The Big BookOF GAMES
← All 40 challenges

SOLO-010 · Killer Sudoku

EXTREME

Unyielding Totals

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

This page contains the solution.

The answer

637412598 / 981375624 / 245896731 / 528961473 / 174238965 / 396754182 / 712589346 / 463127859 / 859643217

Coordinates: lines from top to bottom, columns from left to right.
L / C123456789
19631474121352298
216918812737195624
32458189672031
4517289614783
513171041823218965
639675411982
7197191825278934156
84631122711859
985596432177

Thick stroke: region. Dotted inside the cells: cage and its total. A tint on a diagonal reminds the diagonal constraint, if it applies.

Exact list of cages (coordinates and totals)

The reasoning

  1. Note the candidates in each box by crossing the line, column and region and amounts of cages.
  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 127 states; the 63 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. L8C9: only candidate → 9
  2. L9C2: only candidate → 5
  3. L9C9: only candidate → 7
  4. Nude subset in unit 18: L4C9, L5C9 reserve [3, 5]; remove these numbers from L1C9, L2C9, L3C9, L6C9.
  5. L1C8: only candidate → 9
  6. L6C9: only place for 2 in unit 18 → 2
  7. Nude subset in Unit 21: L1C9, L2C9, L3C9 reserve [1, 4, 8]; remove these numbers from L1C7, L2C7, L2C8, L3C7, L3C8.
  8. L2C8: only candidate → 2
  9. Nude subset in unit 16: L1C7, L2C7 reserve [5, 6]; remove these numbers from L3C7, L4C7, L5C7, L6C7, L7C7, L8C7.
  10. Nude subset in Unit 21: L1C7, L2C7 reserve [5, 6]; remove these numbers from L3C8.
  11. Nude subassembly in Unit 3: L3C7, L3C8 reserve [3, 7]; remove these numbers from L3C1, L3C2, L3C3, L3C4, L3C5, L3C6.
  12. Nude subset in Unit 24: L4C9, L5C9 reserve [3, 5]; remove these numbers from L4C7, L4C8, L5C7, L5C8, L6C7, L6C8.
  13. Nude subset in Unit 27: L8C7, L9C8 reserve [1, 8]; remove these numbers from L7C7, L7C8, L8C8.
  14. L6C8: only candidate → 8
  15. L3C8: only candidate → 3
  16. L3C7: only candidate → 7
  17. L8C7: only candidate → 8
  18. L9C8: only candidate → 1
  19. L4C7: only candidate → 4
  20. L5C6: only candidate → 8
  21. L7C7: only candidate → 3
L1C7 = 5

Assumption: L1C7 = 5

  1. L2C7: only candidate → 6
L4C8 = 6

Assumption: L4C8 = 6

  1. L5C8: only candidate → 7
L4C9 = 3

Assumption: L4C9 = 3

  1. L5C9: only candidate → 5
L5C7 = 1

Assumption: L5C7 = 1

  1. L6C7: only candidate → 9
L7C8 = 4

Assumption: L7C8 = 4

  1. L8C8: only candidate → 5
  2. L7C4: only candidate → 5
  3. L7C5: only candidate → 8
  4. L8C5: only candidate → 2
  5. L7C3: only candidate → 2
  6. L8C4: only candidate → 1
  7. L7C2: only candidate → 1
  8. Nude sub-assembly in Unit 9: L9C4, L9C5 reserve [4, 6]; remove these numbers from L9C1, L9C6.
  9. Nude subset in unit 15: L7C6, L8C6, L9C6 reserve [3, 7, 9]; remove these numbers from L1C6, L2C6, L3C6, L4C6, L6C6.
  10. L3C6: only candidate → 6
  11. Units 3 and 19 overlap. In unit 3, 2 must lie in the overlap. Remove it from L1C1, L1C2.
L3C4 = 8

Assumption: L3C4 = 8

  1. Nude subset in Unit 9: L9C4, L9C5 reserve [4, 6]; remove these numbers from L9C1.
  2. Nude subset in unit 15: L7C6, L8C6, L9C6 reserve [3, 7, 9]; remove these numbers from L1C6, L6C6.
  3. Units 3 and 19 overlap. In unit 3, 2 must lie in the overlap. Remove it from L1C1, L1C2.
L3C9 = 1

Assumption: L3C9 = 1

  1. Nude subset in Unit 9: L9C4, L9C5 reserve [4, 6]; remove these numbers from L9C1.
  2. Nude subset in unit 15: L7C6, L8C6, L9C6 reserve [3, 7, 9]; remove these numbers from L1C6, L6C6.
  3. Units 3 and 19 overlap. In unit 3, 2 must lie in the overlap. Remove it from L1C1, L1C2.
L1C9 = 4

Assumption: L1C9 = 4

  1. L1C3: only candidate → 8
  2. L2C9: only candidate → 8
  3. L9C3: only candidate → 9
  4. L7C1: only candidate → 7
  5. L7C6: only candidate → 9
  6. L8C1: only candidate → 4
  7. L8C6: only candidate → 7
  8. L9C1: only candidate → 8
  9. L9C6: only candidate → 3
  10. L1C2: only place for 7 in unit 1 → 7
  11. L1C1: only candidate → 2

contradiction: a box no longer has no candidate

L1C9 = 8

Assumption: L1C9 = 8

  1. L2C9: only candidate → 4
  2. L6C1: only place for 1 in unit 10 → 1
  3. L5C1: only candidate → 9
  4. L6C2: only candidate → 3
  5. L7C1: only candidate → 7
  6. L2C1: only candidate → 3

contradiction: a box no longer has no candidate

all the possibilities of this bifurcation have been examined

L3C9 = 4

Assumption: L3C9 = 4

  1. Nude subset in Unit 9: L9C4, L9C5 reserve [4, 6]; remove these numbers from L9C1.
  2. Nude subset in unit 14: L5C5, L9C5 reserve [4, 6]; remove these numbers from L1C5, L6C5.
  3. Nude subset in unit 15: L7C6, L8C6, L9C6 reserve [3, 7, 9]; remove these numbers from L1C6, L6C6.
  4. Units 3 and 19 overlap. In unit 3, 1 must lie in the overlap. Remove it from L1C1, L1C3, L2C3.
  5. Units 3 and 19 overlap. In unit 3, 2 must lie in the overlap. Remove it from L1C1, L1C2.
  6. Nude sub-assembly in unit 1: L1C1, L1C2 reserve [3, 6]; remove these numbers from L1C3, L1C4, L1C5.
  7. L1C9: only place for 8 in unit 1 → 8
  8. L2C9: only candidate → 1
  9. Nude subset in unit 19: L1C1, L1C2 reserve [3, 6]; remove these numbers from L2C1, L2C2, L2C3.
  10. L3C2: only candidate → 2
  11. Nude sub-assembly in unit 12: L3C3, L4C3 reserve [1, 5]; remove these numbers from L6C3.
  12. L9C3: only place for 9 in unit 12 → 9
  13. L7C1: only candidate → 7
  14. L4C1: only candidate → 2
  15. L2C6: only candidate → 5
  16. L2C1: only candidate → 9
  17. L3C1: only candidate → 5
  18. L3C3: only candidate → 1
  19. L3C5: only candidate → 9
  20. L4C3: only candidate → 5

contradiction: a box no longer has no candidate

all the possibilities of this bifurcation have been examined

L3C4 = 9

Assumption: L3C4 = 9

  1. L2C4: only candidate → 8
  2. L2C5: only candidate → 3
  3. L4C4: only candidate → 7
  4. L2C1: only place for 9 in unit 2 → 9
  5. L7C1: only candidate → 7
  6. L7C6: only candidate → 9
  7. L8C1: only candidate → 4
  8. L8C6: only candidate → 7
  9. L9C1: only candidate → 8
  10. L9C3: only candidate → 9
  11. L4C3: only candidate → 5
  12. L2C2: only candidate → 7
  13. L1C5: only candidate → 7
  14. L2C3: only candidate → 1
  15. L1C3: only candidate → 4
  16. L1C4: only candidate → 2
  17. L1C6: only candidate → 1
  18. L1C9: only candidate → 8
  19. L2C6: only candidate → 4

contradiction: a box no longer has no candidate

all the possibilities of this bifurcation have been examined

L7C8 = 5

Assumption: L7C8 = 5

  1. L8C8: only candidate → 4
L8C4 = 3

Assumption: L8C4 = 3

  1. L8C5: only candidate → 2
  2. L7C2: only place for 2 in unit 7 → 2
  3. L8C6: only place for 5 in unit 8 → 5
  4. L9C6: only candidate → 6

contradiction: a box no longer has no candidate

L8C4 = 5

Assumption: L8C4 = 5

  1. L7C5: only candidate → 8
  2. L8C5: only candidate → 2
  3. L7C3: only candidate → 2
  4. L7C4: only candidate → 1
  5. Nude subset in Unit 9: L9C4, L9C5 reserve [4, 6]; remove these numbers from L9C1, L9C3, L9C6.
  6. Nude subset in unit 26: L9C4, L9C5 reserve [4, 6]; remove these numbers from L7C6, L8C6.
  7. Nude subset in unit 15: L7C6, L8C6, L9C6 reserve [3, 7, 9]; remove these numbers from L1C6, L2C6, L3C6, L4C6, L6C6.
  8. L3C6: only candidate → 6
  9. Units 3 and 19 overlap. In unit 3, 2 must lie in the overlap. Remove it from L1C1, L1C2.
L3C4 = 8

Assumption: L3C4 = 8

  1. Nude subset in Unit 9: L9C4, L9C5 reserve [4, 6]; remove these numbers from L9C1, L9C3.
  2. Nude subset in unit 15: L7C6, L8C6, L9C6 reserve [3, 7, 9]; remove these numbers from L1C6, L6C6.
  3. Units 3 and 19 overlap. In unit 3, 2 must lie in the overlap. Remove it from L1C1, L1C2.
L3C9 = 1

Assumption: L3C9 = 1

  1. Nude subset in Unit 9: L9C4, L9C5 reserve [4, 6]; remove these numbers from L9C1, L9C3.
  2. Nude subset in unit 15: L7C6, L8C6, L9C6 reserve [3, 7, 9]; remove these numbers from L1C6, L6C6.
  3. Units 3 and 19 overlap. In unit 3, 2 must lie in the overlap. Remove it from L1C1, L1C2.
L1C9 = 4

Assumption: L1C9 = 4

  1. L1C3: only candidate → 8
  2. L2C9: only candidate → 8
  3. L7C2: only candidate → 9
  4. L3C2: only candidate → 2
  5. L4C2: only candidate → 8
  6. L4C3: only candidate → 5
  7. L3C5: only candidate → 5
  8. L2C6: only candidate → 4
  9. L2C2: only candidate → 3

contradiction: a box no longer has no candidate

L1C9 = 8

Assumption: L1C9 = 8

  1. L2C9: only candidate → 4
  2. L6C1: only place for 1 in unit 10 → 1
  3. L5C1: only candidate → 9
  4. L6C2: only candidate → 3
  5. L7C1: only candidate → 4
  6. L2C1: only candidate → 3

contradiction: a box no longer has no candidate

all the possibilities of this bifurcation have been examined

L3C9 = 4

Assumption: L3C9 = 4

  1. Nude subset in Unit 9: L9C4, L9C5 reserve [4, 6]; remove these numbers from L9C1, L9C3.
  2. Nude subset in unit 14: L5C5, L9C5 reserve [4, 6]; remove these numbers from L1C5, L6C5.
  3. Nude subset in unit 15: L7C6, L8C6, L9C6 reserve [3, 7, 9]; remove these numbers from L1C6, L6C6.
  4. Units 3 and 19 overlap. In unit 3, 1 must lie in the overlap. Remove it from L1C1, L1C2, L1C3, L2C2, L2C3.
  5. Units 3 and 19 overlap. In unit 3, 2 must lie in the overlap. Remove it from L1C1, L1C2.
  6. Nude sub-assembly in unit 1: L1C1, L1C2 reserve [3, 6]; remove these numbers from L1C3, L1C4, L1C5.
  7. L1C9: only place for 8 in unit 1 → 8
  8. L2C9: only candidate → 1
  9. Nude subset in unit 19: L1C1, L1C2 reserve [3, 6]; remove these numbers from L2C1, L2C2, L2C3.
  10. Nude subset in unit 19: L1C3, L2C2, L2C3 reserve [4, 7, 8]; remove these numbers from L2C1.
  11. L6C1: only place for 1 in unit 10 → 1
  12. L5C1: only candidate → 9

contradiction: a box no longer has no candidate

all the possibilities of this bifurcation have been examined

L3C4 = 9

Assumption: L3C4 = 9

  1. L2C4: only candidate → 8
  2. L2C5: only candidate → 3
  3. L4C4: only candidate → 7
  4. L2C1: only place for 9 in unit 2 → 9
  5. L7C1: only candidate → 4
  6. L8C1: only candidate → 7
  7. L7C2: only candidate → 9
  8. L7C6: only candidate → 7
  9. L8C6: only candidate → 3
  10. L9C1: only candidate → 8
  11. L9C3: only candidate → 3
  12. L9C6: only candidate → 9
  13. L4C6: only place for 1 in unit 4 → 1
  14. L2C6: only candidate → 5
  15. L3C5: only candidate → 4

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

L5C7 = 9

Assumption: L5C7 = 9

  1. L6C7: only candidate → 1
L7C8 = 4

Assumption: L7C8 = 4

  1. L8C8: only candidate → 5
  2. L7C4: only candidate → 5
  3. L7C5: only candidate → 8
  4. L8C5: only candidate → 2
  5. L7C3: only candidate → 2
  6. L8C4: only candidate → 1
  7. L7C2: only candidate → 1
  8. L1C5: only place for 1 in unit 14 → 1
  9. L4C6: only place for 1 in unit 15 → 1
  10. L5C4: only place for 2 in unit 23 → 2
  11. Nude subset in Unit 4: L4C3, L4C4, L4C5 reserve [5, 7, 9]; remove these numbers from L4C1, L4C2.
  12. Nude sub-assembly in Unit 9: L9C4, L9C5 reserve [4, 6]; remove these numbers from L9C1, L9C6.
  13. Nude subset in unit 15: L7C6, L8C6, L9C6 reserve [3, 7, 9]; remove these numbers from L1C6, L2C6, L6C6.
  14. L2C6: only candidate → 5
  15. L3C6: only candidate → 6
  16. L3C5: only candidate → 9
  17. L3C4: only candidate → 8
  18. L4C4: only candidate → 9
  19. L4C2: only candidate → 8
  20. L2C1: only candidate → 9
  21. L3C1: only candidate → 5
  22. L2C2: only candidate → 7

contradiction: a box no longer has no candidate

L7C8 = 5

Assumption: L7C8 = 5

  1. L8C8: only candidate → 4
L8C4 = 3

Assumption: L8C4 = 3

  1. L8C5: only candidate → 2
  2. L7C2: only place for 2 in unit 7 → 2
  3. L8C6: only place for 5 in unit 8 → 5
  4. L9C6: only candidate → 6

contradiction: a box no longer has no candidate

L8C4 = 5

Assumption: L8C4 = 5

  1. L7C5: only candidate → 8
  2. L8C5: only candidate → 2
  3. L7C3: only candidate → 2
  4. L7C4: only candidate → 1
  5. L1C5: only place for 1 in unit 14 → 1
  6. L4C6: only place for 1 in unit 15 → 1
  7. L5C4: only place for 2 in unit 23 → 2
  8. Nude subset in Unit 4: L4C3, L4C4, L4C5 reserve [5, 7, 9]; remove these numbers from L4C1, L4C2.
  9. Nude subset in Unit 9: L9C4, L9C5 reserve [4, 6]; remove these numbers from L9C1, L9C3, L9C6.
  10. Nude subset in unit 26: L9C4, L9C5 reserve [4, 6]; remove these numbers from L7C6, L8C6.
  11. Nude subset in unit 15: L7C6, L8C6, L9C6 reserve [3, 7, 9]; remove these numbers from L1C6, L2C6, L6C6.
  12. L2C6: only candidate → 5
  13. L3C6: only candidate → 6
  14. L3C5: only candidate → 9
  15. L3C4: only candidate → 8
  16. L4C4: only candidate → 9
  17. L4C2: only candidate → 8
  18. L2C1: only candidate → 9
  19. L3C1: only candidate → 5
  20. L2C2: 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

L4C9 = 5

Assumption: L4C9 = 5

  1. L5C9: only candidate → 3
  2. Units 12 and 19 overlap. In unit 12, 5 must lie in the overlap. Remove it from L2C1, L3C1.
L5C7 = 1

Assumption: L5C7 = 1

  1. L6C7: only candidate → 9
  2. Units 12 and 19 overlap. In unit 12, 5 must lie in the overlap. Remove it from L2C1, L3C1.
L7C8 = 4

Assumption: L7C8 = 4

  1. L8C8: only candidate → 5
  2. L7C4: only candidate → 5
  3. L7C5: only candidate → 8
  4. L8C5: only candidate → 2
  5. L7C3: only candidate → 2
  6. L8C4: only candidate → 1
  7. L7C2: only candidate → 1
  8. Nude sub-assembly in Unit 9: L9C4, L9C5 reserve [4, 6]; remove these numbers from L9C1, L9C6.
  9. Nude subset in unit 15: L7C6, L8C6, L9C6 reserve [3, 7, 9]; remove these numbers from L1C6, L2C6, L3C6, L4C6, L6C6.
  10. L3C6: only candidate → 6
  11. Units 3 and 19 overlap. In unit 3, 2 must lie in the overlap. Remove it from L1C1, L1C2.
  12. Units 12 and 19 overlap. In unit 12, 5 must lie in the overlap. Remove it from L2C1, L3C1.
  13. L3C2: only place for 2 in unit 3 → 2
  14. L4C6: only place for 2 in unit 4 → 2
  15. L2C6: only candidate → 4
  16. L1C4: only candidate → 2
  17. L1C6: only candidate → 1
  18. L6C6: only candidate → 5
  19. L1C5: only place for 7 in unit 1 → 7
  20. L1C3: only candidate → 4
  21. L1C9: only candidate → 8
  22. L2C9: only candidate → 1
  23. L3C9: only candidate → 4
  24. L4C4: only candidate → 7
  25. L2C1: only candidate → 7

contradiction: a box no longer has no candidate

L7C8 = 5

Assumption: L7C8 = 5

  1. L8C8: only candidate → 4
  2. Units 12 and 19 overlap. In unit 12, 5 must lie in the overlap. Remove it from L2C1, L3C1.
L8C4 = 3

Assumption: L8C4 = 3

  1. L8C5: only candidate → 2
  2. L7C2: only place for 2 in unit 7 → 2
  3. L8C6: only place for 5 in unit 8 → 5
  4. L9C6: only candidate → 6

contradiction: a box no longer has no candidate

L8C4 = 5

Assumption: L8C4 = 5

  1. L7C5: only candidate → 8
  2. L8C5: only candidate → 2
  3. L7C3: only candidate → 2
  4. L7C4: only candidate → 1
  5. Nude subset in Unit 9: L9C4, L9C5 reserve [4, 6]; remove these numbers from L9C1, L9C3, L9C6.
  6. Nude subset in unit 26: L9C4, L9C5 reserve [4, 6]; remove these numbers from L7C6, L8C6.
  7. Nude subset in unit 15: L7C6, L8C6, L9C6 reserve [3, 7, 9]; remove these numbers from L1C6, L2C6, L3C6, L4C6, L6C6.
  8. L3C6: only candidate → 6
  9. Units 3 and 19 overlap. In unit 3, 2 must lie in the overlap. Remove it from L1C1, L1C2.
  10. Units 12 and 19 overlap. In unit 12, 5 must lie in the overlap. Remove it from L2C1, L3C1.
  11. L3C2: only place for 2 in unit 3 → 2
  12. L4C6: only place for 2 in unit 4 → 2
  13. L2C6: only candidate → 4
  14. L1C4: only candidate → 2
  15. L1C6: only candidate → 1
  16. L6C6: only candidate → 5
  17. L1C5: only place for 7 in unit 1 → 7
  18. L1C3: only candidate → 4
  19. L1C9: only candidate → 8
  20. L2C9: only candidate → 1
  21. L3C9: only candidate → 4
  22. L4C4: only candidate → 7
  23. L2C1: only candidate → 7
  24. L5C2: only candidate → 6
  25. 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

L5C7 = 9

Assumption: L5C7 = 9

  1. L6C7: only candidate → 1
  2. L6C1: only place for 5 in unit 22 → 5
  3. Units 6 and 23 overlap. In unit 6, 3 must lie in the overlap. Remove it from L4C4, L4C5, L4C6.
  4. Nude subassembly in Unit 4: L4C4, L4C5 reserve [7, 9]; remove these numbers from L4C1, L4C2, L4C3, L4C6.
  5. L5C2: only candidate → 6
  6. L5C1: 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

L4C8 = 7

Assumption: L4C8 = 7

  1. L5C8: only candidate → 6
L4C9 = 3

Assumption: L4C9 = 3

  1. L5C9: only candidate → 5
L5C7 = 1

Assumption: L5C7 = 1

  1. L6C7: only candidate → 9
L7C8 = 4

Assumption: L7C8 = 4

  1. L8C8: only candidate → 5
  2. L7C4: only candidate → 5
  3. L7C5: only candidate → 8
  4. L8C5: only candidate → 2
  5. L7C3: only candidate → 2
  6. L8C4: only candidate → 1
  7. L7C2: only candidate → 1
  8. Nude sub-assembly in Unit 9: L9C4, L9C5 reserve [4, 6]; remove these numbers from L9C1, L9C6.
  9. Nude subset in unit 15: L7C6, L8C6, L9C6 reserve [3, 7, 9]; remove these numbers from L1C6, L2C6, L3C6, L4C6, L6C6.
L4C4 = 6

Assumption: L4C4 = 6

  1. L9C4: only candidate → 4
  2. L9C5: only candidate → 6
  3. L1C5: only place for 3 in unit 14 → 3
  4. L1C9: only place for 4 in unit 1 → 4

contradiction: the number 6 can no longer appear in unit 1

L4C4 = 9

Assumption: L4C4 = 9

  1. L3C5: only place for 9 in unit 14 → 9
  2. Nude sub-assembly in Unit 9: L9C4, L9C5 reserve [4, 6]; remove these numbers from L9C1, L9C6.
  3. Nude subset in unit 15: L7C6, L8C6, L9C6 reserve [3, 7, 9]; remove these numbers from L1C6, L2C6, L6C6.
L3C4 = 6

Assumption: L3C4 = 6

  1. L9C4: only candidate → 4
  2. L5C4: only candidate → 2
  3. L9C5: only candidate → 6
  4. L4C5: only candidate → 5
  5. L2C4: only candidate → 8
  6. L2C5: only candidate → 4

contradiction: a box no longer has no candidate

L3C4 = 8

Assumption: L3C4 = 8

  1. Nude subassembly in Unit 2: L2C4, L2C5 reserve [3, 7]; remove these numbers from L2C1, L2C2, L2C3, L2C6.
  2. Nude subset in unit 2: L2C1, L2C2 reserve [8, 9]; remove these numbers from L2C9.
  3. L1C9: only candidate → 8
  4. Nude sub-assembly in Unit 9: L9C4, L9C5 reserve [4, 6]; remove these numbers from L9C1, L9C6.
  5. Nude subset in unit 15: L7C6, L8C6, L9C6 reserve [3, 7, 9]; remove these numbers from L1C6, L6C6.
  6. Nude sub-assembly in unit 20: L2C4, L2C5 reserve [3, 7]; remove these numbers from L1C4, L1C5.
  7. L3C2: only place for 4 in unit 19 → 4
  8. L2C2: only candidate → 8
  9. L2C1: only candidate → 9
  10. L2C9: only candidate → 4
  11. L3C9: only candidate → 1
  12. L2C3: only candidate → 1
  13. L2C6: only candidate → 5
  14. L3C3: only candidate → 5
  15. L3C6: only candidate → 6
  16. L1C3: only candidate → 7
  17. L3C1: only candidate → 2
  18. L4C1: only candidate → 5
  19. L4C5: only candidate → 6
  20. L4C2: only candidate → 2
  21. L4C3: only candidate → 8
  22. L4C6: only candidate → 1
  23. L1C5: only candidate → 1
  24. L5C2: only candidate → 7
  25. L5C3: only candidate → 4

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

L7C8 = 5

Assumption: L7C8 = 5

  1. L8C8: only candidate → 4
L8C4 = 3

Assumption: L8C4 = 3

  1. L8C5: only candidate → 2
  2. L7C2: only place for 2 in unit 7 → 2
  3. L8C6: only place for 5 in unit 8 → 5
  4. L9C6: only candidate → 6

contradiction: a box no longer has no candidate

L8C4 = 5

Assumption: L8C4 = 5

  1. L7C5: only candidate → 8
  2. L8C5: only candidate → 2
  3. L7C3: only candidate → 2
  4. L7C4: only candidate → 1
  5. Nude subset in Unit 9: L9C4, L9C5 reserve [4, 6]; remove these numbers from L9C1, L9C3, L9C6.
  6. Nude subset in unit 26: L9C4, L9C5 reserve [4, 6]; remove these numbers from L7C6, L8C6.
  7. Nude subset in unit 15: L7C6, L8C6, L9C6 reserve [3, 7, 9]; remove these numbers from L1C6, L2C6, L3C6, L4C6, L6C6.
L4C4 = 6

Assumption: L4C4 = 6

  1. L9C4: only candidate → 4
  2. L9C5: only candidate → 6
  3. L1C5: only place for 3 in unit 14 → 3
  4. L1C9: only place for 4 in unit 1 → 4

contradiction: the number 6 can no longer appear in unit 1

L4C4 = 9

Assumption: L4C4 = 9

  1. L3C5: only place for 9 in unit 14 → 9
  2. Nude subset in Unit 9: L9C4, L9C5 reserve [4, 6]; remove these numbers from L9C1, L9C3, L9C6.
  3. Nude subset in unit 26: L9C4, L9C5 reserve [4, 6]; remove these numbers from L7C6, L8C6.
  4. Nude subset in unit 15: L7C6, L8C6, L9C6 reserve [3, 7, 9]; remove these numbers from L1C6, L2C6, L6C6.
L3C4 = 6

Assumption: L3C4 = 6

  1. L9C4: only candidate → 4
  2. L5C4: only candidate → 2
  3. L9C5: only candidate → 6
  4. L4C5: only candidate → 5
  5. L2C4: only candidate → 8
  6. L2C5: only candidate → 4

contradiction: a box no longer has no candidate

L3C4 = 8

Assumption: L3C4 = 8

  1. Nude subassembly in Unit 2: L2C4, L2C5 reserve [3, 7]; remove these numbers from L2C1, L2C2, L2C3, L2C6.
  2. Nude subset in Unit 9: L9C4, L9C5 reserve [4, 6]; remove these numbers from L9C1, L9C3, L9C6.
  3. Nude subset in unit 20: L2C4, L2C5 reserve [3, 7]; remove these numbers from L1C4, L1C5, L1C6.
  4. Nude subset in unit 26: L9C4, L9C5 reserve [4, 6]; remove these numbers from L7C6, L8C6.
  5. Nude subset in unit 15: L7C6, L8C6, L9C6 reserve [3, 7, 9]; remove these figures from L6C6.
  6. Units 14 and 23 overlap. In unit 14, 5 must lie in the overlap. Remove it from L4C6, L6C6.
L1C3 = 3

Assumption: L1C3 = 3

  1. L2C3: only place for 7 in unit 12 → 7

contradiction: a box no longer has no candidate

L1C3 = 7

Assumption: L1C3 = 7

  1. L3C6: only place for 6 in unit 20 → 6
  2. L4C6: only place for 1 in unit 4 → 1
  3. L1C5: only candidate → 1
  4. L2C6: only candidate → 5
  5. L1C9: only place for 8 in unit 1 → 8
  6. L1C6: only place for 2 in unit 15 → 2
  7. L1C4: only candidate → 4
  8. L9C4: only candidate → 6
  9. L5C4: only candidate → 2
  10. L9C5: only candidate → 4
  11. L4C5: only candidate → 6
  12. L5C5: only candidate → 3
  13. L2C4: only candidate → 3
  14. L2C1: only candidate → 9
  15. L2C5: only candidate → 7
  16. L3C3: only candidate → 5
  17. L3C1: only candidate → 2
  18. L4C1: only candidate → 5
  19. L4C2: only candidate → 2
  20. L4C3: only candidate → 8
  21. L2C2: only candidate → 8
  22. L5C1: only candidate → 4

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

all the possibilities of this bifurcation have been examined

L5C7 = 9

Assumption: L5C7 = 9

  1. L6C7: only candidate → 1
L7C8 = 4

Assumption: L7C8 = 4

  1. L8C8: only candidate → 5
  2. L7C4: only candidate → 5
  3. L7C5: only candidate → 8
  4. L8C5: only candidate → 2
  5. L7C3: only candidate → 2
  6. L8C4: only candidate → 1
  7. L7C2: only candidate → 1
  8. L1C5: only place for 1 in unit 14 → 1
  9. L4C6: only place for 1 in unit 15 → 1
  10. L5C4: only place for 2 in unit 23 → 2
  11. Nude sub-assembly in Unit 9: L9C4, L9C5 reserve [4, 6]; remove these numbers from L9C1, L9C6.
  12. Nude subset in unit 15: L7C6, L8C6, L9C6 reserve [3, 7, 9]; remove these numbers from L1C6, L2C6, L6C6.
  13. L2C6: only candidate → 5
  14. L3C6: only candidate → 6
  15. L3C5: only candidate → 9
  16. L3C4: only candidate → 8
  17. L4C4: only candidate → 9
  18. L6C4: only candidate → 7
  19. L2C4: only candidate → 3
  20. L1C3: only candidate → 7
  21. L1C4: only candidate → 4
  22. L1C6: only candidate → 2
  23. L1C9: only candidate → 8
  24. L2C2: only candidate → 8
  25. L2C1: only candidate → 9
  26. L2C3: only candidate → 1
  27. L2C5: only candidate → 7
  28. L2C9: only candidate → 4
  29. L3C2: only candidate → 4
  30. L3C3: only candidate → 5
  31. L3C1: only candidate → 2
  32. L3C9: only candidate → 1
  33. L4C1: only candidate → 5
  34. L4C3: only candidate → 8
  35. L4C5: only candidate → 6
  36. L4C2: only candidate → 2
  37. L5C2: only candidate → 7
  38. L5C3: only candidate → 4
  39. L5C1: only candidate → 1
  40. L5C5: only candidate → 3
  41. L6C1: only candidate → 3
  42. L1C1: only candidate → 6
  43. L1C2: only candidate → 3
  44. L6C2: only candidate → 9
  45. L6C3: only candidate → 6
  46. L6C5: only candidate → 5
  47. L6C6: only candidate → 4
  48. L7C1: only candidate → 7
  49. L7C6: only candidate → 9
  50. L8C1: only candidate → 4
  51. L8C2: only candidate → 6
  52. L8C3: only candidate → 3
  53. L8C6: only candidate → 7
  54. L9C1: only candidate → 8
  55. L9C3: only candidate → 9
  56. L9C4: only candidate → 6
  57. L9C5: only candidate → 4
  58. L9C6: only candidate → 3

valid complete solution

L7C8 = 5

Assumption: L7C8 = 5

  1. L8C8: only candidate → 4
L8C4 = 3

Assumption: L8C4 = 3

  1. L8C5: only candidate → 2
  2. L7C2: only place for 2 in unit 7 → 2
  3. L8C6: only place for 5 in unit 8 → 5
  4. L9C6: only candidate → 6

contradiction: a box no longer has no candidate

L8C4 = 5

Assumption: L8C4 = 5

  1. L7C5: only candidate → 8
  2. L8C5: only candidate → 2
  3. L7C3: only candidate → 2
  4. L7C4: only candidate → 1
  5. L1C5: only place for 1 in unit 14 → 1
  6. L4C6: only place for 1 in unit 15 → 1
  7. L5C4: only place for 2 in unit 23 → 2
  8. Nude subset in Unit 9: L9C4, L9C5 reserve [4, 6]; remove these numbers from L9C1, L9C3, L9C6.
  9. Nude subset in unit 26: L9C4, L9C5 reserve [4, 6]; remove these numbers from L7C6, L8C6.
  10. Nude subset in unit 15: L7C6, L8C6, L9C6 reserve [3, 7, 9]; remove these numbers from L1C6, L2C6, L6C6.
  11. L2C6: only candidate → 5
  12. L3C6: only candidate → 6
  13. L3C5: only candidate → 9
  14. L3C4: only candidate → 8
  15. L4C4: only candidate → 9
  16. L6C4: only candidate → 7
  17. L2C4: only candidate → 3
  18. L1C3: only candidate → 7
  19. L1C4: only candidate → 4
  20. L1C6: only candidate → 2
  21. L1C9: only candidate → 8
  22. L2C5: only candidate → 7
  23. L3C3: only candidate → 5
  24. L6C5: only candidate → 5
  25. L4C5: only candidate → 6
  26. L2C1: only candidate → 9
  27. L3C1: only candidate → 2
  28. L4C1: only candidate → 5
  29. L4C2: only candidate → 2
  30. L4C3: only candidate → 8
  31. L2C2: only candidate → 8
  32. L5C2: only candidate → 7
  33. L5C5: only candidate → 3
  34. L6C6: only candidate → 4
  35. L7C1: only candidate → 4
  36. L5C1: only candidate → 1
  37. L5C3: only candidate → 4
  38. L2C3: only candidate → 1
  39. L2C9: only candidate → 4
  40. L3C2: only candidate → 4
  41. L3C9: only candidate → 1
  42. L6C1: only candidate → 3
  43. L1C1: only candidate → 6
  44. L1C2: only candidate → 3
  45. L6C2: 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

L4C9 = 5

Assumption: L4C9 = 5

  1. L5C9: only candidate → 3
  2. Units 12 and 19 overlap. In unit 12, 5 must lie in the overlap. Remove it from L2C1, L3C1.
L5C7 = 1

Assumption: L5C7 = 1

  1. L6C7: only candidate → 9
  2. Units 12 and 19 overlap. In unit 12, 5 must lie in the overlap. Remove it from L2C1, L3C1.
L7C8 = 4

Assumption: L7C8 = 4

  1. L8C8: only candidate → 5
  2. L7C4: only candidate → 5
  3. L7C5: only candidate → 8
  4. L8C5: only candidate → 2
  5. L7C3: only candidate → 2
  6. L8C4: only candidate → 1
  7. L7C2: only candidate → 1
  8. Nude sub-assembly in Unit 9: L9C4, L9C5 reserve [4, 6]; remove these numbers from L9C1, L9C6.
  9. Nude subset in unit 15: L7C6, L8C6, L9C6 reserve [3, 7, 9]; remove these numbers from L1C6, L2C6, L3C6, L4C6, L6C6.
  10. Units 11 and 19 overlap. In unit 11, 8 must lie in the overlap. Remove it from L1C3, L2C1, L2C3, L3C1, L3C3.
  11. Units 12 and 19 overlap. In unit 12, 5 must lie in the overlap. Remove it from L2C1, L3C1.
L7C1 = 7

Assumption: L7C1 = 7

  1. L7C6: only candidate → 9
  2. L8C6: only place for 7 in unit 8 → 7
  3. L9C6: only candidate → 3
  4. Units 11 and 19 overlap. In unit 11, 8 must lie in the overlap. Remove it from L1C3, L2C1, L2C3, L3C1, L3C3.
  5. Units 12 and 19 overlap. In unit 12, 5 must lie in the overlap. Remove it from L2C1, L3C1.
  6. L4C3: only place for 8 in unit 4 → 8
  7. L4C2: only candidate → 2
  8. L5C2: only candidate → 7
  9. L9C3: only candidate → 9
  10. L5C3: only candidate → 4
  11. L5C1: only candidate → 9

contradiction: a box no longer has no candidate

L7C1 = 9

Assumption: L7C1 = 9

  1. L7C6: only candidate → 7
  2. L8C6: only candidate → 3
  3. L9C3: only candidate → 8
  4. L9C6: only candidate → 9
  5. L4C1: only place for 8 in unit 4 → 8
  6. L8C1: only place for 7 in unit 8 → 7
  7. L2C1: only candidate → 3

contradiction: a box no longer has no candidate

all the possibilities of this bifurcation have been examined

L7C8 = 5

Assumption: L7C8 = 5

  1. L8C8: only candidate → 4
  2. Units 12 and 19 overlap. In unit 12, 5 must lie in the overlap. Remove it from L2C1, L3C1.
L8C4 = 3

Assumption: L8C4 = 3

  1. L8C5: only candidate → 2
  2. L7C2: only place for 2 in unit 7 → 2
  3. L8C6: only place for 5 in unit 8 → 5
  4. L9C6: only candidate → 6

contradiction: a box no longer has no candidate

L8C4 = 5

Assumption: L8C4 = 5

  1. L7C5: only candidate → 8
  2. L8C5: only candidate → 2
  3. L7C3: only candidate → 2
  4. L7C4: only candidate → 1
  5. Nude subset in Unit 9: L9C4, L9C5 reserve [4, 6]; remove these numbers from L9C1, L9C3, L9C6.
  6. Nude subset in unit 26: L9C4, L9C5 reserve [4, 6]; remove these numbers from L7C6, L8C6.
  7. Nude subset in unit 15: L7C6, L8C6, L9C6 reserve [3, 7, 9]; remove these numbers from L1C6, L2C6, L3C6, L4C6, L6C6.
  8. Units 11 and 19 overlap. In unit 11, 8 must lie in the overlap. Remove it from L1C1, L1C3, L2C1, L2C3, L3C1, L3C3.
  9. Units 12 and 19 overlap. In unit 12, 5 must lie in the overlap. Remove it from L2C1, L3C1.
L7C6 = 7

Assumption: L7C6 = 7

  1. L8C6: only candidate → 3
  2. L9C6: only candidate → 9
  3. L8C1: only place for 7 in unit 8 → 7
  4. Units 11 and 19 overlap. In unit 11, 8 must lie in the overlap. Remove it from L1C1, L1C3, L2C1, L2C3, L3C1, L3C3.
  5. Units 12 and 19 overlap. In unit 12, 5 must lie in the overlap. Remove it from L2C1, L3C1.
  6. L4C3: only place for 8 in unit 4 → 8
  7. L4C2: only candidate → 2
  8. L5C2: only candidate → 7
  9. L7C2: only candidate → 9
  10. L7C1: only candidate → 4
  11. L5C1: only candidate → 9

contradiction: a box no longer has no candidate

L7C6 = 9

Assumption: L7C6 = 9

  1. L9C3: only candidate → 8
  2. L9C1: only candidate → 9
  3. L4C1: only place for 8 in unit 4 → 8
  4. L8C6: only place for 7 in unit 8 → 7
  5. L9C6: only candidate → 3
  6. Units 4 and 23 overlap. In unit 4, 3 must lie in the overlap. Remove it from L6C4, L6C5.
  7. Units 12 and 19 overlap. In unit 12, 5 must lie in the overlap. Remove it from L3C1.
  8. L2C1: only candidate → 7
  9. L3C1: only candidate → 1
  10. L7C1: only candidate → 4
  11. L5C1: only candidate → 2
  12. L5C2: 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

L5C7 = 9

Assumption: L5C7 = 9

  1. L6C7: only candidate → 1
  2. L6C1: only place for 5 in unit 22 → 5
  3. L5C3: only place for 4 in unit 22 → 4
  4. L6C3: only candidate → 6
  5. L5C1: only candidate → 1
  6. L5C2: 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

L1C7 = 6

Assumption: L1C7 = 6

  1. L2C7: only candidate → 5
L4C8 = 6

Assumption: L4C8 = 6

  1. L5C8: only candidate → 7
L4C9 = 3

Assumption: L4C9 = 3

  1. L5C9: only candidate → 5
L5C7 = 1

Assumption: L5C7 = 1

  1. L6C7: only candidate → 9
L7C8 = 4

Assumption: L7C8 = 4

  1. L8C8: only candidate → 5
  2. L7C4: only candidate → 5
  3. L7C5: only candidate → 8
  4. L8C5: only candidate → 2
  5. L7C3: only candidate → 2
  6. L8C4: only candidate → 1
  7. L7C2: only candidate → 1
  8. Nude sub-assembly in Unit 9: L9C4, L9C5 reserve [4, 6]; remove these numbers from L9C1, L9C6.
  9. Nude subset in unit 15: L7C6, L8C6, L9C6 reserve [3, 7, 9]; remove these numbers from L1C6, L2C6, L3C6, L4C6, L6C6.
  10. Units 3 and 19 overlap. In unit 3, 2 must lie in the overlap. Remove it from L1C1, L1C2.
L1C1 = 1

Assumption: L1C1 = 1

  1. L1C2: only candidate → 8
  2. L1C9: only candidate → 4

contradiction: a box no longer has no candidate

L1C1 = 5

Assumption: L1C1 = 5

  1. L1C2: only candidate → 4

contradiction: the number 7 can no longer appear in unit 1

all the possibilities of this bifurcation have been examined

L7C8 = 5

Assumption: L7C8 = 5

  1. L8C8: only candidate → 4
L8C4 = 3

Assumption: L8C4 = 3

  1. L8C5: only candidate → 2
  2. L7C2: only place for 2 in unit 7 → 2
  3. L8C6: only place for 5 in unit 8 → 5
  4. L9C6: only candidate → 6

contradiction: a box no longer has no candidate

L8C4 = 5

Assumption: L8C4 = 5

  1. L7C5: only candidate → 8
  2. L8C5: only candidate → 2
  3. L7C3: only candidate → 2
  4. L7C4: only candidate → 1
  5. Nude subset in Unit 9: L9C4, L9C5 reserve [4, 6]; remove these numbers from L9C1, L9C3, L9C6.
  6. Nude subset in unit 26: L9C4, L9C5 reserve [4, 6]; remove these numbers from L7C6, L8C6.
  7. Nude subset in unit 15: L7C6, L8C6, L9C6 reserve [3, 7, 9]; remove these numbers from L1C6, L2C6, L3C6, L4C6, L6C6.
  8. Units 3 and 19 overlap. In unit 3, 2 must lie in the overlap. Remove it from L1C1, L1C2.
L4C4 = 7

Assumption: L4C4 = 7

  1. L5C1: only place for 2 in unit 5 → 2
  2. L4C3: only candidate → 5
  3. L4C5: only candidate → 9
  4. L2C5: only candidate → 3
  5. L3C5: only candidate → 5
  6. L4C2: only candidate → 8
  7. L4C1: only candidate → 1
  8. L4C6: only candidate → 2
  9. L1C4: only candidate → 2
  10. L5C2: only candidate → 4

contradiction: a box no longer has no candidate

L4C4 = 9

Assumption: L4C4 = 9

  1. L3C5: only place for 9 in unit 14 → 9
  2. L4C5: only candidate → 5
  3. L5C5: only candidate → 4
  4. L5C4: only candidate → 2
  5. L1C6: only candidate → 2
  6. L2C6: only candidate → 6
  7. L3C4: only candidate → 8
  8. L3C6: only candidate → 5
  9. L4C6: 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

L5C7 = 9

Assumption: L5C7 = 9

  1. L6C7: only candidate → 1
L7C8 = 4

Assumption: L7C8 = 4

  1. L8C8: only candidate → 5
  2. L7C4: only candidate → 5
  3. L7C5: only candidate → 8
  4. L8C5: only candidate → 2
  5. L7C3: only candidate → 2
  6. L8C4: only candidate → 1
  7. L7C2: only candidate → 1
  8. L1C5: only place for 1 in unit 14 → 1
  9. L1C1: only place for 5 in unit 1 → 5
  10. L1C2: only candidate → 4
  11. L1C9: only candidate → 8

contradiction: a box no longer has no candidate

L7C8 = 5

Assumption: L7C8 = 5

  1. L8C8: only candidate → 4
L8C4 = 3

Assumption: L8C4 = 3

  1. L8C5: only candidate → 2
  2. L7C2: only place for 2 in unit 7 → 2
  3. L8C6: only place for 5 in unit 8 → 5
  4. L9C6: only candidate → 6

contradiction: a box no longer has no candidate

L8C4 = 5

Assumption: L8C4 = 5

  1. L7C5: only candidate → 8
  2. L8C5: only candidate → 2
  3. L7C3: only candidate → 2
  4. L7C4: only candidate → 1
  5. L1C5: only place for 1 in unit 14 → 1
  6. L1C1: only place for 5 in unit 1 → 5
  7. L1C2: only candidate → 4
  8. L1C9: only candidate → 8

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

L4C9 = 5

Assumption: L4C9 = 5

  1. L5C9: only candidate → 3
  2. Units 12 and 19 overlap. In unit 12, 5 must lie in the overlap. Remove it from L1C1, L3C1.
L5C7 = 1

Assumption: L5C7 = 1

  1. L6C7: only candidate → 9
  2. Units 12 and 19 overlap. In unit 12, 5 must lie in the overlap. Remove it from L1C1, L3C1.
L7C8 = 4

Assumption: L7C8 = 4

  1. L8C8: only candidate → 5
  2. L7C4: only candidate → 5
  3. L7C5: only candidate → 8
  4. L8C5: only candidate → 2
  5. L7C3: only candidate → 2
  6. L8C4: only candidate → 1
  7. L7C2: only candidate → 1
  8. Nude sub-assembly in Unit 9: L9C4, L9C5 reserve [4, 6]; remove these numbers from L9C1, L9C6.
  9. Nude subset in unit 15: L7C6, L8C6, L9C6 reserve [3, 7, 9]; remove these numbers from L1C6, L2C6, L3C6, L4C6, L6C6.
  10. Units 3 and 19 overlap. In unit 3, 2 must lie in the overlap. Remove it from L1C1, L1C2.
  11. Units 12 and 19 overlap. In unit 12, 5 must lie in the overlap. Remove it from L1C1, L3C1.
  12. L1C1: only candidate → 1
  13. L1C2: only candidate → 8
  14. L1C9: only candidate → 4

contradiction: a box no longer has no candidate

L7C8 = 5

Assumption: L7C8 = 5

  1. L8C8: only candidate → 4
  2. Units 12 and 19 overlap. In unit 12, 5 must lie in the overlap. Remove it from L1C1, L3C1.
L8C4 = 3

Assumption: L8C4 = 3

  1. L8C5: only candidate → 2
  2. L7C2: only place for 2 in unit 7 → 2
  3. L8C6: only place for 5 in unit 8 → 5
  4. L9C6: only candidate → 6

contradiction: a box no longer has no candidate

L8C4 = 5

Assumption: L8C4 = 5

  1. L7C5: only candidate → 8
  2. L8C5: only candidate → 2
  3. L7C3: only candidate → 2
  4. L7C4: only candidate → 1
  5. Nude subset in Unit 9: L9C4, L9C5 reserve [4, 6]; remove these numbers from L9C1, L9C3, L9C6.
  6. Nude subset in unit 26: L9C4, L9C5 reserve [4, 6]; remove these numbers from L7C6, L8C6.
  7. Nude subset in unit 15: L7C6, L8C6, L9C6 reserve [3, 7, 9]; remove these numbers from L1C6, L2C6, L3C6, L4C6, L6C6.
  8. Units 3 and 19 overlap. In unit 3, 2 must lie in the overlap. Remove it from L1C1, L1C2.
  9. Units 12 and 19 overlap. In unit 12, 5 must lie in the overlap. Remove it from L1C1, L3C1.
  10. Nude subset in unit 1: L1C1, L1C2 reserve [1, 8]; remove these numbers from L1C3, L1C4, L1C5, L1C6, L1C9.
  11. L1C9: only candidate → 4

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

L5C7 = 9

Assumption: L5C7 = 9

  1. L6C7: only candidate → 1
  2. L6C1: only place for 5 in unit 22 → 5
  3. Units 6 and 23 overlap. In unit 6, 3 must lie in the overlap. Remove it from L4C4, L4C5, L4C6.
  4. Nude subassembly in Unit 4: L4C4, L4C5 reserve [7, 9]; remove these numbers from L4C1, L4C2, L4C3, L4C6.
  5. L5C2: only candidate → 6
  6. L5C1: 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

L4C8 = 7

Assumption: L4C8 = 7

  1. L5C8: only candidate → 6
L4C9 = 3

Assumption: L4C9 = 3

  1. L5C9: only candidate → 5
L5C7 = 1

Assumption: L5C7 = 1

  1. L6C7: only candidate → 9
L7C8 = 4

Assumption: L7C8 = 4

  1. L8C8: only candidate → 5
  2. L7C4: only candidate → 5
  3. L7C5: only candidate → 8
  4. L8C5: only candidate → 2
  5. L7C3: only candidate → 2
  6. L8C4: only candidate → 1
  7. L7C2: only candidate → 1
  8. Nude sub-assembly in Unit 9: L9C4, L9C5 reserve [4, 6]; remove these numbers from L9C1, L9C6.
  9. Nude subset in unit 15: L7C6, L8C6, L9C6 reserve [3, 7, 9]; remove these numbers from L1C6, L2C6, L3C6, L4C6, L6C6.
L4C4 = 6

Assumption: L4C4 = 6

  1. L9C4: only candidate → 4
  2. L2C5: only candidate → 4
  3. L3C5: only candidate → 6

contradiction: a box no longer has no candidate

L4C4 = 9

Assumption: L4C4 = 9

  1. L3C5: only place for 9 in unit 14 → 9
  2. Nude sub-assembly in Unit 9: L9C4, L9C5 reserve [4, 6]; remove these numbers from L9C1, L9C6.
  3. Nude subset in unit 15: L7C6, L8C6, L9C6 reserve [3, 7, 9]; remove these numbers from L1C6, L2C6, L6C6.
L4C5 = 5

Assumption: L4C5 = 5

  1. L5C5: only candidate → 4
  2. L5C4: only candidate → 2
  3. L1C6: only candidate → 2
  4. L3C6: only candidate → 5
  5. L9C4: only candidate → 4
  6. L3C4: only candidate → 8
  7. L1C5: only candidate → 1
  8. L1C1: only candidate → 5
  9. L1C2: only candidate → 4
  10. L1C3: only candidate → 8

contradiction: a box no longer has no candidate

L4C5 = 6

Assumption: L4C5 = 6

  1. L5C4: only candidate → 2
  2. L1C6: only candidate → 2
  3. L5C5: only candidate → 3
  4. L9C4: only candidate → 6
  5. L2C4: only candidate → 3
  6. L2C5: only candidate → 7
  7. L3C4: only candidate → 8
  8. L1C4: only candidate → 4
  9. L1C1: 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

L7C8 = 5

Assumption: L7C8 = 5

  1. L8C8: only candidate → 4
L8C4 = 3

Assumption: L8C4 = 3

  1. L8C5: only candidate → 2
  2. L7C2: only place for 2 in unit 7 → 2
  3. L8C6: only place for 5 in unit 8 → 5
  4. L9C6: only candidate → 6

contradiction: a box no longer has no candidate

L8C4 = 5

Assumption: L8C4 = 5

  1. L7C5: only candidate → 8
  2. L8C5: only candidate → 2
  3. L7C3: only candidate → 2
  4. L7C4: only candidate → 1
  5. Nude subset in Unit 9: L9C4, L9C5 reserve [4, 6]; remove these numbers from L9C1, L9C3, L9C6.
  6. Nude subset in unit 26: L9C4, L9C5 reserve [4, 6]; remove these numbers from L7C6, L8C6.
  7. Nude subset in unit 15: L7C6, L8C6, L9C6 reserve [3, 7, 9]; remove these numbers from L1C6, L2C6, L3C6, L4C6, L6C6.
L4C4 = 6

Assumption: L4C4 = 6

  1. L9C4: only candidate → 4
  2. L2C5: only candidate → 4
  3. L3C5: only candidate → 6

contradiction: a box no longer has no candidate

L4C4 = 9

Assumption: L4C4 = 9

  1. L3C5: only place for 9 in unit 14 → 9
  2. Nude subset in Unit 9: L9C4, L9C5 reserve [4, 6]; remove these numbers from L9C1, L9C3, L9C6.
  3. Nude subset in unit 26: L9C4, L9C5 reserve [4, 6]; remove these numbers from L7C6, L8C6.
  4. Nude subset in unit 15: L7C6, L8C6, L9C6 reserve [3, 7, 9]; remove these numbers from L1C6, L2C6, L6C6.
L4C5 = 5

Assumption: L4C5 = 5

  1. L5C5: only candidate → 4
  2. L5C4: only candidate → 2
  3. L1C6: only candidate → 2
  4. L3C6: only candidate → 5
  5. L9C4: only candidate → 4
  6. L3C4: only candidate → 8
  7. L1C5: only candidate → 1
  8. L1C1: only candidate → 5
  9. L1C2: only candidate → 4
  10. L1C3: only candidate → 8

contradiction: a box no longer has no candidate

L4C5 = 6

Assumption: L4C5 = 6

  1. L5C4: only candidate → 2
  2. L1C6: only candidate → 2
  3. L5C5: only candidate → 3
  4. L9C4: only candidate → 6
  5. L2C4: only candidate → 3
  6. L2C5: only candidate → 7
  7. L3C4: only candidate → 8
  8. L1C4: only candidate → 4
  9. L6C4: only candidate → 7
  10. L9C5: only candidate → 4
  11. L6C5: only candidate → 5
  12. L1C3: only candidate → 7
  13. L1C5: 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

all the possibilities of this bifurcation have been examined

L5C7 = 9

Assumption: L5C7 = 9

  1. L6C7: only candidate → 1
L7C8 = 4

Assumption: L7C8 = 4

  1. L8C8: only candidate → 5
  2. L7C4: only candidate → 5
  3. L7C5: only candidate → 8
  4. L8C5: only candidate → 2
  5. L7C3: only candidate → 2
  6. L8C4: only candidate → 1
  7. L7C2: only candidate → 1
  8. L1C5: only place for 1 in unit 14 → 1
  9. L1C1: only place for 5 in unit 1 → 5
  10. L1C2: only candidate → 4
  11. L1C9: only candidate → 8

contradiction: a box no longer has no candidate

L7C8 = 5

Assumption: L7C8 = 5

  1. L8C8: only candidate → 4
L8C4 = 3

Assumption: L8C4 = 3

  1. L8C5: only candidate → 2
  2. L7C2: only place for 2 in unit 7 → 2
  3. L8C6: only place for 5 in unit 8 → 5
  4. L9C6: only candidate → 6

contradiction: a box no longer has no candidate

L8C4 = 5

Assumption: L8C4 = 5

  1. L7C5: only candidate → 8
  2. L8C5: only candidate → 2
  3. L7C3: only candidate → 2
  4. L7C4: only candidate → 1
  5. L1C5: only place for 1 in unit 14 → 1
  6. L1C1: only place for 5 in unit 1 → 5
  7. L1C2: only candidate → 4
  8. L1C9: only candidate → 8

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

L4C9 = 5

Assumption: L4C9 = 5

  1. L5C9: only candidate → 3
  2. Units 12 and 19 overlap. In unit 12, 5 must lie in the overlap. Remove it from L1C1, L3C1.
L5C7 = 1

Assumption: L5C7 = 1

  1. L6C7: only candidate → 9
  2. Units 12 and 19 overlap. In unit 12, 5 must lie in the overlap. Remove it from L1C1, L3C1.
L7C8 = 4

Assumption: L7C8 = 4

  1. L8C8: only candidate → 5
  2. L7C4: only candidate → 5
  3. L7C5: only candidate → 8
  4. L8C5: only candidate → 2
  5. L7C3: only candidate → 2
  6. L8C4: only candidate → 1
  7. L7C2: only candidate → 1
  8. Nude sub-assembly in Unit 9: L9C4, L9C5 reserve [4, 6]; remove these numbers from L9C1, L9C6.
  9. Nude subset in unit 15: L7C6, L8C6, L9C6 reserve [3, 7, 9]; remove these numbers from L1C6, L2C6, L3C6, L4C6, L6C6.
  10. Units 11 and 19 overlap. In unit 11, 8 must lie in the overlap. Remove it from L1C3, L2C1, L2C3, L3C1, L3C3.
  11. Units 12 and 19 overlap. In unit 12, 5 must lie in the overlap. Remove it from L1C1, L3C1.
L7C1 = 7

Assumption: L7C1 = 7

  1. L7C6: only candidate → 9
  2. L8C6: only place for 7 in unit 8 → 7
  3. L9C6: only candidate → 3
  4. Units 11 and 19 overlap. In unit 11, 8 must lie in the overlap. Remove it from L1C3, L2C1, L2C3, L3C1, L3C3.
  5. Units 12 and 19 overlap. In unit 12, 5 must lie in the overlap. Remove it from L1C1, L3C1.
L1C1 = 1

Assumption: L1C1 = 1

  1. L1C2: only candidate → 8
  2. L1C9: only candidate → 4

contradiction: a box no longer has no candidate

L1C1 = 2

Assumption: L1C1 = 2

contradiction: a box no longer has no candidate

all the possibilities of this bifurcation have been examined

L7C1 = 9

Assumption: L7C1 = 9

  1. L7C6: only candidate → 7
  2. L8C6: only candidate → 3
  3. L9C3: only candidate → 8
  4. L9C6: only candidate → 9
  5. L4C1: only place for 8 in unit 4 → 8
  6. L8C1: only place for 7 in unit 8 → 7
  7. L9C1: only candidate → 3
  8. L2C1: only candidate → 6
  9. L3C1: only candidate → 2
  10. L2C3: only candidate → 1
  11. L1C1: only candidate → 5

contradiction: a box no longer has no candidate

all the possibilities of this bifurcation have been examined

L7C8 = 5

Assumption: L7C8 = 5

  1. L8C8: only candidate → 4
  2. Units 12 and 19 overlap. In unit 12, 5 must lie in the overlap. Remove it from L1C1, L3C1.
L8C4 = 3

Assumption: L8C4 = 3

  1. L8C5: only candidate → 2
  2. L7C2: only place for 2 in unit 7 → 2
  3. L8C6: only place for 5 in unit 8 → 5
  4. L9C6: only candidate → 6

contradiction: a box no longer has no candidate

L8C4 = 5

Assumption: L8C4 = 5

  1. L7C5: only candidate → 8
  2. L8C5: only candidate → 2
  3. L7C3: only candidate → 2
  4. L7C4: only candidate → 1
  5. Nude subset in Unit 9: L9C4, L9C5 reserve [4, 6]; remove these numbers from L9C1, L9C3, L9C6.
  6. Nude subset in unit 26: L9C4, L9C5 reserve [4, 6]; remove these numbers from L7C6, L8C6.
  7. Nude subset in unit 15: L7C6, L8C6, L9C6 reserve [3, 7, 9]; remove these numbers from L1C6, L2C6, L3C6, L4C6, L6C6.
  8. Units 11 and 19 overlap. In unit 11, 8 must lie in the overlap. Remove it from L1C1, L1C3, L2C1, L2C3, L3C1, L3C3.
  9. Units 12 and 19 overlap. In unit 12, 5 must lie in the overlap. Remove it from L1C1, L3C1.
L7C6 = 7

Assumption: L7C6 = 7

  1. L8C6: only candidate → 3
  2. L9C6: only candidate → 9
  3. L8C1: only place for 7 in unit 8 → 7
  4. Units 11 and 19 overlap. In unit 11, 8 must lie in the overlap. Remove it from L1C1, L1C3, L2C1, L2C3, L3C1, L3C3.
  5. Units 12 and 19 overlap. In unit 12, 5 must lie in the overlap. Remove it from L1C1, L3C1.
L1C1 = 1

Assumption: L1C1 = 1

  1. L1C2: only candidate → 8
  2. L1C9: only candidate → 4

contradiction: a box no longer has no candidate

L1C1 = 2

Assumption: L1C1 = 2

contradiction: a box no longer has no candidate

all the possibilities of this bifurcation have been examined

L7C6 = 9

Assumption: L7C6 = 9

  1. L9C3: only candidate → 8
  2. L9C1: only candidate → 9
  3. L4C1: only place for 8 in unit 4 → 8
  4. L8C6: only place for 7 in unit 8 → 7
  5. L9C6: only candidate → 3
  6. Units 4 and 23 overlap. In unit 4, 3 must lie in the overlap. Remove it from L6C4, L6C5.
  7. Units 12 and 19 overlap. In unit 12, 5 must lie in the overlap. Remove it from L1C1, L3C1.
L2C1 = 6

Assumption: L2C1 = 6

  1. L3C1: only candidate → 2
  2. L3C3: only candidate → 5
  3. L1C1: only candidate → 1

contradiction: a box no longer has no candidate

L2C1 = 7

Assumption: L2C1 = 7

  1. L3C1: only candidate → 1
  2. L1C1: only candidate → 5
  3. L1C2: only candidate → 4

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

L5C7 = 9

Assumption: L5C7 = 9

  1. L6C7: only candidate → 1
  2. L6C1: only place for 5 in unit 22 → 5
  3. L5C3: only place for 4 in unit 22 → 4
  4. L6C3: only candidate → 6
  5. L5C1: only candidate → 1
  6. L5C2: 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

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": 127,
  "branches": 63,
  "contradictions": 63,
  "depth": 9,
  "pairs": 102,
  "locked": 55
}

After unique candidates, single places, bare pairs/triples and interactions between units, the solver still reaches bifurcations. The exhaustive evidence reaches 9 intertwined hypotheses, examines 127 states and closes 63 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 Maybe it's shorter.

← Return to puzzle SOLO-010