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SOLO-007 · Irregular Sudoku

EXPERT

The Living Border

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

This page contains the solution.

The answer

564912378 / 783694125 / 128537946 / 215873469 / 379465281 / 496281537 / 637149852 / 942758613 / 851326794

Coordinates: lines from top to bottom, columns from left to right.
L / C123456789
1564912378
2783694125
3128537946
4215873469
5379465281
6496281537
7637149852
8942758613
9851326794

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 3 states; the 1 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. L1C6: only place for 2 in unit 1 → 2
  2. L2C8: only place for 2 in unit 2 → 2
  3. L7C7: only place for 8 in unit 16 → 8
  4. L3C3: only place for 8 in unit 12 → 8
  5. L2C4: only candidate → 6
  6. L3C4: only candidate → 5
  7. Units 1 and 21 overlap. In unit 1, 3 must lie in the overlap. Remove it from L4C7.
  8. Units 5 and 23 overlap. In unit 5, 4 must lie in the overlap. Remove it from L4C5.
  9. Units 5 and 23 overlap. In unit 5, 5 must lie in the overlap. Remove it from L6C5, L6C6.
  10. Units 6 and 23 overlap. In unit 6, 2 must lie in the overlap. Remove it from L4C5.
  11. Units 4 and 22 overlap. In unit 4, 2 must lie in the overlap. Remove it from L7C1.
  12. Units 8 and 27 overlap. In unit 8, 6 must lie in the overlap. Remove it from L7C8, L7C9.
  13. L7C1: only place for 6 in unit 7 → 6
  14. L1C2: only place for 6 in unit 11 → 6
  15. L1C1: only place for 5 in unit 1 → 5
  16. L1C3: only place for 4 in unit 19 → 4
  17. Nude subset in Unit 21: L1C7, L1C8 reserve [3, 7]; remove these numbers from L2C7, L3C7, L3C9, L4C7.
  18. Units 11 and 25 overlap. In unit 11, 4 must lie in the overlap. Remove it from L7C4.
  19. L5C4: only place for 4 in unit 13 → 4
  20. Units 14 and 23 overlap. In unit 14, 8 must lie in the overlap. Remove it from L6C4.
  21. L4C4: only place for 8 in unit 13 → 8
  22. L4C1: only place for 2 in unit 4 → 2
  23. L6C5: only place for 8 in unit 6 → 8
  24. L6C4: only place for 2 in unit 6 → 2
  25. Units 9 and 26 overlap. In unit 9, 2 must lie in the overlap. Remove it from L7C5, L8C5.
  26. L9C5: only place for 2 in unit 14 → 2
  27. Units 17 and 27 overlap. In unit 17, 9 must lie in the overlap. Remove it from L9C7.
  28. Units 23 and 15 overlap. In unit 23, 3 must lie in the overlap. Remove it from L7C6.
  29. L9C4: only place for 3 in unit 26 → 3
  30. L7C4: only candidate → 1
  31. L8C3: only candidate → 2
  32. L7C3: only candidate → 7
  33. L9C1: only candidate → 8
  34. L9C2: only candidate → 5
  35. L2C2: only place for 8 in unit 2 → 8
  36. L7C9: only place for 2 in unit 7 → 2
  37. L5C1: only place for 3 in unit 10 → 3
  38. L9C3: only place for 1 in unit 26 → 1
  39. L5C3: only candidate → 9
  40. L9C7: only candidate → 7
  41. L1C7: only candidate → 3
  42. L1C8: only candidate → 7
  43. L9C8: only candidate → 9
  44. L6C2: only place for 9 in unit 6 → 9
L2C1 = 1

Assumption: L2C1 = 1

  1. L2C7: only candidate → 9
  2. L2C5: only candidate → 7
  3. L3C1: only candidate → 7
  4. L3C6: only candidate → 9
  5. L4C5: only candidate → 6
  6. L5C5: only candidate → 5
  7. L7C6: only candidate → 5
  8. L7C8: only candidate → 3
  9. L7C2: only candidate → 4
  10. L7C5: only candidate → 9
  11. L8C2: only candidate → 3
  12. L8C5: only candidate → 4
  13. L4C6: only place for 3 in unit 4 → 3
  14. L4C2: only place for 7 in unit 4 → 7
  15. L5C2: only candidate → 1
  16. L5C6: only candidate → 7
  17. L5C9: only candidate → 6
  18. L3C9: only candidate → 1

contradiction: a box no longer has no candidate

L2C1 = 7

Assumption: L2C1 = 7

  1. L2C5: only candidate → 9
  2. L2C7: only candidate → 1
  3. L3C1: only candidate → 1
  4. L3C6: only candidate → 7
  5. L3C9: only candidate → 6
  6. L3C8: only candidate → 4
  7. L3C7: only candidate → 9
  8. L4C7: only candidate → 4
  9. L6C7: only candidate → 5
  10. L8C7: only candidate → 6
  11. L5C5: only place for 6 in unit 5 → 6
  12. L4C5: only candidate → 7
  13. L4C2: only candidate → 1
  14. L4C6: only candidate → 3
  15. L4C8: only candidate → 6
  16. L5C2: only candidate → 7
  17. L5C9: only candidate → 1
  18. L5C6: only candidate → 5
  19. L6C6: only candidate → 1
  20. L6C8: only candidate → 3
  21. L6C9: only candidate → 7
  22. L7C6: only candidate → 9
  23. L7C8: only candidate → 5
  24. L7C5: only candidate → 4
  25. L7C2: only candidate → 3
  26. L8C2: only candidate → 4
  27. L8C5: only candidate → 5
  28. L8C8: only candidate → 1
  29. L8C9: only candidate → 3

valid complete solution

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": 3,
  "branches": 1,
  "contradictions": 1,
  "depth": 1,
  "pairs": 1,
  "locked": 11
}

After single candidates, single places, bare pairs/triples and interactions between units, the solver still reaches bifurcations. The exhaustive evidence reaches 1 intertwined hypotheses, examines 3 states and closes 1 branches by contradiction. The Expert level asks to keep a chain of possibilities in addition to the interactions. Editorial evaluation according to the protocol of the collection, without calibration on a panel of players; another logical path can be shorter.

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