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Sudoku #31 — the solutions

The three Sudoku boards from October 31, 2026 — Easy, Medium and Hard — each with its solved grid and a path through it, step by step, that never needs a guess.

Easy — 36 digits given

Every cell falls to scanning: a digit with only one place left in a row, a column or a box.

The board

· 9 6 | · 5 · | · 2 ·
8 4 · | · 2 · | 9 5 7
· · 7 | 4 · · | · 6 ·
------+-------+------
4 3 · | · 7 · | · 9 ·
9 · · | · · · | · · 4
· 6 · | · 4 · | · 7 5
------+-------+------
· 2 · | · · 9 | 8 · ·
6 1 3 | · 8 · | · 4 9
· 8 · | · 6 · | 5 1 ·

The solution

3 9 6 | 1 5 7 | 4 2 8
8 4 1 | 6 2 3 | 9 5 7
2 5 7 | 4 9 8 | 1 6 3
------+-------+------
4 3 5 | 8 7 6 | 2 9 1
9 7 2 | 5 3 1 | 6 8 4
1 6 8 | 9 4 2 | 3 7 5
------+-------+------
5 2 4 | 7 1 9 | 8 3 6
6 1 3 | 2 8 5 | 7 4 9
7 8 9 | 3 6 4 | 5 1 2

A path through it

The order a solver takes — always the cheapest move left, so a pattern is only reached for when the singles run dry. 45 steps; yours need not match, and any order that never guesses ends on the same grid.

  1. Row 3, column 1 is 2. 2 has only one place left in the top-left box.
  2. Row 1, column 1 is 3. 3 has only one place left in the top-left box.
  3. Row 2, column 3 is 1. 1 has only one place left in the top-left box.
  4. Row 3, column 2 is 5. 5 has only one place left in the top-left box.
  5. Row 3, column 5 is 9. 9 has only one place left in the top-center box.
  6. Row 1, column 7 is 4. 4 has only one place left in the top-right box.
  7. Row 6, column 1 is 1. 1 has only one place left in the middle-left box.
  8. Row 5, column 2 is 7. 7 has only one place left in the middle-left box.
  9. Row 6, column 4 is 9. 9 has only one place left in the center box.
  10. Row 9, column 3 is 9. 9 has only one place left in the bottom-left box.
  11. Row 7, column 3 is 4. 4 has only one place left in the bottom-left box.
  12. Row 7, column 1 is 5. 5 has only one place left in the bottom-left box.
  13. Row 9, column 1 is 7. 7 has only one place left in the bottom-left box.
  14. Row 9, column 6 is 4. 4 has only one place left in the bottom-center box.
  15. Row 7, column 9 is 6. 6 has only one place left in the bottom-right box.
  16. Row 8, column 7 is 7. 7 has only one place left in the bottom-right box.
  17. Row 7, column 4 is 7. 7 has only one place left in the bottom-center box.
  18. Row 1, column 6 is 7. 7 has only one place left in the top-center box.
  19. Row 7, column 5 is 1. 1 has only one place left in the bottom-center box.
  20. Row 9, column 4 is 3. 3 has only one place left in the bottom-center box.
  21. Row 9, column 9 is 2. 2 has only one place left in the bottom-right box.
  22. Row 7, column 8 is 3. 3 has only one place left in the bottom-right box.
  23. Row 2, column 6 is 3. 3 has only one place left in row 2.
  24. Row 2, column 4 is 6. 6 has only one place left in the top-center box.
  25. Row 5, column 5 is 3. 3 has only one place left in the center box.
  26. Row 6, column 7 is 3. 3 has only one place left in the middle-right box.
  27. Row 3, column 9 is 3. 3 has only one place left in the top-right box.
  28. Row 1, column 9 is 8. 8 has only one place left in the top-right box.
  29. Row 3, column 6 is 8. 8 has only one place left in the top-center box.
  30. Row 1, column 4 is 1. 1 has only one place left in the top-center box.
  31. Row 3, column 7 is 1. 1 has only one place left in the top-right box.
  32. Row 4, column 9 is 1. 1 has only one place left in the middle-right box.
  33. Row 5, column 6 is 1. 1 has only one place left in the center box.
  34. Row 4, column 6 is 6. 6 has only one place left in the center box.
  35. Row 5, column 7 is 6. 6 has only one place left in the middle-right box.
  36. Row 4, column 7 is 2. 2 has only one place left in the middle-right box.
  37. Row 5, column 8 is 8. 8 has only one place left in the middle-right box.
  38. Row 4, column 4 is 8. 8 has only one place left in the center box.
  39. Row 6, column 3 is 8. 8 has only one place left in the middle-left box.
  40. Row 5, column 3 is 2. 2 has only one place left in the middle-left box.
  41. Row 4, column 3 is 5. 5 has only one place left in the middle-left box.
  42. Row 6, column 6 is 2. 2 has only one place left in the center box.
  43. Row 5, column 4 is 5. 5 has only one place left in the center box.
  44. Row 8, column 4 is 2. 2 has only one place left in the bottom-center box.
  45. Row 8, column 6 is 5. 5 has only one place left in the bottom-center box.

Medium — 29 digits given

Beyond singles, this board asks for a pointing line.

The board

· · 4 | 5 · · | · · ·
· · · | 7 · · | 4 3 ·
· · 2 | 4 · · | · 6 8
------+-------+------
· · 6 | 8 7 5 | · 1 ·
· · · | · 1 · | · · ·
· 2 · | 9 4 6 | 5 · ·
------+-------+------
2 9 · | · · 4 | 3 · ·
· 6 5 | · · 7 | · · ·
· · · | · · 8 | 2 · ·

The solution

6 3 4 | 5 8 1 | 7 2 9
9 8 1 | 7 6 2 | 4 3 5
5 7 2 | 4 3 9 | 1 6 8
------+-------+------
3 4 6 | 8 7 5 | 9 1 2
8 5 9 | 2 1 3 | 6 4 7
1 2 7 | 9 4 6 | 5 8 3
------+-------+------
2 9 8 | 1 5 4 | 3 7 6
4 6 5 | 3 2 7 | 8 9 1
7 1 3 | 6 9 8 | 2 5 4

A path through it

The order a solver takes — always the cheapest move left, so a pattern is only reached for when the singles run dry. 53 steps; yours need not match, and any order that never guesses ends on the same grid.

  1. Row 2, column 9 is 5. 5 has only one place left in the top-right box.
  2. Row 4, column 9 is 2. 2 has only one place left in row 4.
  3. Row 1, column 8 is 2. 2 has only one place left in the top-right box.
  4. Row 5, column 7 is 6. 6 has only one place left in column 7.
  5. Row 8, column 7 is 8. 8 has only one place left in column 7.
  6. Row 7, column 3 is 8. 8 has only one place left in the bottom-left box.
  7. Row 4, column 7 is 9. Nothing but 9 is left for this cell.
  8. Row 1, column 9 is 9. 9 has only one place left in the top-right box.
  9. In the top-center box, 6 can only sit in column 5, so it leaves the rest of that column.
  10. Row 7, column 5 is 5. Nothing but 5 is left for this cell.
  11. Row 9, column 8 is 5. 5 has only one place left in the bottom-right box.
  12. Row 8, column 8 is 9. 9 has only one place left in the bottom-right box.
  13. Row 9, column 5 is 9. 9 has only one place left in the bottom-center box.
  14. Row 5, column 8 is 4. 4 has only one place left in column 8.
  15. Row 6, column 8 is 8. 8 has only one place left in the middle-right box.
  16. Row 7, column 8 is 7. 7 has only one place left in column 8.
  17. Row 3, column 5 is 3. Nothing but 3 is left for this cell.
  18. Row 5, column 6 is 3. 3 has only one place left in column 6.
  19. Row 5, column 4 is 2. 2 has only one place left in the center box.
  20. Row 6, column 9 is 3. 3 has only one place left in the middle-right box.
  21. Row 5, column 9 is 7. 7 has only one place left in the middle-right box.
  22. Row 8, column 5 is 2. 2 has only one place left in the bottom-center box.
  23. Row 2, column 6 is 2. 2 has only one place left in the top-center box.
  24. Row 3, column 6 is 9. 9 has only one place left in the top-center box.
  25. Row 1, column 6 is 1. 1 has only one place left in the top-center box.
  26. Row 3, column 7 is 1. 1 has only one place left in the top-right box.
  27. Row 1, column 7 is 7. 7 has only one place left in the top-right box.
  28. Row 9, column 3 is 3. 3 has only one place left in column 3.
  29. Row 8, column 4 is 3. 3 has only one place left in the bottom-center box.
  30. Row 6, column 3 is 7. 7 has only one place left in column 3.
  31. Row 6, column 1 is 1. 1 has only one place left in the middle-left box.
  32. Row 9, column 2 is 1. 1 has only one place left in the bottom-left box.
  33. Row 2, column 3 is 1. 1 has only one place left in the top-left box.
  34. Row 2, column 1 is 9. 9 has only one place left in the top-left box.
  35. Row 1, column 1 is 6. 6 has only one place left in the top-left box.
  36. Row 1, column 2 is 3. 3 has only one place left in the top-left box.
  37. Row 2, column 2 is 8. 8 has only one place left in the top-left box.
  38. Row 2, column 5 is 6. 6 has only one place left in the top-center box.
  39. Row 1, column 5 is 8. 8 has only one place left in the top-center box.
  40. Row 4, column 1 is 3. 3 has only one place left in the middle-left box.
  41. Row 4, column 2 is 4. 4 has only one place left in the middle-left box.
  42. Row 5, column 1 is 8. 8 has only one place left in the middle-left box.
  43. Row 5, column 2 is 5. 5 has only one place left in the middle-left box.
  44. Row 3, column 1 is 5. 5 has only one place left in the top-left box.
  45. Row 3, column 2 is 7. 7 has only one place left in the top-left box.
  46. Row 5, column 3 is 9. 9 has only one place left in the middle-left box.
  47. Row 9, column 1 is 7. 7 has only one place left in the bottom-left box.
  48. Row 8, column 1 is 4. 4 has only one place left in the bottom-left box.
  49. Row 7, column 4 is 1. 1 has only one place left in the bottom-center box.
  50. Row 9, column 4 is 6. 6 has only one place left in the bottom-center box.
  51. Row 8, column 9 is 1. 1 has only one place left in the bottom-right box.
  52. Row 9, column 9 is 4. 4 has only one place left in the bottom-right box.
  53. Row 7, column 9 is 6. 6 has only one place left in the bottom-right box.

Hard — 26 digits given

Beyond singles, this board asks for a pointing line (2 times) and a naked triple.

The board

· · · | · · 3 | · 5 ·
· · · | 7 · · | 9 · 8
4 · · | · 5 · | · 6 ·
------+-------+------
8 9 · | · · 4 | · · 3
· · 2 | · · · | 6 · ·
3 · · | 8 · · | · 2 7
------+-------+------
· 1 · | · 9 · | · · 6
6 · 3 | · · 2 | · · ·
· 2 · | 3 · · | · · ·

The solution

2 8 9 | 6 4 3 | 7 5 1
5 3 6 | 7 2 1 | 9 4 8
4 7 1 | 9 5 8 | 3 6 2
------+-------+------
8 9 7 | 2 6 4 | 5 1 3
1 4 2 | 5 3 7 | 6 8 9
3 6 5 | 8 1 9 | 4 2 7
------+-------+------
7 1 8 | 4 9 5 | 2 3 6
6 5 3 | 1 7 2 | 8 9 4
9 2 4 | 3 8 6 | 1 7 5

A path through it

The order a solver takes — always the cheapest move left, so a pattern is only reached for when the singles run dry. 58 steps; yours need not match, and any order that never guesses ends on the same grid.

  1. Row 5, column 5 is 3. 3 has only one place left in the center box.
  2. Row 5, column 8 is 8. 8 has only one place left in the middle-right box.
  3. Row 5, column 9 is 9. 9 has only one place left in the middle-right box.
  4. Row 6, column 6 is 9. 9 has only one place left in the center box.
  5. Row 6, column 7 is 4. 4 has only one place left in the middle-right box.
  6. Row 5, column 2 is 4. 4 has only one place left in the middle-left box.
  7. Row 4, column 7 is 5. 5 has only one place left in the middle-right box.
  8. Row 4, column 8 is 1. 1 has only one place left in the middle-right box.
  9. Row 7, column 7 is 2. 2 has only one place left in the bottom-right box.
  10. Row 7, column 8 is 3. 3 has only one place left in the bottom-right box.
  11. Row 3, column 7 is 3. 3 has only one place left in the top-right box.
  12. Row 2, column 2 is 3. 3 has only one place left in the top-left box.
  13. Row 1, column 7 is 7. 7 has only one place left in the top-right box.
  14. Row 8, column 8 is 9. 9 has only one place left in row 8.
  15. Row 9, column 8 is 7. 7 has only one place left in the bottom-right box.
  16. Row 2, column 8 is 4. 4 has only one place left in column 8.
  17. In the top-right box, 1 can only sit in column 9, so it leaves the rest of that column.
  18. In the center box, 5 can only sit in row 5, so it leaves the rest of that row.
  19. Three cells in column 4 hold only 1, 4 and 5 between them, so no other cell there can.
  20. Row 1, column 5 is 4. 4 has only one place left in the top-center box.
  21. Row 3, column 6 is 8. 8 has only one place left in the top-center box.
  22. Row 7, column 3 is 8. 8 has only one place left in row 7.
  23. Row 1, column 2 is 8. 8 has only one place left in the top-left box.
  24. Row 9, column 3 is 4. 4 has only one place left in the bottom-left box.
  25. Row 9, column 1 is 9. 9 has only one place left in the bottom-left box.
  26. Row 8, column 9 is 4. 4 has only one place left in the bottom-right box.
  27. Row 7, column 4 is 4. 4 has only one place left in the bottom-center box.
  28. Row 9, column 9 is 5. 5 has only one place left in the bottom-right box.
  29. Row 6, column 2 is 6. 6 has only one place left in column 2.
  30. Row 6, column 3 is 5. 5 has only one place left in the middle-left box.
  31. Row 2, column 1 is 5. 5 has only one place left in the top-left box.
  32. Row 1, column 1 is 2. 2 has only one place left in the top-left box.
  33. Row 3, column 9 is 2. 2 has only one place left in the top-right box.
  34. Row 2, column 5 is 2. 2 has only one place left in the top-center box.
  35. Row 2, column 6 is 1. 1 has only one place left in the top-center box.
  36. Row 1, column 4 is 6. 6 has only one place left in the top-center box.
  37. Row 2, column 3 is 6. 6 has only one place left in the top-left box.
  38. Row 3, column 4 is 9. 9 has only one place left in the top-center box.
  39. Row 1, column 3 is 9. 9 has only one place left in the top-left box.
  40. Row 3, column 3 is 1. 1 has only one place left in the top-left box.
  41. Row 3, column 2 is 7. 7 has only one place left in the top-left box.
  42. Row 1, column 9 is 1. 1 has only one place left in the top-right box.
  43. Row 5, column 1 is 1. 1 has only one place left in the middle-left box.
  44. Row 4, column 3 is 7. 7 has only one place left in the middle-left box.
  45. Row 6, column 5 is 1. 1 has only one place left in the center box.
  46. Row 4, column 4 is 2. 2 has only one place left in the center box.
  47. Row 4, column 5 is 6. 6 has only one place left in the center box.
  48. Row 5, column 6 is 7. 7 has only one place left in the center box.
  49. Row 5, column 4 is 5. 5 has only one place left in the center box.
  50. Row 8, column 2 is 5. 5 has only one place left in the bottom-left box.
  51. Row 7, column 1 is 7. 7 has only one place left in the bottom-left box.
  52. Row 8, column 4 is 1. 1 has only one place left in the bottom-center box.
  53. Row 7, column 6 is 5. 5 has only one place left in the bottom-center box.
  54. Row 9, column 6 is 6. 6 has only one place left in the bottom-center box.
  55. Row 8, column 5 is 7. 7 has only one place left in the bottom-center box.
  56. Row 9, column 5 is 8. 8 has only one place left in the bottom-center box.
  57. Row 9, column 7 is 1. 1 has only one place left in the bottom-right box.
  58. Row 8, column 7 is 8. 8 has only one place left in the bottom-right box.

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About Sudoku

Sudoku on Noggin is three boards a day, on the second shelf: every entry is checked at once, a hint fills the next cell a solver would and says why, and the first board finished is the day’s score, outside the daily line-up. How to play Sudoku, or play today’s.