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SOLO-006 · Diagonal Sudoku

EXTREME

The Stubborn Mirror

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

This page contains the solution.

The answer

679852413 / 432671859 / 815943672 / 356297148 / 284516937 / 791438265 / 548369721 / 123784596 / 967125384

Coordinates: lines from top to bottom, columns from left to right.
L / C123456789
1679852413
2432671859
3815943672
4356297148
5284516937
6791438265
7548369721
8123784596
9967125384

The reasoning

  1. Note candidates in each box by crossing lines, columns and regions, diagonals.
  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 37 states; the 18 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. L1C7: only place for 4 in unit 1 → 4
  2. L8C6: only place for 4 in unit 15 → 4
  3. L9C9: only place for 4 in unit 28 → 4
  4. L7C2: only place for 4 in unit 7 → 4
  5. L7C9: only place for 1 in unit 7 → 1
  6. Units 1 and 19 overlap. In unit 1, 6 must lie in the overlap. Remove it from L3C1, L3C2, L3C3.
  7. Units 9 and 25 overlap. In unit 9, 7 must lie in the overlap. Remove it from L8C2, L8C3.
L6C6 = 3

Assumption: L6C6 = 3

  1. Units 1 and 19 overlap. In unit 1, 6 must lie in the overlap. Remove it from L3C1, L3C2, L3C3.
  2. Units 9 and 25 overlap. In unit 9, 7 must lie in the overlap. Remove it from L8C2, L8C3.
L2C6 = 1

Assumption: L2C6 = 1

  1. L5C5: only place for 1 in unit 28 → 1
  2. L4C7: only place for 1 in unit 4 → 1
  3. L8C1: only place for 1 in unit 8 → 1
  4. L3C2: only place for 1 in unit 3 → 1
  5. Units 1 and 19 overlap. In unit 1, 6 must lie in the overlap. Remove it from L3C1, L3C3.
  6. Units 9 and 25 overlap. In unit 9, 7 must lie in the overlap. Remove it from L8C2, L8C3.
  7. Units 29 and 21 overlap. In unit 29, 5 must lie in the overlap. Remove it from L3C8, L3C9.
  8. Units 29 and 25 overlap. In unit 29, 9 must lie in the overlap. Remove it from L8C3, L9C2, L9C3.
L2C2 = 2

Assumption: L2C2 = 2

  1. L5C4: only place for 2 in unit 13 → 2
  2. L4C1: only place for 2 in unit 10 → 2
  3. Units 1 and 19 overlap. In unit 1, 6 must lie in the overlap. Remove it from L3C1, L3C3.
  4. Units 5 and 24 overlap. In unit 5, 7 must lie in the overlap. Remove it from L4C8, L4C9.
  5. Units 9 and 25 overlap. In unit 9, 7 must lie in the overlap. Remove it from L8C2, L8C3.
  6. Units 29 and 21 overlap. In unit 29, 5 must lie in the overlap. Remove it from L3C8, L3C9.
  7. Units 29 and 25 overlap. In unit 29, 9 must lie in the overlap. Remove it from L8C3, L9C2, L9C3.
L2C8 = 5

Assumption: L2C8 = 5

  1. Nude subset in Unit 3: L3C7, L3C8, L3C9 reserve [2, 6, 7]; remove these numbers from L3C1, L3C3, L3C4, L3C6.
  2. L3C6: only candidate → 8
  3. L4C6: only candidate → 7
  4. Units 9 and 25 overlap. In unit 9, 7 must lie in the overlap. Remove it from L8C3.
  5. Units 29 and 25 overlap. In unit 29, 8 must lie in the overlap. Remove it from L8C3, L9C2, L9C3.
  6. Units 29 and 25 overlap. In unit 29, 9 must lie in the overlap. Remove it from L8C3, L9C2, L9C3.
L2C3 = 3

Assumption: L2C3 = 3

  1. L2C5: only candidate → 7
  2. L3C4: only place for 3 in unit 3 → 3
  3. L7C4: only candidate → 8
  4. L7C3: only candidate → 2
  5. L3C7: only candidate → 6
  6. L3C1: only candidate → 9
  7. L3C3: only candidate → 5
  8. L4C4: only candidate → 9
  9. L1C4: only candidate → 5
  10. L1C5: only candidate → 9
  11. L7C8: only candidate → 3
  12. L8C4: only candidate → 7
  13. L8C5: only candidate → 3
  14. L9C1: only candidate → 8
  15. L1C1: only candidate → 6
  16. L5C1: only candidate → 3
  17. L8C2: only candidate → 9
  18. L8C3: only candidate → 6
  19. L8C8: only candidate → 8
  20. L9C3: only candidate → 7
  21. L1C3: only candidate → 8
  22. L1C2: only candidate → 7
  23. L4C3: only candidate → 4
  24. L4C8: only candidate → 6
  25. L5C3: only candidate → 9
  26. L5C7: only candidate → 5
  27. L4C9: only candidate → 8
  28. L4C2: only candidate → 5

contradiction: a box no longer has no candidate

L2C3 = 7

Assumption: L2C3 = 7

  1. L2C5: only candidate → 3
  2. L3C1: only place for 3 in unit 3 → 3
  3. L9C2: only place for 7 in unit 9 → 7
  4. Nude sub-assembly in Unit 3: L3C7, L3C8, L3C9 reserve [2, 6, 7]; remove these numbers from L3C3, L3C4.
  5. Units 11 and 22 overlap. In unit 11, 3 must lie in the overlap. Remove it from L4C3, L5C3.
  6. Units 29 and 25 overlap. In unit 29, 8 must lie in the overlap. Remove it from L8C3, L9C3.
  7. Units 29 and 25 overlap. In unit 29, 9 must lie in the overlap. Remove it from L8C3, L9C3.
L3C3 = 5

Assumption: L3C3 = 5

  1. L3C4: only place for 9 in unit 3 → 9
  2. L4C4: only candidate → 8
  3. L7C4: only candidate → 3
  4. L8C4: only candidate → 7
  5. L1C4: only candidate → 5
  6. L1C5: only candidate → 7
  7. L8C5: only candidate → 8
  8. Nude subset in Unit 8: L8C2, L8C8 reserve [6, 9]; remove these numbers from L8C3, L8C7, L8C9.
  9. Units 11 and 22 overlap. In unit 11, 3 must lie in the overlap. Remove it from L4C3, L5C3.
  10. Units 18 and 24 overlap. In unit 18, 8 must lie in the overlap. Remove it from L5C8, L6C8.
  11. Units 29 and 25 overlap. In unit 29, 8 must lie in the overlap. Remove it from L9C3.
  12. Units 29 and 25 overlap. In unit 29, 9 must lie in the overlap. Remove it from L9C3.
L1C1 = 6

Assumption: L1C1 = 6

  1. L8C8: only candidate → 9
  2. L8C2: only candidate → 6
  3. L3C7: only candidate → 2
  4. L7C3: only candidate → 8
  5. L1C3: only candidate → 9
  6. L1C2: only candidate → 8
  7. L7C8: only candidate → 2
  8. L8C9: only candidate → 5
  9. L4C9: only candidate → 6
  10. L3C9: only candidate → 7
  11. L3C8: only candidate → 6
  12. L5C9: only candidate → 8

contradiction: a box no longer has no candidate

L1C1 = 9

Assumption: L1C1 = 9

  1. L5C1: only candidate → 8
  2. L8C8: only candidate → 6
  3. L8C2: only candidate → 9
  4. L9C1: only candidate → 6
  5. L3C7: only candidate → 2
  6. L3C8: only candidate → 7
  7. L3C9: only candidate → 6
  8. L4C9: only candidate → 5
  9. L4C5: only candidate → 9
  10. L5C9: only candidate → 7
  11. L6C5: only candidate → 5
  12. L6C2: only candidate → 6
  13. L1C2: only candidate → 8
  14. L1C3: only candidate → 6
  15. L4C2: only candidate → 3
  16. L4C3: only candidate → 4

contradiction: a box no longer has no candidate

all the possibilities of this bifurcation have been examined

L3C3 = 9

Assumption: L3C3 = 9

  1. L3C4: only place for 5 in unit 3 → 5
  2. L4C4: only candidate → 8
  3. L1C1: 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

L2C8 = 7

Assumption: L2C8 = 7

  1. L4C6: only candidate → 8
  2. L3C6: only candidate → 7
  3. L7C3: only candidate → 2
  4. L5C9: only place for 7 in unit 5 → 7
  5. L4C5: only place for 7 in unit 4 → 7
  6. L8C4: only place for 7 in unit 13 → 7
  7. L3C7: only place for 5 in unit 29 → 5
  8. Nude subset in Unit 3: L3C8, L3C9 reserve [2, 6]; remove these numbers from L3C1, L3C3.
  9. Nude subset in Unit 25: L8C2, L9C1 reserve [6, 9]; remove these numbers from L8C3, L9C2, L9C3.
  10. Nude subassembly in Unit 8: L8C3, L8C5 reserve [3, 8]; remove these numbers from L8C7, L8C8, L8C9.
  11. L6C9: only place for 8 in unit 18 → 8
  12. Units 28 and 19 overlap. In unit 28, 8 must lie in the overlap. Remove it from L1C2, L1C3, L3C1.
L2C3 = 3

Assumption: L2C3 = 3

  1. L2C5: only candidate → 5
  2. L6C5: only candidate → 9
  3. L1C5: only candidate → 8
  4. L1C4: only candidate → 9
  5. L1C1: only candidate → 6
  6. L3C4: only candidate → 3
  7. L4C4: only candidate → 5
  8. L4C9: only candidate → 6
  9. L3C9: only candidate → 2
  10. L3C8: only candidate → 6
  11. L6C7: only candidate → 2
  12. L6C8: only candidate → 5
  13. L6C2: only candidate → 6
  14. L7C4: only candidate → 8
  15. L7C8: only candidate → 3
  16. L8C2: only candidate → 9

contradiction: a box no longer has no candidate

L2C3 = 5

Assumption: L2C3 = 5

  1. L2C5: only candidate → 3
  2. L8C5: only candidate → 8
  3. L7C4: only candidate → 3
  4. L7C8: only candidate → 8
  5. L3C1: only place for 3 in unit 3 → 3
  6. Nude subassembly in Unit 3: L3C8, L3C9 reserve [2, 6]; remove these figures from L3C3.
  7. Nude subset in Unit 9: L9C1, L9C7, L9C8 reserve [3, 6, 9]; remove these numbers from L9C2, L9C3.
  8. L8C3: only place for 3 in unit 25 → 3
  9. Units 28 and 19 overlap. In unit 28, 8 must lie in the overlap. Remove it from L1C2, L1C3.
L1C5 = 5

Assumption: L1C5 = 5

  1. L6C5: only candidate → 9
  2. L4C4: only candidate → 5
  3. L4C9: only candidate → 6
  4. L3C9: only candidate → 2
  5. L3C8: only candidate → 6
  6. L6C7: only candidate → 2
  7. L6C8: only candidate → 5
  8. L6C2: only candidate → 6
  9. L8C2: only candidate → 9

contradiction: a box no longer has no candidate

L1C5 = 9

Assumption: L1C5 = 9

  1. L3C4: only candidate → 8
  2. L1C4: only candidate → 5
  3. L4C4: only candidate → 9
  4. L3C3: only candidate → 6
  5. L1C1: only candidate → 8
  6. L1C2: only candidate → 7

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

L2C2 = 5

Assumption: L2C2 = 5

  1. L3C7: only place for 5 in unit 29 → 5
  2. L8C9: only place for 5 in unit 8 → 5
  3. Nude sub-assembly in unit 29: L2C8, L4C6, L7C3 reserve [2, 7, 8]; remove these numbers from L8C2, L9C1.
  4. Nude subset in Unit 25: L8C2, L9C1 reserve [6, 9]; remove these numbers from L8C3, L9C2, L9C3.
  5. Units 1 and 19 overlap. In unit 1, 6 must lie in the overlap. Remove it from L3C1, L3C3.
  6. Units 9 and 25 overlap. In unit 9, 7 must lie in the overlap. Remove it from L8C3.
  7. Units 11 and 22 overlap. In unit 11, 2 must lie in the overlap. Remove it from L4C1, L4C3, L5C1, L5C3.
  8. L3C1: only place for 2 in unit 10 → 2
  9. L2C8: only place for 2 in unit 2 → 2
  10. L7C3: only candidate → 8
  11. L3C3: only candidate → 9
  12. L4C6: only candidate → 7
  13. L3C6: only candidate → 8
  14. L7C4: only candidate → 3

contradiction: a box no longer has no candidate

all the possibilities of this bifurcation have been examined

L2C6 = 7

Assumption: L2C6 = 7

  1. L8C2: only place for 7 in unit 29 → 7
  2. L1C3: only place for 7 in unit 1 → 7
  3. L8C1: only place for 1 in unit 8 → 1

contradiction: the number 7 can no longer be included in unit 9

all the possibilities of this bifurcation have been examined

L6C6 = 8

Assumption: L6C6 = 8

  1. Units 1 and 19 overlap. In unit 1, 6 must lie in the overlap. Remove it from L3C1, L3C2, L3C3.
  2. Units 9 and 25 overlap. In unit 9, 7 must lie in the overlap. Remove it from L8C2, L8C3.
  3. Units 15 and 20 overlap. In unit 15, 3 must lie in the overlap. Remove it from L2C5, L3C4.
  4. Units 29 and 25 overlap. In unit 29, 8 must lie in the overlap. Remove it from L8C1, L8C3, L9C2, L9C3.
L1C1 = 6

Assumption: L1C1 = 6

  1. Units 9 and 25 overlap. In unit 9, 7 must lie in the overlap. Remove it from L8C2, L8C3.
  2. Units 15 and 20 overlap. In unit 15, 3 must lie in the overlap. Remove it from L2C5, L3C4.
  3. Units 29 and 25 overlap. In unit 29, 8 must lie in the overlap. Remove it from L8C1, L8C3, L9C2, L9C3.
L4C6 = 1

Assumption: L4C6 = 1

  1. L5C7: only place for 1 in unit 5 → 1
  2. L8C1: only place for 1 in unit 8 → 1
  3. L3C2: only place for 1 in unit 3 → 1
  4. L2C5: only place for 1 in unit 2 → 1

contradiction: the number 1 can no longer appear in unit 28

L4C6 = 7

Assumption: L4C6 = 7

  1. Nude sub-assembly in unit 20: L2C6, L3C6 reserve [1, 3]; remove these numbers from L2C5, L3C4.
  2. Units 9 and 25 overlap. In unit 9, 7 must lie in the overlap. Remove it from L8C3.
  3. Units 21 and 3 overlap. In unit 21, 7 must lie in the overlap. Remove it from L3C2, L3C4.
  4. Units 29 and 25 overlap. In unit 29, 8 must lie in the overlap. Remove it from L8C1, L8C3, L9C2, L9C3.
L2C5 = 5

Assumption: L2C5 = 5

  1. L2C8: only candidate → 2
  2. L7C3: only candidate → 8
  3. L7C4: only candidate → 3

contradiction: a box no longer has no candidate

L2C5 = 7

Assumption: L2C5 = 7

  1. L8C4: only place for 7 in unit 13 → 7
  2. Nude sub-assembly in unit 20: L2C6, L3C6 reserve [1, 3]; remove these figures from L3C4.
  3. Units 1 and 19 overlap. In unit 1, 7 must lie in the overlap. Remove it from L3C2.
  4. Units 29 and 25 overlap. In unit 29, 8 must lie in the overlap. Remove it from L8C1, L8C3, L9C2, L9C3.
L2C6 = 1

Assumption: L2C6 = 1

  1. L3C6: only candidate → 3
  2. L5C5: only place for 1 in unit 28 → 1
  3. L4C7: only place for 1 in unit 4 → 1
  4. L8C1: only place for 1 in unit 8 → 1
  5. L3C2: only place for 1 in unit 3 → 1
  6. Units 10 and 22 overlap. In unit 10, 3 must lie in the overlap. Remove it from L4C2, L4C3, L5C2, L5C3, L6C2.
  7. Units 29 and 21 overlap. In unit 29, 5 must lie in the overlap. Remove it from L3C8, L3C9.
  8. Units 29 and 25 overlap. In unit 29, 8 must lie in the overlap. Remove it from L8C3, L9C2, L9C3.
  9. Units 29 and 25 overlap. In unit 29, 9 must lie in the overlap. Remove it from L8C3, L9C2, L9C3.
L2C8 = 2

Assumption: L2C8 = 2

  1. L7C3: only candidate → 8
  2. L7C4: only candidate → 3

contradiction: a box no longer has no candidate

L2C8 = 5

Assumption: L2C8 = 5

  1. Nude subassembly in Unit 3: L3C7, L3C8, L3C9 reserve [2, 6, 7]; remove these numbers from L3C1, L3C3.
  2. Nude subset in Unit 10: L3C1, L9C1 reserve [8, 9]; remove these numbers from L4C1, L5C1.
  3. Nude sub-assembly in unit 22: L4C1, L5C1 reserve [2, 3]; remove these numbers from L4C2, L4C3, L5C2, L5C3, L6C2.
  4. Units 6 and 24 overlap. In unit 6, 2 must lie in the overlap. Remove it from L4C8, L4C9, L5C7, L5C8, L5C9.
  5. Units 29 and 25 overlap. In unit 29, 8 must lie in the overlap. Remove it from L8C3, L9C2, L9C3.
  6. Units 29 and 25 overlap. In unit 29, 9 must lie in the overlap. Remove it from L8C3, L9C2, L9C3.
L2C2 = 2

Assumption: L2C2 = 2

  1. L2C3: only candidate → 3
  2. L5C4: only place for 2 in unit 13 → 2
  3. L4C1: only place for 2 in unit 10 → 2
  4. L5C1: only place for 3 in unit 10 → 3
  5. L9C2: only place for 3 in unit 11 → 3
  6. L9C3: only place for 7 in unit 9 → 7
  7. L1C2: only place for 7 in unit 1 → 7
  8. Units 9 and 27 overlap. In unit 9, 6 must lie in the overlap. Remove it from L8C7, L8C9.
  9. Units 11 and 22 overlap. In unit 11, 5 must lie in the overlap. Remove it from L4C3, L5C3.
  10. Units 29 and 25 overlap. In unit 29, 8 must lie in the overlap. Remove it from L8C3.
  11. Units 29 and 25 overlap. In unit 29, 9 must lie in the overlap. Remove it from L8C3.
L3C1 = 8

Assumption: L3C1 = 8

  1. L9C1: only candidate → 9
  2. L9C7: only candidate → 6
  3. L3C7: only candidate → 2
  4. L7C3: only candidate → 8
  5. L7C4: only candidate → 3
  6. L7C8: only candidate → 2
  7. L8C2: only candidate → 6
  8. L8C3: only candidate → 2
  9. L8C5: only candidate → 8
  10. L8C9: only candidate → 5
  11. L9C8: only candidate → 8
  12. L1C4: only place for 8 in unit 1 → 8
  13. L6C9: only place for 2 in unit 6 → 2
  14. L6C8: only place for 6 in unit 6 → 6
  15. L3C8: only candidate → 7
  16. L3C9: only candidate → 6
  17. L4C9: only candidate → 8
  18. L5C9: only candidate → 7
  19. L4C3: only place for 6 in unit 4 → 6
  20. L4C8: only place for 4 in unit 4 → 4
  21. L5C8: only candidate → 9
  22. L5C7: only candidate → 5
  23. L5C2: only candidate → 8
  24. L5C3: only candidate → 4
  25. L6C7: only candidate → 3
  26. L8C7: only candidate → 9
  27. L8C8: only candidate → 3
  28. L4C5: only place for 3 in unit 4 → 3
L1C3 = 5

Assumption: L1C3 = 5

  1. L1C5: only candidate → 9
  2. L3C3: only candidate → 9
  3. L3C4: only candidate → 5

contradiction: a box no longer has no candidate

L1C3 = 9

Assumption: L1C3 = 9

  1. L1C5: only candidate → 5
  2. L3C3: only candidate → 5
  3. L3C4: only candidate → 9

contradiction: a box no longer has no candidate

all the possibilities of this bifurcation have been examined

L3C1 = 9

Assumption: L3C1 = 9

  1. L3C3: only candidate → 5
  2. L1C3: only candidate → 8
  3. L3C4: only candidate → 8
  4. L7C3: only candidate → 2
  5. L3C7: only candidate → 6
  6. L7C4: only candidate → 3
  7. L4C4: only candidate → 9
  8. L1C4: only candidate → 5
  9. L1C5: only candidate → 9
  10. L7C8: only candidate → 8
  11. L8C5: only candidate → 8
  12. L8C2: only candidate → 9
  13. L8C3: only candidate → 6
  14. L4C3: only candidate → 4
  15. L5C3: only candidate → 9
  16. L5C7: only candidate → 5
  17. L5C2: only candidate → 8
  18. L5C9: only candidate → 7
  19. L3C9: only candidate → 2
  20. L3C8: only candidate → 7
  21. L5C8: only candidate → 4
  22. L6C9: only candidate → 6
  23. L4C8: only candidate → 3

contradiction: a box no longer has no candidate

all the possibilities of this bifurcation have been examined

L2C2 = 3

Assumption: L2C2 = 3

  1. L2C3: only candidate → 2
  2. L7C3: only candidate → 8
  3. L7C4: only candidate → 3
  4. L7C8: only candidate → 2
  5. L8C5: only candidate → 8
  6. L8C8: only candidate → 9
  7. L3C3: only candidate → 5
  8. L4C4: only candidate → 2
  9. L9C1: only candidate → 9
  10. L3C1: only candidate → 8
  11. L3C4: only candidate → 9
  12. L1C5: only candidate → 5
  13. L1C4: only candidate → 8
  14. L4C1: only candidate → 3
  15. L4C5: only candidate → 9
  16. L5C1: only candidate → 2
  17. L5C4: only candidate → 5
  18. L6C5: only candidate → 3
  19. L6C8: only candidate → 6
  20. L3C8: only candidate → 7
  21. L5C9: only place for 7 in unit 5 → 7
  22. L8C2: only place for 2 in unit 8 → 2
  23. L3C7: only candidate → 6
  24. L3C9: only candidate → 2
  25. L6C9: only candidate → 5
  26. L4C9: only candidate → 8
  27. L4C8: only candidate → 4
  28. L4C3: only candidate → 6
  29. L4C2: only candidate → 5
  30. L5C8: only candidate → 3
  31. L5C7: only candidate → 9
  32. L5C2: only candidate → 8
  33. L5C3: only candidate → 4
  34. L6C2: only candidate → 9
  35. L1C2: only candidate → 7
  36. L1C3: only candidate → 9
  37. L6C7: only candidate → 2
  38. L8C3: only candidate → 3
  39. L8C7: only candidate → 5
  40. L8C9: only candidate → 6
  41. L9C2: only candidate → 6
  42. L9C3: only candidate → 7
  43. L9C7: only candidate → 3
  44. L9C8: only candidate → 8

valid complete solution

all the possibilities of this bifurcation have been examined

all the possibilities of this bifurcation have been examined

L2C6 = 3

Assumption: L2C6 = 3

  1. L3C6: only candidate → 1
  2. L2C2: only place for 1 in unit 2 → 1
  3. L5C7: only place for 1 in unit 5 → 1
  4. L4C5: only place for 1 in unit 4 → 1
  5. L8C1: only place for 1 in unit 8 → 1

contradiction: the number 1 can no longer appear in unit 29

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 = 9

Assumption: L1C1 = 9

  1. L3C4: only place for 9 in unit 3 → 9
  2. L8C2: only place for 9 in unit 29 → 9
  3. L8C1: only place for 1 in unit 8 → 1
  4. Units 1 and 19 overlap. In unit 1, 6 must lie in the overlap. Remove it from L3C1, L3C2, L3C3.
  5. L8C8: only place for 6 in unit 28 → 6
  6. Units 3 and 19 overlap. In unit 3, 8 must lie in the overlap. Remove it from L1C2, L1C3.
  7. Units 9 and 25 overlap. In unit 9, 7 must lie in the overlap. Remove it from L8C3.
  8. Units 15 and 20 overlap. In unit 15, 3 must lie in the overlap. Remove it from L2C5.
  9. Units 25 and 12 overlap. In unit 25, 2 must lie in the overlap. Remove it from L2C3, L3C3, L4C3, L5C3.
  10. Units 29 and 23 overlap. In unit 29, 1 must lie in the overlap. Remove it from L4C5.
  11. Units 29 and 25 overlap. In unit 29, 8 must lie in the overlap. Remove it from L8C3, L9C2, L9C3.
L3C3 = 3

Assumption: L3C3 = 3

  1. L2C6: only place for 3 in unit 15 → 3
  2. L9C2: only place for 3 in unit 25 → 3
  3. L9C7: only candidate → 9
  4. L9C8: only candidate → 8
  5. L9C1: only candidate → 6
  6. L9C3: only candidate → 7
  7. L3C9: only place for 6 in unit 21 → 6
  8. L7C3: only place for 8 in unit 29 → 8
  9. L7C4: only candidate → 3
  10. L7C8: only candidate → 2
  11. L8C3: only candidate → 2
  12. L2C3: only candidate → 5
  13. L1C3: only candidate → 6
  14. L2C8: only candidate → 7
  15. L2C5: only candidate → 1
  16. L2C2: only candidate → 2
  17. L3C1: only candidate → 8
  18. L1C2: only candidate → 7
  19. L3C2: only candidate → 1
  20. L3C6: only candidate → 7
  21. L3C8: only candidate → 5
  22. L3C7: only candidate → 2
  23. L4C4: only candidate → 5

contradiction: a box no longer has no candidate

L3C3 = 5

Assumption: L3C3 = 5

  1. L5C5: only candidate → 1
  2. L4C6: only candidate → 7
  3. L2C6: only place for 1 in unit 2 → 1
  4. L3C6: only candidate → 3
  5. L3C2: only place for 1 in unit 3 → 1
  6. L3C1: only place for 8 in unit 3 → 8
  7. L9C1: only candidate → 6
  8. L3C7: only candidate → 2
  9. L2C8: only candidate → 5
  10. L2C5: only candidate → 7
  11. L3C8: only candidate → 7
  12. L3C9: only candidate → 6
  13. L7C3: only candidate → 8
  14. L7C4: only candidate → 3
  15. L4C4: only candidate → 2
  16. L2C2: only candidate → 3
  17. L2C3: only candidate → 2
  18. L4C1: only candidate → 3
  19. L5C1: only candidate → 2
  20. L5C4: only candidate → 5
  21. L1C4: only candidate → 8
  22. L1C5: only candidate → 5
  23. L4C5: only candidate → 9
  24. L5C2: only candidate → 8
  25. L5C9: only candidate → 7
  26. L6C5: only candidate → 3
  27. L7C8: only candidate → 2
  28. L6C8: only candidate → 9
  29. L5C7: only candidate → 3
  30. L5C8: only candidate → 4
  31. L4C8: only candidate → 8
  32. L4C9: only candidate → 5
  33. L4C2: only candidate → 6
  34. L1C2: only candidate → 7

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

How we verified this answer

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

{
  "nodes": 37,
  "branches": 18,
  "contradictions": 18,
  "depth": 9,
  "pairs": 15,
  "locked": 58
}

After single candidates, single places, bare pairs/triples and interactions between units, the solver still reaches bifurcations. The exhaustive evidence reaches 9 intertwined hypotheses, examines 37 states and closes 18 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 be shorter.

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