4, L6C4, L8C4.
  3. L8C4: only candidate → 4
  4. L2C4: only candidate → 8
  5. L5C5: only place for 8 in unit 5 → 8
  6. Nude sub-assembly in Unit 23: L5C4, L6C4 reserve [1, 3]; remove these numbers from L6C6, L6C7.
  7. Units 3 and 21 overlap. In unit 3, 5 must lie in the overlap. Remove it from L1C9, L2C9.
  8. Units 5 and 24 overlap. In unit 5, 5 must lie in the overlap. Remove it from L6C8, L6C9.
  9. Units 8 and 27 overlap. In unit 8, 2 must lie in the overlap. Remove it from L9C8, L9C9.
  10. Units 11 and 22 overlap. In unit 11, 4 must lie in the overlap. Remove it from L5C3.
  11. L2C3: only place for 4 in unit 12 → 4
  12. L2C9: only candidate → 2
  13. L2C2: only candidate → 5
  14. L2C5: only candidate → 7
  15. L1C9: only place for 4 in unit 1 → 4
  16. L3C4: only place for 2 in unit 3 → 2
  17. L9C4: only candidate → 6
  18. L4C4: only candidate → 9
  19. L4C5: only candidate → 6
  20. L4C8: only candidate → 2
  21. L7C6: only candidate → 7
  22. L6C6: only candidate → 5
  23. L1C6: only candidate → 3
  24. L3C6: only candidate → 6

contradiction: a box no longer has no candidate

all the possibilities of this bifurcation have been examined

L2C6 = 2

Assumption: L2C6 = 2

  1. L3C4: only place for 2 in unit 3 → 2
  2. L9C4: only candidate → 6
  3. L4C4: only candidate → 9
  4. L4C5: only candidate → 6
  5. L7C6: only candidate → 7
  6. L9C3: only candidate → 2
  7. L9C9: only candidate → 5
  8. L1C2: only place for 2 in unit 1 → 2
  9. L4C2: only candidate → 1
  10. L4C8: only candidate → 2

contradiction: the number 2 can no longer be included in unit 5

all the possibilities of this bifurcation have been examined

L4C1 = 6

Assumption: L4C1 = 6

  1. Units 3 and 21 overlap. In unit 3, 6 must lie in the overlap. Remove it from L1C9.
  2. Units 3 and 21 overlap. In unit 3, 7 must lie in the overlap. Remove it from L2C6.
  3. Units 8 and 27 overlap. In unit 8, 2 must lie in the overlap. Remove it from L9C8, L9C9.
  4. Units 13 and 23 overlap. In unit 13, 3 must lie in the overlap. Remove it from L6C6, L6C7.
  5. Units 27 and 17 overlap. In unit 27, 8 must lie in the overlap. Remove it from L1C8.
L3C1 = 4

Assumption: L3C1 = 4

  1. Nude subset in Unit 13: L3C4, L4C4 reserve [2, 9]; remove these numbers from L2C4, L5C4, L6C4, L8C4, L9C4.
  2. L9C4: only candidate → 6
  3. L7C6: only candidate → 7
  4. L9C3: only candidate → 2
  5. L9C9: only candidate → 5
  6. Units 3 and 21 overlap. In unit 3, 5 must lie in the overlap. Remove it from L2C6.
  7. Units 3 and 21 overlap. In unit 3, 6 must lie in the overlap. Remove it from L1C9.
  8. Units 13 and 23 overlap. In unit 13, 3 must lie in the overlap. Remove it from L6C6, L6C7.
  9. Units 19 and 11 overlap. In unit 19, 2 must lie in the overlap. Remove it from L5C2.
  10. L4C4: only place for 2 in unit 22 → 2
  11. L3C4: only candidate → 9
  12. L1C9: only place for 9 in unit 1 → 9
  13. L1C8: only place for 4 in unit 1 → 4
  14. L2C9: only place for 4 in unit 2 → 4
  15. L6C2: only place for 4 in unit 6 → 4

contradiction: the number 4 can no longer be included in unit 5

L3C1 = 5

Assumption: L3C1 = 5

  1. Units 3 and 21 overlap. In unit 3, 6 must lie in the overlap. Remove it from L1C9.
  2. Units 3 and 21 overlap. In unit 3, 7 must lie in the overlap. Remove it from L2C6.
  3. Units 8 and 27 overlap. In unit 8, 2 must lie in the overlap. Remove it from L9C8, L9C9.
  4. Units 13 and 23 overlap. In unit 13, 3 must lie in the overlap. Remove it from L6C6, L6C7.
  5. Units 27 and 17 overlap. In unit 27, 8 must lie in the overlap. Remove it from L1C8.
L1C1 = 1

Assumption: L1C1 = 1

  1. L4C2: only candidate → 2
  2. L4C4: only candidate → 9
  3. L4C5: only candidate → 5
  4. L4C8: only candidate → 1
  5. L5C4: only place for 1 in unit 5 → 1
  6. L5C5: only place for 8 in unit 5 → 8
  7. L1C5: only candidate → 9
  8. L2C5: only candidate → 7
  9. L3C5: only candidate → 6

contradiction: the number 1 can no longer appear in unit 6

L1C1 = 4

Assumption: L1C1 = 4

  1. L5C1: only candidate → 7
  2. L8C1: only candidate → 1
  3. Units 3 and 21 overlap. In unit 3, 6 must lie in the overlap. Remove it from L1C9.
  4. Units 3 and 21 overlap. In unit 3, 7 must lie in the overlap. Remove it from L2C6.
  5. Units 8 and 27 overlap. In unit 8, 2 must lie in the overlap. Remove it from L9C8, L9C9.
  6. Units 11 and 25 overlap. In unit 11, 7 must lie in the overlap. Remove it from L7C3.
  7. Units 13 and 23 overlap. In unit 13, 3 must lie in the overlap. Remove it from L6C6, L6C7.
  8. Units 27 and 17 overlap. In unit 27, 8 must lie in the overlap. Remove it from L1C8.
L4C2 = 1

Assumption: L4C2 = 1

  1. Units 3 and 21 overlap. In unit 3, 6 must lie in the overlap. Remove it from L1C9.
  2. Units 3 and 21 overlap. In unit 3, 7 must lie in the overlap. Remove it from L2C6.
  3. Units 8 and 27 overlap. In unit 8, 2 must lie in the overlap. Remove it from L9C8, L9C9.
  4. Units 11 and 25 overlap. In unit 11, 7 must lie in the overlap. Remove it from L7C3.
  5. Units 13 and 23 overlap. In unit 13, 3 must lie in the overlap. Remove it from L6C6, L6C7.
  6. Units 27 and 17 overlap. In unit 27, 8 must lie in the overlap. Remove it from L1C8.
L2C2 = 2

Assumption: L2C2 = 2

  1. Nude subset in unit 1: L1C2, L1C3 reserve [6, 8]; remove these numbers from L1C5, L1C8, L1C9.
  2. Nude subset in unit 14: L1C5, L4C5 reserve [5, 9]; remove these numbers from L2C5, L3C5, L5C5.
  3. Units 2 and 21 overlap. In unit 2, 5 must lie in the overlap. Remove it from L1C9.
  4. Units 3 and 21 overlap. In unit 3, 7 must lie in the overlap. Remove it from L2C6.
  5. Units 8 and 27 overlap. In unit 8, 2 must lie in the overlap. Remove it from L9C8, L9C9.
  6. Units 11 and 25 overlap. In unit 11, 7 must lie in the overlap. Remove it from L7C3.
  7. Units 13 and 23 overlap. In unit 13, 3 must lie in the overlap. Remove it from L6C6, L6C7.
L1C2 = 6

Assumption: L1C2 = 6

  1. L1C3: only candidate → 8
  2. Nude subset in unit 14: L1C5, L4C5 reserve [5, 9]; remove these numbers from L2C5, L3C5, L5C5.
  3. Units 2 and 21 overlap. In unit 2, 5 must lie in the overlap. Remove it from L1C9.
  4. Units 3 and 21 overlap. In unit 3, 7 must lie in the overlap. Remove it from L2C6.
  5. Units 8 and 27 overlap. In unit 8, 2 must lie in the overlap. Remove it from L9C8, L9C9.
  6. Units 11 and 25 overlap. In unit 11, 7 must lie in the overlap. Remove it from L7C3.
  7. Units 13 and 23 overlap. In unit 13, 3 must lie in the overlap. Remove it from L6C6, L6C7.
L1C5 = 5

Assumption: L1C5 = 5

  1. L4C5: only candidate → 9
  2. L4C4: only candidate → 2
  3. L4C8: only candidate → 5
  4. L9C4: only candidate → 6
  5. L7C6: only candidate → 7
  6. L9C3: only candidate → 2
  7. L9C9: only candidate → 5
  8. L2C6: only place for 5 in unit 2 → 5
  9. L5C2: only place for 5 in unit 5 → 5
  10. L6C7: only place for 5 in unit 6 → 5
  11. L6C3: only place for 7 in unit 6 → 7
  12. L2C3: only candidate → 4
  13. L2C9: only candidate → 1
  14. L2C4: only candidate → 8
  15. L2C5: only candidate → 7
  16. L3C4: only candidate → 9
  17. L3C5: only candidate → 6
  18. L3C6: only candidate → 2
  19. L1C9: only candidate → 9
  20. L3C7: only candidate → 7
  21. L3C8: only candidate → 4
  22. L5C3: only candidate → 9
  23. L5C5: only candidate → 8
  24. L6C2: only candidate → 4
  25. L7C3: only candidate → 6
  26. L7C9: only candidate → 3
  27. L6C9: only candidate → 6
  28. L8C4: only candidate → 4
  29. L8C9: only candidate → 2
  30. L5C9: only candidate → 4
  31. L8C7: only candidate → 9
  32. L7C7: only candidate → 1
  33. L7C8: only candidate → 8
  34. L7C2: only candidate → 9
  35. L8C2: only candidate → 7
  36. L8C8: only candidate → 6
  37. L9C2: only candidate → 8
  38. L9C8: only candidate → 7

contradiction: the number 6 can no longer appear in unit 5

L1C5 = 9

Assumption: L1C5 = 9

  1. L4C5: only candidate → 5
  2. Units 2 and 21 overlap. In unit 2, 5 must lie in the overlap. Remove it from L1C9.
  3. Units 3 and 21 overlap. In unit 3, 7 must lie in the overlap. Remove it from L2C6.
  4. Units 8 and 27 overlap. In unit 8, 2 must lie in the overlap. Remove it from L9C8, L9C9.
  5. Units 11 and 25 overlap. In unit 11, 7 must lie in the overlap. Remove it from L7C3.
  6. Units 13 and 23 overlap. In unit 13, 3 must lie in the overlap. Remove it from L6C6, L6C7.
L1C9 = 1

Assumption: L1C9 = 1

  1. L2C4: only place for 1 in unit 2 → 1
  2. L2C5: only place for 8 in unit 2 → 8
  3. L5C5: only candidate → 6
  4. L3C5: only candidate → 7
  5. L2C6: only candidate → 5
  6. L2C9: only candidate → 4
  7. L2C3: only candidate → 7
  8. L6C3: only candidate → 9
  9. L6C4: only candidate → 3
  10. L5C4: only candidate → 8
  11. L7C3: only candidate → 6
  12. L7C6: only candidate → 7
  13. L6C6: only candidate → 1
  14. L6C7: only candidate → 7
  15. L9C3: only candidate → 2
  16. L5C3: only candidate → 4
  17. L6C2: only candidate → 5
  18. L5C2: only candidate → 9
  19. L4C4: only candidate → 2
  20. L3C4: only candidate → 4
  21. L4C8: only candidate → 9
  22. L6C9: only candidate → 6
  23. L6C8: only candidate → 4
  24. L7C2: only candidate → 8
  25. L7C8: only candidate → 1
  26. L8C4: only candidate → 9
  27. L8C7: only candidate → 2

contradiction: a box no longer has no candidate

L1C9 = 2

Assumption: L1C9 = 2

  1. L3C4: only place for 2 in unit 3 → 2
  2. L4C4: only candidate → 9
  3. L4C8: only candidate → 2
  4. L9C4: only candidate → 6
  5. L7C6: only candidate → 7
  6. L3C6: only candidate → 6
  7. L3C5: only candidate → 7
  8. L2C5: only candidate → 8
  9. L3C7: only candidate → 9
  10. L3C8: only candidate → 4
  11. L5C5: only candidate → 6
  12. L8C4: only candidate → 4
  13. L2C4: only candidate → 1
  14. L1C8: only candidate → 5
  15. L1C6: only candidate → 3

contradiction: a box no longer has no candidate

all the possibilities of this bifurcation have been examined

all the possibilities of this bifurcation have been examined

L1C2 = 8

Assumption: L1C2 = 8

  1. L1C3: only candidate → 6
  2. L9C8: only place for 8 in unit 9 → 8
  3. L7C3: only place for 8 in unit 7 → 8
  4. L9C9: only place for 5 in unit 9 → 5
  5. L2C6: only place for 5 in unit 21 → 5
  6. Nude subset in unit 14: L1C5, L4C5 reserve [5, 9]; remove these numbers from L3C5, L5C5.
  7. Units 11 and 25 overlap. In unit 11, 6 must lie in the overlap. Remove it from L8C4.
  8. Nude subset in Unit 13: L3C4, L4C4, L8C4 reserve [2, 4, 9]; remove these numbers from L2C4, L5C4, L6C4, L9C4.
  9. L9C4: only candidate → 6
  10. L7C6: only candidate → 7
  11. L9C2: only candidate → 7
  12. L9C3: only candidate → 2
  13. L4C4: only place for 2 in unit 22 → 2
  14. Units 3 and 21 overlap. In unit 3, 2 must lie in the overlap. Remove it from L1C9.
  15. Units 13 and 23 overlap. In unit 13, 3 must lie in the overlap. Remove it from L6C6, L6C7.
  16. Units 21 and 18 overlap. In unit 21, 1 must lie in the overlap. Remove it from L5C9, L6C9, L7C9.
L1C5 = 5

Assumption: L1C5 = 5

  1. L4C5: only candidate → 9
  2. L4C8: only candidate → 5
  3. L6C3: only candidate → 7
  4. L2C3: only candidate → 4
  5. L2C9: only candidate → 1
  6. L2C4: only candidate → 8
  7. L2C5: only candidate → 7
  8. L3C4: only candidate → 9
  9. L3C5: only candidate → 6
  10. L3C6: only candidate → 2
  11. L1C9: only candidate → 9
  12. L3C7: only candidate → 7
  13. L3C8: only candidate → 4
  14. L5C3: only candidate → 9
  15. L5C5: only candidate → 8
  16. L8C4: only candidate → 4
  17. L5C2: only place for 5 in unit 5 → 5
  18. L6C2: only candidate → 4
  19. L5C9: only place for 4 in unit 5 → 4
  20. L6C7: only place for 5 in unit 6 → 5
  21. L6C8: only place for 9 in unit 6 → 9
  22. L8C8: only place for 7 in unit 8 → 7
  23. L8C9: only place for 2 in unit 18 → 2
  24. L8C7: only candidate → 9
  25. L8C2: only candidate → 6
  26. L7C2: only candidate → 9
  27. L6C6: only place for 6 in unit 23 → 6
  28. L6C9: only candidate → 3
  29. L5C6: only candidate → 1
  30. L1C6: only candidate → 3
  31. L5C4: only candidate → 3
  32. L5C7: only candidate → 2
  33. L1C7: only candidate → 1
  34. L1C8: only candidate → 2
  35. L5C8: only candidate → 6
  36. L6C4: only candidate → 1
  37. L7C7: only candidate → 3
  38. L7C8: only candidate → 1
  39. L7C9: only candidate → 6

valid complete solution

L1C5 = 9

Assumption: L1C5 = 9

  1. L3C4: only candidate → 4
  2. L2C3: only candidate → 7
  3. L2C5: only candidate → 8
  4. L2C4: only candidate → 1
  5. L2C9: only candidate → 4
  6. L4C5: only candidate → 5
  7. L4C8: only candidate → 9
  8. L5C5: only candidate → 6
  9. L3C5: only candidate → 7
  10. L6C3: only candidate → 9
  11. L5C3: only candidate → 4
  12. L6C2: only candidate → 5
  13. L5C2: only candidate → 9
  14. L6C4: only candidate → 3
  15. L5C4: only candidate → 8
  16. L6C6: only candidate → 1
  17. L6C7: only candidate → 7
  18. L6C9: only candidate → 6
  19. L6C8: only candidate → 4
  20. L7C2: only candidate → 6
  21. L7C8: only candidate → 1
  22. L8C2: only candidate → 4
  23. L8C4: only candidate → 9
  24. L8C7: only candidate → 2

contradiction: a box no longer has no candidate

all the possibilities of this bifurcation have been examined

all the possibilities of this bifurcation have been examined

L2C2 = 8

Assumption: L2C2 = 8

  1. L9C8: only place for 8 in unit 9 → 8
  2. L1C5: only place for 8 in unit 1 → 8
  3. L5C4: only place for 8 in unit 5 → 8
  4. L7C3: only place for 8 in unit 7 → 8
  5. L9C9: only place for 5 in unit 9 → 5
  6. L6C4: only place for 3 in unit 13 → 3
  7. L2C4: only place for 1 in unit 13 → 1
  8. L1C9: only place for 1 in unit 1 → 1
  9. L2C6: only place for 5 in unit 21 → 5
  10. L2C5: only candidate → 7
  11. Nude subassembly in Unit 1: L1C2, L1C3 reserve [2, 6]; remove these numbers from L1C6, L1C7, L1C8.
  12. L1C6: only candidate → 3
  13. Nude subassembly in unit 20: L1C7, L1C8 reserve [5, 9]; remove these numbers from L3C4.
  14. Units 5 and 24 overlap. In unit 5, 1 must lie in the overlap. Remove it from L6C8.
  15. Units 14 and 23 overlap. In unit 14, 5 must lie in the overlap. Remove it from L6C7.
L1C2 = 2

Assumption: L1C2 = 2

  1. L1C3: only candidate → 6
  2. Nude subassembly in unit 20: L1C7, L1C8 reserve [5, 9]; remove these numbers from L3C4.
  3. Units 5 and 24 overlap. In unit 5, 1 must lie in the overlap. Remove it from L6C8.
  4. Units 11 and 25 overlap. In unit 11, 6 must lie in the overlap. Remove it from L8C4.
  5. L9C4: only place for 6 in unit 13 → 6
  6. L7C6: only candidate → 7
  7. L9C2: only candidate → 7
  8. L9C3: only candidate → 2
  9. L2C3: only candidate → 4
  10. L2C9: only candidate → 2
  11. L3C4: only candidate → 2
  12. L3C6: only candidate → 6
  13. L3C5: only candidate → 9
  14. L3C7: only candidate → 7
  15. L3C8: only candidate → 4
  16. L4C4: only candidate → 9

contradiction: a box no longer has no candidate

L1C2 = 6

Assumption: L1C2 = 6

  1. L1C3: only candidate → 2
  2. L2C3: only candidate → 4
  3. L2C9: only candidate → 2
  4. L5C3: only candidate → 9
  5. L4C4: only candidate → 2
  6. L3C4: only candidate → 9
  7. L1C7: only candidate → 5

contradiction: a box no longer has no candidate

all the possibilities of this bifurcation have been examined

all the possibilities of this bifurcation have been examined

L4C2 = 2

Assumption: L4C2 = 2

  1. L4C4: only candidate → 9
  2. L4C5: only candidate → 5
  3. L4C8: only candidate → 1
  4. L5C4: only place for 1 in unit 5 → 1
  5. L5C5: only place for 8 in unit 5 → 8
  6. L1C5: only candidate → 9
  7. L2C5: only candidate → 7
  8. L3C5: only candidate → 6

contradiction: the number 1 can no longer appear in unit 6

all the possibilities of this bifurcation have been examined

all the possibilities of this bifurcation have been examined

all the possibilities of this bifurcation have been examined

all the possibilities of this bifurcation have been examined

How we verified this answer

Exact enumeration, shutdown after two solutions, terminal verification of all units and cages.

{
  "nodes": 27,
  "branches": 13,
  "contradictions": 13,
  "depth": 8,
  "pairs": 14,
  "locked": 78
}

After single candidates, single places, bare pairs/triples and interactions between units, the solver still reaches bifurcations. The exhaustive evidence reaches 8 intertwined hypotheses, examines 27 states and closes 13 branches by contradiction. The Extreme level combines eliminations of candidates and deep branched analysis; this is not a ranking based on the number of empty boxes. Editorial evaluation according to the protocol of the collection, without calibration on a panel of players; another logical path can be made to the extent that it is possible to determine the number of empty boxes. be shorter.

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