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SOLO-002 · Classic Sudoku

EXTREME

The Hidden Crossroads

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

This page contains the solution.

The answer

745163829 / 123958746 / 986247351 / 269714538 / 418395672 / 537826194 / 374689215 / 691532487 / 852471963

Coordinates: lines from top to bottom, columns from left to right.
L / C123456789
1745163829
2123958746
3986247351
4269714538
5418395672
6537826194
7374689215
8691532487
9852471963

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 29 states; the 14 contradictory branches are closed. Finally check each unit and each starting index.

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. L1C8: only candidate → 2
  2. L5C9: only place for 2 in unit 5 → 2
  3. L6C7: only place for 1 in unit 6 → 1
  4. L3C9: only place for 1 in unit 18 → 1
  5. L4C9: only place for 8 in unit 18 → 8
  6. L9C9: only place for 3 in unit 18 → 3
  7. Nude subset in Unit 4: L4C2, L4C8 reserve [3, 6]; remove these numbers from L4C4, L4C5, L4C7.
  8. L4C7: only candidate → 5
  9. L5C4: only place for 3 in unit 13 → 3
  10. Nude subset in Unit 5: L5C5, L5C6, L5C7 reserve [5, 6, 9]; remove these numbers from L5C1, L5C3.
  11. L6C1: only place for 5 in unit 22 → 5
  12. Nude subset in Unit 11: L4C2, L6C2 reserve [3, 6]; remove these numbers from L2C2, L3C2, L7C2, L8C2.
  13. Nude subset in Unit 27: L7C9, L8C9 reserve [5, 7]; remove these numbers from L8C7, L9C7.
  14. Nude subset in unit 16: L5C7, L8C7, L9C7 reserve [4, 6, 9]; remove these numbers from L2C7, L3C7.
  15. L2C8: only place for 4 in unit 21 → 4
  16. Units 11 and 19 overlap. In unit 11, 8 must lie in the overlap. Remove it from L1C1, L1C3, L2C1, L2C3, L3C1, L3C3.
  17. L1C7: only place for 8 in unit 1 → 8
L2C1 = 1

Assumption: L2C1 = 1

  1. L8C3: only place for 1 in unit 8 → 1
  2. Nude subset in Unit 4: L4C2, L4C8 reserve [3, 6]; remove these numbers from L4C4, L4C5.
  3. Nude subset in Unit 5: L5C5, L5C6, L5C7 reserve [5, 6, 9]; remove these numbers from L5C1, L5C3.
  4. Nude subset in Unit 11: L4C2, L6C2 reserve [3, 6]; remove these numbers from L2C2, L3C2, L7C2, L8C2.
  5. Nude subset in unit 16: L2C7, L3C7 reserve [3, 7]; remove these numbers from L8C7, L9C7.
  6. Units 11 and 19 overlap. In unit 11, 8 must lie in the overlap. Remove it from L2C3, L3C1, L3C3.
L1C1 = 6

Assumption: L1C1 = 6

  1. L1C3: only candidate → 5
  2. Nude subset in Unit 4: L4C2, L4C8 reserve [3, 6]; remove these numbers from L4C4, L4C5.
  3. Nude subset in Unit 5: L5C5, L5C6, L5C7 reserve [5, 6, 9]; remove these numbers from L5C3.
  4. Nude subset in Unit 11: L4C2, L6C2 reserve [3, 6]; remove these numbers from L2C2, L3C2, L7C2, L8C2.
  5. Nude subset in unit 13: L1C4, L4C4 reserve [1, 7]; remove these numbers from L3C4, L7C4, L8C4, L9C4.
  6. Nude sub-assembly in unit 14: L1C5, L4C5 reserve [1, 7]; remove these numbers from L2C5, L3C5, L9C5.
  7. L2C5: only candidate → 5
  8. L5C6: only place for 5 in unit 5 → 5
  9. Nude subset in unit 16: L2C7, L3C7 reserve [3, 7]; remove these numbers from L8C7, L9C7.
  10. L9C1: only place for 7 in unit 9 → 7
  11. L7C2: only candidate → 9
  12. L8C1: only candidate → 4
  13. L5C1: only candidate → 8
  14. L3C1: only candidate → 9
  15. L5C3: only candidate → 4
  16. L7C3: only candidate → 6
  17. L7C6: only candidate → 7
  18. L7C9: only candidate → 5
  19. L7C4: only candidate → 4
  20. L8C2: only candidate → 2
  21. L8C9: only candidate → 7
  22. L9C3: only candidate → 8
  23. L3C5: only place for 4 in unit 3 → 4
  24. L8C4: only place for 5 in unit 8 → 5
  25. L9C4: only place for 2 in unit 9 → 2
  26. L3C4: only candidate → 6
  27. L9C7: only place for 4 in unit 9 → 4
L1C4 = 1

Assumption: L1C4 = 1

  1. L1C5: only candidate → 7
  2. L4C4: only candidate → 7
  3. L4C5: only place for 1 in unit 4 → 1
  4. Nude subassembly in Unit 11: L4C2, L6C2 reserve [3, 6]; remove these numbers from L2C2, L3C2.
L2C2 = 7

Assumption: L2C2 = 7

  1. L2C7: only candidate → 3
  2. L2C3: only candidate → 2
  3. L2C6: only candidate → 8
  4. L3C3: only candidate → 3
  5. L3C2: only candidate → 8
  6. L3C6: only candidate → 2
  7. L3C7: only candidate → 7
L4C2 = 3

Assumption: L4C2 = 3

  1. L4C8: only candidate → 6
  2. L5C7: only candidate → 9
  3. L5C5: only candidate → 6
  4. L6C2: only candidate → 6
  5. L6C6: only candidate → 9
  6. L6C8: only candidate → 3
  7. L8C6: only candidate → 6

contradiction: a box no longer has no candidate

L4C2 = 6

Assumption: L4C2 = 6

  1. L4C8: only candidate → 3
  2. L6C2: only candidate → 3
L5C5 = 6

Assumption: L5C5 = 6

  1. L5C7: only candidate → 9
  2. L6C6: only candidate → 9
  3. L6C8: only candidate → 6
  4. L8C6: only candidate → 6

contradiction: a box no longer has no candidate

L5C5 = 9

Assumption: L5C5 = 9

  1. L5C7: only candidate → 6
  2. L6C6: only candidate → 6
  3. L6C8: only candidate → 9
  4. L8C6: only candidate → 9

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. L2C6: only candidate → 2
  2. L2C3: only candidate → 3
  3. L2C7: only candidate → 7
  4. L3C2: only candidate → 7
  5. L3C3: only candidate → 2
  6. L3C6: only candidate → 8
  7. L3C7: only candidate → 3
L4C2 = 3

Assumption: L4C2 = 3

  1. L4C8: only candidate → 6
  2. L5C7: only candidate → 9
  3. L5C5: only candidate → 6
  4. L6C2: only candidate → 6
  5. L6C6: only candidate → 9
  6. L6C8: only candidate → 3
  7. L8C6: only candidate → 6

contradiction: a box no longer has no candidate

L4C2 = 6

Assumption: L4C2 = 6

  1. L4C8: only candidate → 3
  2. L6C2: only candidate → 3
L5C5 = 6

Assumption: L5C5 = 6

  1. L5C7: only candidate → 9
  2. L6C6: only candidate → 9
  3. L6C8: only candidate → 6
  4. L8C6: only candidate → 6

contradiction: a box no longer has no candidate

L5C5 = 9

Assumption: L5C5 = 9

  1. L5C7: only candidate → 6
  2. L6C6: only candidate → 6
  3. L6C8: only candidate → 9
  4. L8C6: only candidate → 9

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

all the possibilities of this bifurcation have been examined

L1C4 = 7

Assumption: L1C4 = 7

  1. L1C5: only candidate → 1
  2. L4C4: only candidate → 1
  3. L4C5: only place for 7 in unit 4 → 7
  4. Nude subassembly in Unit 11: L4C2, L6C2 reserve [3, 6]; remove these numbers from L2C2, L3C2.
L2C2 = 7

Assumption: L2C2 = 7

  1. L2C7: only candidate → 3
  2. L2C3: only candidate → 2
  3. L2C6: only candidate → 8
  4. L3C3: only candidate → 3
  5. L3C2: only candidate → 8
  6. L3C6: only candidate → 2
  7. L3C7: only candidate → 7
L4C2 = 3

Assumption: L4C2 = 3

  1. L4C8: only candidate → 6
  2. L5C7: only candidate → 9
  3. L5C5: only candidate → 6
  4. L6C2: only candidate → 6
  5. L6C6: only candidate → 9
  6. L6C8: only candidate → 3
  7. L8C6: only candidate → 6

contradiction: a box no longer has no candidate

L4C2 = 6

Assumption: L4C2 = 6

  1. L4C8: only candidate → 3
  2. L6C2: only candidate → 3
L5C5 = 6

Assumption: L5C5 = 6

  1. L5C7: only candidate → 9
  2. L6C6: only candidate → 9
  3. L6C8: only candidate → 6
  4. L8C6: only candidate → 6

contradiction: a box no longer has no candidate

L5C5 = 9

Assumption: L5C5 = 9

  1. L5C7: only candidate → 6
  2. L6C6: only candidate → 6
  3. L6C8: only candidate → 9
  4. L8C6: only candidate → 9

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. L2C6: only candidate → 2
  2. L2C3: only candidate → 3
  3. L2C7: only candidate → 7
  4. L3C2: only candidate → 7
  5. L3C3: only candidate → 2
  6. L3C6: only candidate → 8
  7. L3C7: only candidate → 3
L4C2 = 3

Assumption: L4C2 = 3

  1. L4C8: only candidate → 6
  2. L5C7: only candidate → 9
  3. L5C5: only candidate → 6
  4. L6C2: only candidate → 6
  5. L6C6: only candidate → 9
  6. L6C8: only candidate → 3
  7. L8C6: only candidate → 6

contradiction: a box no longer has no candidate

L4C2 = 6

Assumption: L4C2 = 6

  1. L4C8: only candidate → 3
  2. L6C2: only candidate → 3
L5C5 = 6

Assumption: L5C5 = 6

  1. L5C7: only candidate → 9
  2. L6C6: only candidate → 9
  3. L6C8: only candidate → 6
  4. L8C6: only candidate → 6

contradiction: a box no longer has no candidate

L5C5 = 9

Assumption: L5C5 = 9

  1. L5C7: only candidate → 6
  2. L6C6: only candidate → 6
  3. L6C8: only candidate → 9
  4. L8C6: only candidate → 9

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

all the possibilities of this bifurcation have been examined

all the possibilities of this bifurcation have been examined

L1C1 = 7

Assumption: L1C1 = 7

  1. Nude subset in Unit 4: L4C2, L4C8 reserve [3, 6]; remove these numbers from L4C4, L4C5.
  2. Nude subset in Unit 5: L5C5, L5C6, L5C7 reserve [5, 6, 9]; remove these numbers from L5C1, L5C3.
  3. Nude subset in Unit 11: L4C2, L6C2 reserve [3, 6]; remove these numbers from L2C2, L3C2, L7C2, L8C2.
  4. Nude subset in unit 16: L2C7, L3C7 reserve [3, 7]; remove these numbers from L8C7, L9C7.
  5. Units 9 and 26 overlap. In unit 9, 7 must lie in the overlap. Remove it from L7C4, L7C6, L8C4, L8C6.
  6. Nude subset in unit 15: L5C6, L6C6, L7C6 reserve [5, 6, 9]; remove these numbers from L2C6, L3C6, L8C6.
  7. L8C6: only candidate → 2
  8. L9C3: only place for 2 in unit 9 → 2
  9. L2C2: only place for 2 in unit 2 → 2
  10. L3C4: only place for 2 in unit 3 → 2
  11. L3C5: only place for 4 in unit 3 → 4
  12. L9C1: only place for 8 in unit 9 → 8
  13. L5C1: only candidate → 4
  14. L5C3: only candidate → 8
  15. L2C6: only place for 8 in unit 2 → 8
  16. L3C6: only candidate → 7
  17. L2C5: only candidate → 5
  18. L2C3: only candidate → 3
  19. L2C7: only candidate → 7
  20. L3C3: only candidate → 6
  21. L1C3: only candidate → 5
  22. L3C1: only candidate → 9
  23. L3C2: only candidate → 8
  24. L3C7: only candidate → 3
  25. L7C3: only candidate → 4
  26. L8C1: only candidate → 6
  27. L5C6: only place for 5 in unit 5 → 5
  28. Units 7 and 26 overlap. In unit 7, 6 must lie in the overlap. Remove it from L9C4, L9C5.
L1C4 = 1

Assumption: L1C4 = 1

  1. L1C5: only candidate → 6
  2. L5C5: only candidate → 9
  3. L5C7: only candidate → 6
  4. L4C8: only candidate → 3
  5. L4C2: only candidate → 6
  6. L4C4: only candidate → 7
  7. L4C5: only candidate → 1
  8. L6C2: only candidate → 3
  9. L6C6: only candidate → 6
  10. L6C8: only candidate → 9
  11. L7C6: only candidate → 9
  12. L7C2: only candidate → 7
  13. L7C9: only candidate → 5
  14. L7C4: only candidate → 6
  15. L8C2: only candidate → 9
  16. L8C7: only candidate → 4
  17. L8C4: only candidate → 5
  18. L8C9: only candidate → 7
  19. L9C4: only candidate → 4
  20. L9C5: only candidate → 7
  21. L9C7: only candidate → 9
  22. L9C8: only candidate → 6

valid complete solution

L1C4 = 6

Assumption: L1C4 = 6

  1. L1C5: only candidate → 1
  2. L4C4: only place for 1 in unit 4 → 1
  3. L4C5: only place for 7 in unit 4 → 7
  4. L7C6: only place for 6 in unit 7 → 6
  5. L6C6: only candidate → 9
  6. L5C5: only candidate → 6
  7. L5C7: only candidate → 9
  8. L8C7: only candidate → 4
  9. L9C5: only candidate → 9
  10. L9C7: only candidate → 6

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

L2C1 = 7

Assumption: L2C1 = 7

  1. L2C7: only candidate → 3
  2. L3C7: only candidate → 7
  3. L3C3: only place for 3 in unit 12 → 3
  4. Nude subset in Unit 4: L4C2, L4C8 reserve [3, 6]; remove these numbers from L4C4, L4C5.
  5. Nude subset in Unit 5: L5C5, L5C6, L5C7 reserve [5, 6, 9]; remove these numbers from L5C1, L5C3.
  6. Nude subset in Unit 11: L4C2, L6C2 reserve [3, 6]; remove these numbers from L3C2, L7C2, L8C2.
  7. Units 9 and 26 overlap. In unit 9, 7 must lie in the overlap. Remove it from L7C4, L7C6, L8C4, L8C6.

contradiction: the number 7 can no longer be included in unit 15

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": 29,
  "branches": 14,
  "contradictions": 14,
  "depth": 6,
  "pairs": 25,
  "locked": 5
}

After single candidates, single places, bare pairs/triples and interactions between units, the solver still reaches bifurcations. The exhaustive evidence reaches 6 intertwined hypotheses, examines 29 states and closes 14 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 by the two sides. be shorter.

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