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SOLO-003 · Classic Sudoku

EXPERT

The Inverted Mesh

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

This page contains the solution.

The answer

345278916 / 791635824 / 862491537 / 529713468 / 673984152 / 184562379 / 218347695 / 937856241 / 456129783

Coordinates: lines from top to bottom, columns from left to right.
L / C123456789
1345278916
2791635824
3862491537
4529713468
5673984152
6184562379
7218347695
8937856241
9456129783

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. L2C2: only place for 9 in unit 2 → 9
  2. L3C9: only place for 7 in unit 3 → 7
  3. L5C5: only place for 8 in unit 5 → 8
  4. L6C9: only place for 9 in unit 6 → 9
  5. L5C4: only place for 9 in unit 5 → 9
  6. L5C2: only place for 7 in unit 5 → 7
  7. L4C4: only place for 7 in unit 4 → 7
  8. L5C9: only place for 2 in unit 5 → 2
  9. L4C2: only place for 2 in unit 4 → 2
  10. L4C1: only place for 5 in unit 4 → 5
  11. L6C7: only place for 3 in unit 6 → 3
  12. L4C6: only place for 3 in unit 4 → 3
  13. L7C8: only place for 9 in unit 7 → 9
  14. L7C4: only place for 3 in unit 7 → 3
  15. L8C3: only place for 7 in unit 8 → 7
  16. L9C5: only place for 2 in unit 14 → 2
  17. L9C4: only candidate → 1
  18. L8C9: only place for 1 in unit 8 → 1
  19. L8C5: only place for 5 in unit 14 → 5
  20. L9C6: only candidate → 9
  21. L8C6: only candidate → 6
  22. L7C5: only candidate → 4
  23. L7C3: only candidate → 8
  24. L7C7: only candidate → 6
  25. L5C7: only candidate → 1
  26. L4C7: only candidate → 4
  27. L4C8: only candidate → 6
  28. L4C5: only candidate → 1
  29. L5C1: only candidate → 6
  30. L6C5: only candidate → 6
  31. L3C2: only place for 6 in unit 3 → 6
  32. L8C1: only place for 9 in unit 8 → 9
  33. L9C8: only place for 8 in unit 9 → 8
  34. L9C2: only place for 5 in unit 9 → 5
  35. Nude subassembly in Unit 2: L2C4, L2C8, L2C9 reserve [2, 4, 6]; remove these figures from L2C3.
  36. Units 2 and 21 overlap. In unit 2, 4 must lie in the overlap. Remove it from L1C9.
L1C2 = 3

Assumption: L1C2 = 3

  1. L8C2: only candidate → 4
  2. L8C8: only candidate → 3
  3. L3C8: only candidate → 2
  4. L2C8: only candidate → 4
  5. L1C9: only candidate → 6

contradiction: a box no longer has no candidate

L1C2 = 4

Assumption: L1C2 = 4

  1. L8C2: only candidate → 3
  2. L8C8: only candidate → 4
  3. L2C8: only candidate → 2
  4. L2C4: only candidate → 6
  5. L1C4: only candidate → 2
  6. L1C3: only candidate → 5
  7. L1C6: only candidate → 8
  8. L1C1: only candidate → 3
  9. L1C9: only candidate → 6
  10. L2C3: only candidate → 1
  11. L2C6: only candidate → 5
  12. L2C7: only candidate → 8
  13. L2C9: only candidate → 4
  14. L3C1: only candidate → 8
  15. L3C3: only candidate → 2
  16. L3C6: only candidate → 1
  17. L3C7: only candidate → 5
  18. L3C8: only candidate → 3
  19. L6C3: only candidate → 4
  20. L6C1: only candidate → 1
  21. L9C1: only candidate → 4
  22. L9C9: 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": 1
}

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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