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SOLO-004 · Classic Sudoku

EXTREME

Branches of Silence

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

This page contains the solution.

The answer

762983145 / 395142876 / 481657329 / 146298753 / 859376412 / 273514968 / 618429537 / 924735681 / 537861294

Coordinates: lines from top to bottom, columns from left to right.
L / C123456789
1762983145
2395142876
3481657329
4146298753
5859376412
6273514968
7618429537
8924735681
9537861294

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 81 states; the 40 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. L5C8: only candidate → 1
  2. L1C9: only place for 5 in unit 1 → 5
  3. L1C2: only place for 6 in unit 1 → 6
  4. L1C7: only place for 1 in unit 1 → 1
  5. L2C3: only place for 5 in unit 2 → 5
  6. L2C9: only place for 6 in unit 2 → 6
  7. L6C4: only place for 5 in unit 6 → 5
  8. L4C8: only place for 5 in unit 4 → 5
  9. L9C1: only place for 5 in unit 9 → 5
  10. L3C6: only place for 7 in unit 20 → 7
  11. L2C5: only place for 4 in unit 20 → 4
  12. Nude subset in unit 13: L1C4, L5C4 reserve [3, 9]; remove these numbers from L4C4, L8C4, L9C4.
  13. L8C5: only place for 3 in unit 8 → 3
  14. Nude subset in unit 26: L7C5, L7C6, L9C5 reserve [2, 6, 9]; remove these numbers from L8C4, L9C4.
  15. L4C4: only place for 2 in unit 13 → 2
  16. L6C5: only candidate → 1
L1C4 = 3

Assumption: L1C4 = 3

  1. L1C6: only candidate → 9
  2. L5C4: only candidate → 9
  3. L4C5: only candidate → 6
  4. L7C6: only candidate → 6
  5. L5C3: only place for 6 in unit 5 → 6

contradiction: the number 6 can no longer appear in unit 9

L1C4 = 9

Assumption: L1C4 = 9

  1. L1C6: only candidate → 3
  2. L5C4: only candidate → 3
  3. L5C7: only candidate → 4
  4. Nude subset in unit 15: L5C6, L7C6 reserve [6, 9]; remove these figures from L4C6.
L2C2 = 8

Assumption: L2C2 = 8

  1. L2C7: only candidate → 7
  2. L2C8: only candidate → 9
  3. Nude subset in Unit 9: L9C4, L9C7, L9C8 reserve [2, 7, 8]; remove these numbers from L9C3, L9C5, L9C9.
  4. L7C5: only place for 2 in unit 14 → 2
  5. Nude subset in unit 15: L5C6, L7C6 reserve [6, 9]; remove these figures from L4C6.
  6. Nude subassembly in Unit 18: L3C9, L4C9, L6C9 reserve [3, 7, 8]; remove these numbers from L7C9, L8C9.
  7. L7C2: only place for 7 in unit 7 → 7
  8. Nude subassembly in Unit 6: L6C1, L6C2 reserve [2, 4]; remove these numbers from L6C3, L6C6.
  9. L6C6: only candidate → 8
  10. L4C6: only candidate → 4
  11. Nude subassembly in Unit 4: L4C1, L4C2, L4C5 reserve [1, 6, 9]; remove these numbers from L4C3.
  12. Units 9 and 27 overlap. In unit 9, 2 must lie in the overlap. Remove it from L8C8.
L3C8 = 2

Assumption: L3C8 = 2

  1. L9C7: only place for 2 in unit 9 → 2
  2. Nude subassembly in Unit 4: L4C1, L4C2, L4C5 reserve [1, 6, 9]; remove these numbers from L4C3.
  3. Nude sub-assembly in Unit 6: L6C1, L6C2 reserve [2, 4]; remove these figures from L6C3.
  4. Nude subset in Unit 8: L8C4, L8C8 reserve [7, 8]; remove these numbers from L8C9.
  5. Nude sub-assembly in Unit 9: L9C4, L9C8 reserve [7, 8]; remove these numbers from L9C9.
L3C7 = 3

Assumption: L3C7 = 3

  1. L3C9: only candidate → 8
  2. L4C7: only candidate → 8
  3. Nude subassembly in Unit 4: L4C1, L4C2, L4C5 reserve [1, 6, 9]; remove these numbers from L4C3.
  4. Nude sub-assembly in Unit 6: L6C1, L6C2 reserve [2, 4]; remove these figures from L6C3.
  5. Nude subset in Unit 8: L8C4, L8C8 reserve [7, 8]; remove these numbers from L8C9.
  6. Nude sub-assembly in Unit 9: L9C4, L9C8 reserve [7, 8]; remove these numbers from L9C9.
L4C2 = 1

Assumption: L4C2 = 1

  1. Nude subassembly in Unit 4: L4C1, L4C5 reserve [6, 9]; remove these numbers from L4C3.
  2. Nude sub-assembly in Unit 6: L6C1, L6C2 reserve [2, 4]; remove these figures from L6C3.
  3. Nude subset in Unit 8: L8C4, L8C8 reserve [7, 8]; remove these numbers from L8C9.
  4. Nude sub-assembly in Unit 9: L9C4, L9C8 reserve [7, 8]; remove these numbers from L9C9.
L3C2 = 4

Assumption: L3C2 = 4

  1. L6C2: only candidate → 2
  2. L6C1: only candidate → 4
  3. L8C2: only candidate → 9
  4. L8C1: only place for 2 in unit 8 → 2
  5. Nude subassembly in Unit 4: L4C1, L4C5 reserve [6, 9]; remove these numbers from L4C3.
  6. Nude subset in Unit 8: L8C4, L8C8 reserve [7, 8]; remove these numbers from L8C9.
  7. Nude sub-assembly in Unit 9: L9C4, L9C8 reserve [7, 8]; remove these numbers from L9C9.
L3C1 = 1

Assumption: L3C1 = 1

  1. L3C3: only candidate → 9
  2. L5C3: only candidate → 6
  3. L4C1: only candidate → 9
  4. L4C5: only candidate → 6
  5. L5C6: only candidate → 9
  6. L7C1: only candidate → 6

contradiction: a box no longer has no candidate

L3C1 = 9

Assumption: L3C1 = 9

  1. L3C3: only candidate → 1
  2. L4C1: only candidate → 6
  3. L4C5: only candidate → 9
  4. L5C3: only candidate → 9
  5. L5C6: only candidate → 6
  6. L7C1: only candidate → 1
  7. L7C6: only candidate → 9

contradiction: a box no longer has no candidate

all the possibilities of this bifurcation have been examined

L3C2 = 9

Assumption: L3C2 = 9

  1. Nude subassembly in Unit 4: L4C1, L4C5 reserve [6, 9]; remove these numbers from L4C3.
  2. Nude sub-assembly in Unit 6: L6C1, L6C2 reserve [2, 4]; remove these figures from L6C3.
  3. Nude subset in Unit 8: L8C4, L8C8 reserve [7, 8]; remove these numbers from L8C9.
  4. Nude sub-assembly in Unit 9: L9C4, L9C8 reserve [7, 8]; remove these numbers from L9C9.
L3C1 = 1

Assumption: L3C1 = 1

  1. L3C3: only candidate → 4
  2. L7C9: only place for 1 in unit 7 → 1
  3. L8C3: only place for 1 in unit 8 → 1
  4. L9C9: only place for 4 in unit 9 → 4
  5. L8C9: only place for 9 in unit 18 → 9
  6. Nude subassembly in Unit 4: L4C1, L4C5 reserve [6, 9]; remove these numbers from L4C3.
L4C1 = 6

Assumption: L4C1 = 6

  1. L4C5: only candidate → 9
  2. L5C3: only candidate → 9
  3. L5C6: only candidate → 6
  4. L7C1: only candidate → 9

contradiction: a box no longer has no candidate

L4C1 = 9

Assumption: L4C1 = 9

  1. L4C5: only candidate → 6
  2. L5C3: only candidate → 6
  3. L5C6: only candidate → 9
  4. L7C1: only candidate → 6

contradiction: a box no longer has no candidate

all the possibilities of this bifurcation have been examined

L3C1 = 4

Assumption: L3C1 = 4

  1. L3C3: only candidate → 1
  2. L6C1: only candidate → 2
  3. L6C2: only candidate → 4
  4. L8C2: only candidate → 2
  5. Nude subassembly in Unit 4: L4C1, L4C5 reserve [6, 9]; remove these numbers from L4C3.
  6. Nude subset in Unit 8: L8C4, L8C8 reserve [7, 8]; remove these numbers from L8C9.
  7. Nude sub-assembly in Unit 9: L9C4, L9C8 reserve [7, 8]; remove these numbers from L9C9.
L4C1 = 6

Assumption: L4C1 = 6

  1. L4C5: only candidate → 9
  2. L5C3: only candidate → 9
  3. L5C6: only candidate → 6
  4. L7C6: only candidate → 9
  5. L7C1: only candidate → 1

contradiction: a box no longer has no candidate

L4C1 = 9

Assumption: L4C1 = 9

  1. L4C5: only candidate → 6
  2. L5C3: only candidate → 6
  3. L5C6: only candidate → 9
  4. L7C6: only candidate → 6
  5. L7C1: only candidate → 1

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

L4C2 = 9

Assumption: L4C2 = 9

  1. L4C5: only candidate → 6
  2. L4C1: only candidate → 1
  3. L5C3: only candidate → 6
  4. L5C6: only candidate → 9
  5. L7C6: only candidate → 6
  6. L7C1: only candidate → 9
  7. L3C1: only candidate → 4
  8. L3C2: only candidate → 1
  9. L3C3: only candidate → 9
  10. L6C1: only candidate → 2

contradiction: a box no longer has no candidate

all the possibilities of this bifurcation have been examined

L3C7 = 8

Assumption: L3C7 = 8

  1. L3C9: only candidate → 3
  2. L4C7: only candidate → 3
  3. L6C9: only candidate → 7
  4. L4C9: only candidate → 8
  5. L4C3: only place for 7 in unit 4 → 7
  6. L6C3: only place for 3 in unit 6 → 3
L4C2 = 1

Assumption: L4C2 = 1

L3C2 = 4

Assumption: L3C2 = 4

  1. L6C2: only candidate → 2
  2. L6C1: only candidate → 4
  3. L8C2: only candidate → 9
  4. L8C1: only place for 2 in unit 8 → 2
L3C1 = 1

Assumption: L3C1 = 1

  1. L3C3: only candidate → 9
  2. L5C3: only candidate → 6
  3. L4C1: only candidate → 9
  4. L4C5: only candidate → 6
  5. L5C6: only candidate → 9
  6. L7C1: only candidate → 6

contradiction: a box no longer has no candidate

L3C1 = 9

Assumption: L3C1 = 9

  1. L3C3: only candidate → 1
  2. L4C1: only candidate → 6
  3. L4C5: only candidate → 9
  4. L5C3: only candidate → 9
  5. L5C6: only candidate → 6
  6. L7C1: only candidate → 1
  7. L7C6: only candidate → 9

contradiction: a box no longer has no candidate

all the possibilities of this bifurcation have been examined

L3C2 = 9

Assumption: L3C2 = 9

L3C1 = 1

Assumption: L3C1 = 1

  1. L3C3: only candidate → 4
  2. L7C9: only place for 1 in unit 7 → 1
  3. L8C3: only place for 1 in unit 8 → 1
  4. L9C9: only place for 4 in unit 9 → 4
  5. L8C9: only candidate → 9
L4C1 = 6

Assumption: L4C1 = 6

  1. L4C5: only candidate → 9
  2. L5C3: only candidate → 9
  3. L5C6: only candidate → 6
  4. L7C1: only candidate → 9

contradiction: a box no longer has no candidate

L4C1 = 9

Assumption: L4C1 = 9

  1. L4C5: only candidate → 6
  2. L5C3: only candidate → 6
  3. L5C6: only candidate → 9
  4. L7C1: only candidate → 6

contradiction: a box no longer has no candidate

all the possibilities of this bifurcation have been examined

L3C1 = 4

Assumption: L3C1 = 4

  1. L3C3: only candidate → 1
  2. L6C1: only candidate → 2
  3. L6C2: only candidate → 4
  4. L8C2: only candidate → 2
L4C1 = 6

Assumption: L4C1 = 6

  1. L4C5: only candidate → 9
  2. L5C3: only candidate → 9
  3. L5C6: only candidate → 6
  4. L7C6: only candidate → 9
  5. L7C1: only candidate → 1

contradiction: a box no longer has no candidate

L4C1 = 9

Assumption: L4C1 = 9

  1. L4C5: only candidate → 6
  2. L5C3: only candidate → 6
  3. L5C6: only candidate → 9
  4. L7C6: only candidate → 6
  5. L7C1: only candidate → 1

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

L4C2 = 9

Assumption: L4C2 = 9

  1. L4C5: only candidate → 6
  2. L4C1: only candidate → 1
  3. L5C3: only candidate → 6
  4. L5C6: only candidate → 9
  5. L7C6: only candidate → 6
  6. L7C1: only candidate → 9
  7. L3C1: only candidate → 4
  8. L3C2: only candidate → 1
  9. L3C3: only candidate → 9
  10. L6C1: 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

L3C8 = 8

Assumption: L3C8 = 8

  1. L3C9: only candidate → 3
  2. L3C7: only candidate → 2
  3. L6C9: only candidate → 7
  4. L4C9: only candidate → 8
  5. L4C7: only candidate → 3
  6. L9C7: only candidate → 8
  7. L9C4: only candidate → 7
  8. L8C4: only candidate → 8
  9. L9C8: only candidate → 2
  10. L8C8: only candidate → 7
  11. L4C3: only place for 7 in unit 4 → 7
  12. L6C3: only place for 3 in unit 6 → 3
L4C2 = 1

Assumption: L4C2 = 1

L3C2 = 4

Assumption: L3C2 = 4

  1. L6C2: only candidate → 2
  2. L6C1: only candidate → 4
  3. L8C2: only candidate → 9
  4. L8C1: only place for 2 in unit 8 → 2
L3C1 = 1

Assumption: L3C1 = 1

  1. L3C3: only candidate → 9
  2. L5C3: only candidate → 6
  3. L4C1: only candidate → 9
  4. L4C5: only candidate → 6
  5. L5C6: only candidate → 9
  6. L7C1: only candidate → 6

contradiction: a box no longer has no candidate

L3C1 = 9

Assumption: L3C1 = 9

  1. L3C3: only candidate → 1
  2. L4C1: only candidate → 6
  3. L4C5: only candidate → 9
  4. L5C3: only candidate → 9
  5. L5C6: only candidate → 6
  6. L7C1: only candidate → 1
  7. L7C6: only candidate → 9

contradiction: a box no longer has no candidate

all the possibilities of this bifurcation have been examined

L3C2 = 9

Assumption: L3C2 = 9

L3C1 = 1

Assumption: L3C1 = 1

  1. L3C3: only candidate → 4
  2. L7C9: only place for 1 in unit 7 → 1
  3. L8C3: only place for 1 in unit 8 → 1
  4. L9C9: only place for 4 in unit 9 → 4
  5. L8C9: only candidate → 9
L4C1 = 6

Assumption: L4C1 = 6

  1. L4C5: only candidate → 9
  2. L5C3: only candidate → 9
  3. L5C6: only candidate → 6
  4. L7C1: only candidate → 9

contradiction: a box no longer has no candidate

L4C1 = 9

Assumption: L4C1 = 9

  1. L4C5: only candidate → 6
  2. L5C3: only candidate → 6
  3. L5C6: only candidate → 9
  4. L7C1: only candidate → 6

contradiction: a box no longer has no candidate

all the possibilities of this bifurcation have been examined

L3C1 = 4

Assumption: L3C1 = 4

  1. L3C3: only candidate → 1
  2. L6C1: only candidate → 2
  3. L6C2: only candidate → 4
  4. L8C2: only candidate → 2
L4C1 = 6

Assumption: L4C1 = 6

  1. L4C5: only candidate → 9
  2. L5C3: only candidate → 9
  3. L5C6: only candidate → 6
  4. L7C6: only candidate → 9
  5. L7C1: only candidate → 1

contradiction: a box no longer has no candidate

L4C1 = 9

Assumption: L4C1 = 9

  1. L4C5: only candidate → 6
  2. L5C3: only candidate → 6
  3. L5C6: only candidate → 9
  4. L7C6: only candidate → 6
  5. L7C1: only candidate → 1

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

L4C2 = 9

Assumption: L4C2 = 9

  1. L4C5: only candidate → 6
  2. L4C1: only candidate → 1
  3. L5C3: only candidate → 6
  4. L5C6: only candidate → 9
  5. L7C6: only candidate → 6
  6. L7C1: only candidate → 9
  7. L3C1: only candidate → 4
  8. L3C2: only candidate → 1
  9. L3C3: only candidate → 9
  10. L6C1: 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 = 9

Assumption: L2C2 = 9

  1. L3C2: only place for 8 in unit 11 → 8
  2. Nude subset in unit 15: L5C6, L7C6 reserve [6, 9]; remove these figures from L4C6.
L2C7 = 7

Assumption: L2C7 = 7

  1. L2C8: only candidate → 8
  2. Nude subset in unit 15: L5C6, L7C6 reserve [6, 9]; remove these figures from L4C6.
  3. Units 17 and 27 overlap. In unit 17, 7 must lie in the overlap. Remove it from L7C9, L8C9, L9C9.
  4. L7C2: only place for 7 in unit 7 → 7
  5. Nude subassembly in Unit 6: L6C1, L6C2 reserve [2, 4]; remove these numbers from L6C3, L6C6.
  6. L6C6: only candidate → 8
  7. L4C6: only candidate → 4
  8. L4C2: only candidate → 1
  9. Nude subassembly in Unit 4: L4C1, L4C5 reserve [6, 9]; remove these numbers from L4C3.
L3C1 = 1

Assumption: L3C1 = 1

  1. L3C3: only candidate → 4
  2. L7C9: only place for 1 in unit 7 → 1
  3. L8C3: only place for 1 in unit 8 → 1
  4. L9C9: only place for 4 in unit 9 → 4
  5. Nude subassembly in Unit 4: L4C1, L4C5 reserve [6, 9]; remove these numbers from L4C3.
  6. Units 17 and 27 overlap. In unit 17, 7 must lie in the overlap. Remove it from L8C9.
L3C7 = 2

Assumption: L3C7 = 2

  1. L3C8: only candidate → 9
  2. L3C9: only candidate → 3
  3. L6C9: only candidate → 7
  4. L4C9: only candidate → 8
  5. L4C7: only candidate → 3
  6. L6C3: only candidate → 3
  7. L8C9: only candidate → 9
  8. L9C7: only candidate → 8
  9. L9C4: only candidate → 7
  10. L8C4: only candidate → 8
  11. L9C8: only candidate → 2
  12. L8C8: only candidate → 7
  13. L4C3: only place for 7 in unit 4 → 7
  14. L7C5: only place for 2 in unit 14 → 2
L4C1 = 6

Assumption: L4C1 = 6

  1. L4C5: only candidate → 9
  2. L5C3: only candidate → 9
  3. L5C6: only candidate → 6
  4. L7C1: only candidate → 9

contradiction: a box no longer has no candidate

L4C1 = 9

Assumption: L4C1 = 9

  1. L4C5: only candidate → 6
  2. L5C3: only candidate → 6
  3. L5C6: only candidate → 9
  4. L7C1: only candidate → 6

contradiction: a box no longer has no candidate

all the possibilities of this bifurcation have been examined

L3C7 = 3

Assumption: L3C7 = 3

  1. L3C9: only candidate → 9
  2. L3C8: only candidate → 2
  3. L4C7: only candidate → 8
  4. L9C7: only candidate → 2
  5. L9C4: only place for 8 in unit 9 → 8
  6. L8C4: only candidate → 7
  7. L8C8: only candidate → 9
  8. L8C9: only candidate → 8
  9. L9C8: only candidate → 7
  10. L7C5: only place for 2 in unit 14 → 2
  11. Nude subassembly in Unit 4: L4C1, L4C5 reserve [6, 9]; remove these numbers from L4C3.
L4C1 = 6

Assumption: L4C1 = 6

  1. L4C5: only candidate → 9
  2. L5C3: only candidate → 9
  3. L5C6: only candidate → 6
  4. L7C1: only candidate → 9

contradiction: a box no longer has no candidate

L4C1 = 9

Assumption: L4C1 = 9

  1. L4C5: only candidate → 6
  2. L5C3: only candidate → 6
  3. L5C6: only candidate → 9
  4. L7C1: 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

L3C1 = 4

Assumption: L3C1 = 4

  1. L3C3: only candidate → 1
  2. L6C1: only candidate → 2
  3. L6C2: only candidate → 4
  4. L8C2: only candidate → 2
  5. L7C5: only place for 2 in unit 7 → 2
  6. Nude subassembly in Unit 4: L4C1, L4C5 reserve [6, 9]; remove these numbers from L4C3.
  7. Units 17 and 27 overlap. In unit 17, 7 must lie in the overlap. Remove it from L8C9, L9C9.
L3C7 = 2

Assumption: L3C7 = 2

  1. L3C8: only candidate → 9
  2. L3C9: only candidate → 3
  3. L6C9: only candidate → 7
  4. L4C9: only candidate → 8
  5. L4C7: only candidate → 3
  6. L6C3: only candidate → 3
  7. L8C8: only candidate → 7
  8. L8C4: only candidate → 8
  9. L9C4: only candidate → 7
  10. L9C7: only candidate → 8
  11. L9C8: only candidate → 2
  12. L4C3: only place for 7 in unit 4 → 7
L4C1 = 6

Assumption: L4C1 = 6

  1. L4C5: only candidate → 9
  2. L5C3: only candidate → 9
  3. L5C6: only candidate → 6
  4. L7C6: only candidate → 9
  5. L7C1: only candidate → 1

contradiction: a box no longer has no candidate

L4C1 = 9

Assumption: L4C1 = 9

  1. L4C5: only candidate → 6
  2. L5C3: only candidate → 6
  3. L5C6: only candidate → 9
  4. L7C6: only candidate → 6
  5. L7C1: only candidate → 1

contradiction: a box no longer has no candidate

all the possibilities of this bifurcation have been examined

L3C7 = 3

Assumption: L3C7 = 3

  1. L3C9: only candidate → 9
  2. L3C8: only candidate → 2
  3. L4C7: only candidate → 8
  4. L7C9: only candidate → 1
  5. L9C7: only candidate → 2
  6. L8C1: only place for 1 in unit 8 → 1
  7. Nude subassembly in Unit 4: L4C1, L4C5 reserve [6, 9]; remove these numbers from L4C3.
  8. Nude subset in unit 18: L4C9, L6C9 reserve [3, 7]; remove these numbers from L8C9, L9C9.
L4C1 = 6

Assumption: L4C1 = 6

  1. L4C5: only candidate → 9
  2. L5C3: only candidate → 9
  3. L5C6: only candidate → 6
  4. L7C1: only candidate → 9

contradiction: a box no longer has no candidate

L4C1 = 9

Assumption: L4C1 = 9

  1. L4C5: only candidate → 6
  2. L5C3: only candidate → 6
  3. L5C6: only candidate → 9
  4. L7C1: 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

all the possibilities of this bifurcation have been examined

L2C7 = 8

Assumption: L2C7 = 8

  1. L2C8: only candidate → 7
  2. Nude subset in unit 15: L5C6, L7C6 reserve [6, 9]; remove these figures from L4C6.
  3. Units 17 and 27 overlap. In unit 17, 8 must lie in the overlap. Remove it from L8C9, L9C9.
L3C1 = 1

Assumption: L3C1 = 1

  1. L3C3: only candidate → 4
  2. L9C9: only place for 4 in unit 9 → 4
  3. Nude subset in Unit 7: L7C1, L7C5, L7C6 reserve [2, 6, 9]; remove these numbers from L7C2, L7C9.
  4. Nude subset in unit 15: L5C6, L7C6 reserve [6, 9]; remove these figures from L4C6.
  5. Units 17 and 27 overlap. In unit 17, 8 must lie in the overlap. Remove it from L8C9.
L3C7 = 2

Assumption: L3C7 = 2

  1. L3C8: only candidate → 9
  2. L3C9: only candidate → 3
  3. L9C7: only candidate → 7
  4. L4C7: only candidate → 3
  5. L9C4: only candidate → 8
  6. L8C4: only candidate → 7
  7. L9C8: only candidate → 2
  8. L8C8: only candidate → 8
  9. L6C3: only place for 3 in unit 6 → 3
  10. L7C2: only place for 7 in unit 7 → 7
  11. L6C9: only place for 7 in unit 6 → 7
  12. L4C9: only candidate → 8
  13. L4C3: only place for 7 in unit 4 → 7
  14. L4C2: only place for 1 in unit 4 → 1
  15. L6C6: only place for 8 in unit 6 → 8
  16. L7C9: only place for 1 in unit 7 → 1
  17. L8C9: only candidate → 9
  18. L8C3: only candidate → 1
  19. L7C5: only place for 2 in unit 14 → 2
  20. L4C6: only place for 4 in unit 15 → 4
L4C1 = 6

Assumption: L4C1 = 6

  1. L4C5: only candidate → 9
  2. L5C3: only candidate → 9
  3. L5C6: only candidate → 6
  4. L7C1: only candidate → 9

contradiction: a box no longer has no candidate

L4C1 = 9

Assumption: L4C1 = 9

  1. L4C5: only candidate → 6
  2. L5C3: only candidate → 6
  3. L5C6: only candidate → 9
  4. L7C1: only candidate → 6

contradiction: a box no longer has no candidate

all the possibilities of this bifurcation have been examined

L3C7 = 3

Assumption: L3C7 = 3

  1. L3C9: only candidate → 9
  2. L3C8: only candidate → 2
  3. L4C7: only candidate → 7
  4. L9C7: only candidate → 2
  5. L7C5: only place for 2 in unit 14 → 2
  6. Nude subset in unit 15: L5C6, L7C6 reserve [6, 9]; remove these figures from L4C6.
  7. Nude sub-assembly in Unit 18: L4C9, L6C9 reserve [3, 8]; remove these numbers from L8C9.
L4C2 = 1

Assumption: L4C2 = 1

  1. L7C2: only candidate → 7
  2. L7C9: only candidate → 1
  3. L6C3: only place for 7 in unit 6 → 7
  4. L6C9: only place for 3 in unit 6 → 3
  5. L4C9: only candidate → 8
  6. L8C9: only candidate → 7
  7. L8C4: only candidate → 8
  8. L8C8: only candidate → 9
  9. L8C3: only candidate → 1
  10. L9C4: only candidate → 7
  11. L9C8: only candidate → 8
  12. L4C3: only place for 3 in unit 4 → 3
  13. L6C6: only place for 8 in unit 6 → 8
  14. L4C6: only place for 4 in unit 15 → 4
L4C1 = 6

Assumption: L4C1 = 6

  1. L4C5: only candidate → 9
  2. L5C3: only candidate → 9
  3. L5C6: only candidate → 6
  4. L7C1: only candidate → 9

contradiction: a box no longer has no candidate

L4C1 = 9

Assumption: L4C1 = 9

  1. L4C5: only candidate → 6
  2. L5C3: only candidate → 6
  3. L5C6: only candidate → 9
  4. L7C1: only candidate → 6

contradiction: a box no longer has no candidate

all the possibilities of this bifurcation have been examined

L4C2 = 4

Assumption: L4C2 = 4

  1. L6C1: only candidate → 2
  2. L6C2: only candidate → 7
  3. L6C3: only candidate → 3
  4. L6C9: only candidate → 8
  5. L4C9: only candidate → 3
  6. L6C6: only candidate → 4
  7. L7C2: only candidate → 1
  8. L7C9: only candidate → 7
  9. L8C2: only candidate → 2
  10. L8C9: only candidate → 1
  11. L4C6: only place for 8 in unit 4 → 8
  12. L4C3: only place for 1 in unit 4 → 1
  13. L8C1: only place for 4 in unit 8 → 4
L4C1 = 6

Assumption: L4C1 = 6

  1. L4C5: only candidate → 9
  2. L5C3: only candidate → 9
  3. L5C6: only candidate → 6
  4. L7C1: only candidate → 9

contradiction: a box no longer has no candidate

L4C1 = 9

Assumption: L4C1 = 9

  1. L4C5: only candidate → 6
  2. L5C3: only candidate → 6
  3. L5C6: only candidate → 9
  4. L7C1: 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

all the possibilities of this bifurcation have been examined

L3C1 = 4

Assumption: L3C1 = 4

  1. L3C3: only candidate → 1
  2. L6C1: only candidate → 2
  3. Nude subset in unit 15: L5C6, L7C6 reserve [6, 9]; remove these figures from L4C6.
  4. Units 17 and 27 overlap. In unit 17, 8 must lie in the overlap. Remove it from L8C9, L9C9.
L3C7 = 2

Assumption: L3C7 = 2

  1. L3C8: only candidate → 9
  2. L3C9: only candidate → 3
  3. L9C7: only candidate → 7
  4. L4C7: only candidate → 3
  5. L9C4: only candidate → 8
  6. L8C4: only candidate → 7
  7. L9C8: only candidate → 2
  8. L8C8: only candidate → 8
  9. L6C3: only place for 3 in unit 6 → 3
  10. L7C2: only place for 7 in unit 7 → 7
  11. L6C2: only candidate → 4
  12. L4C2: only candidate → 1
  13. L6C6: only candidate → 8
  14. L6C9: only candidate → 7
  15. L4C9: only candidate → 8
  16. L8C2: only candidate → 2
  17. L4C6: only place for 4 in unit 4 → 4
  18. L4C3: only place for 7 in unit 4 → 7
  19. L7C5: only place for 2 in unit 7 → 2
L4C1 = 6

Assumption: L4C1 = 6

  1. L4C5: only candidate → 9
  2. L5C3: only candidate → 9
  3. L5C6: only candidate → 6
  4. L7C6: only candidate → 9
  5. L7C1: only candidate → 1

contradiction: a box no longer has no candidate

L4C1 = 9

Assumption: L4C1 = 9

  1. L4C5: only candidate → 6
  2. L5C3: only candidate → 6
  3. L5C6: only candidate → 9
  4. L7C6: only candidate → 6
  5. L7C1: only candidate → 1

contradiction: a box no longer has no candidate

all the possibilities of this bifurcation have been examined

L3C7 = 3

Assumption: L3C7 = 3

  1. L3C9: only candidate → 9
  2. L3C8: only candidate → 2
  3. L4C7: only candidate → 7
  4. L9C7: only candidate → 2
  5. L8C2: only place for 2 in unit 8 → 2
  6. L7C5: only place for 2 in unit 7 → 2
  7. Nude subset in Unit 7: L7C2, L7C9 reserve [1, 7]; remove these numbers from L7C1.
  8. Nude subset in unit 15: L5C6, L7C6 reserve [6, 9]; remove these figures from L4C6.
  9. Nude subset in Unit 18: L4C9, L6C9 reserve [3, 8]; remove these numbers from L8C9, L9C9.
  10. Units 11 and 22 overlap. In unit 11, 4 must lie in the overlap. Remove it from L4C3, L6C3.
L4C2 = 1

Assumption: L4C2 = 1

  1. L7C2: only candidate → 7
  2. L6C2: only candidate → 4
  3. L6C6: only candidate → 8
  4. L6C9: only candidate → 3
  5. L4C9: only candidate → 8
  6. L6C3: only candidate → 7
  7. L7C9: only candidate → 1
  8. L4C3: only place for 3 in unit 4 → 3
  9. L4C6: only place for 4 in unit 4 → 4
  10. L8C1: only place for 1 in unit 8 → 1
L4C1 = 6

Assumption: L4C1 = 6

  1. L4C5: only candidate → 9
  2. L5C3: only candidate → 9
  3. L5C6: only candidate → 6
  4. L7C1: only candidate → 9

contradiction: a box no longer has no candidate

L4C1 = 9

Assumption: L4C1 = 9

  1. L4C5: only candidate → 6
  2. L5C3: only candidate → 6
  3. L5C6: only candidate → 9
  4. L7C1: only candidate → 6

contradiction: a box no longer has no candidate

all the possibilities of this bifurcation have been examined

L4C2 = 4

Assumption: L4C2 = 4

  1. L6C2: only candidate → 7
  2. L6C3: only candidate → 3
  3. L6C9: only candidate → 8
  4. L4C9: only candidate → 3
  5. L6C6: only candidate → 4
  6. L7C2: only candidate → 1
  7. L7C9: only candidate → 7
  8. L8C1: only candidate → 9
  9. L7C1: only candidate → 6
  10. L4C1: only candidate → 1
  11. L7C6: only candidate → 9
  12. L5C6: only candidate → 6
  13. L4C5: only candidate → 9
  14. L4C3: only candidate → 6
  15. L4C6: only candidate → 8
  16. L5C3: only candidate → 9
  17. L8C8: only candidate → 8
  18. L8C4: only candidate → 7
  19. L8C3: only candidate → 4
  20. L8C9: only candidate → 1
  21. L9C3: only candidate → 7
  22. L9C4: only candidate → 8
  23. L9C5: only candidate → 6
  24. L9C8: only candidate → 9
  25. L9C9: only candidate → 4

valid complete solution

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

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": 81,
  "branches": 40,
  "contradictions": 40,
  "depth": 8,
  "pairs": 49,
  "locked": 8
}

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 81 states and closes 40 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 a single candidate, single places, bare pairs/triples and interactions between units. be shorter.

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