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Sudoku #13 — the solutions

The three Sudoku boards from October 13, 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

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

The solution

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

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

Medium — 28 digits given

Beyond singles, this board asks for a pointing line and a naked pair.

The board

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

The solution

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

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. 55 steps; yours need not match, and any order that never guesses ends on the same grid.

  1. Row 2, column 4 is 9. 9 has only one place left in the top-center box.
  2. Row 1, column 1 is 2. 2 has only one place left in row 1.
  3. Row 1, column 3 is 9. 9 has only one place left in the top-left box.
  4. Row 5, column 2 is 2. 2 has only one place left in the middle-left box.
  5. Row 8, column 1 is 9. 9 has only one place left in the bottom-left box.
  6. Row 7, column 7 is 9. 9 has only one place left in the bottom-right box.
  7. Row 5, column 8 is 9. 9 has only one place left in the middle-right box.
  8. Row 4, column 5 is 9. 9 has only one place left in the center box.
  9. Row 7, column 9 is 6. 6 has only one place left in the bottom-right box.
  10. Row 4, column 7 is 6. 6 has only one place left in the middle-right box.
  11. Row 1, column 8 is 6. 6 has only one place left in row 1.
  12. Row 1, column 9 is 5. 5 has only one place left in the top-right box.
  13. Row 2, column 7 is 2. 2 has only one place left in row 2.
  14. Row 3, column 7 is 8. 8 has only one place left in the top-right box.
  15. Row 3, column 8 is 4. 4 has only one place left in the top-right box.
  16. Row 2, column 9 is 1. 1 has only one place left in the top-right box.
  17. Row 3, column 3 is 1. 1 has only one place left in the top-left box.
  18. Row 2, column 3 is 6. 6 has only one place left in the top-left box.
  19. Row 3, column 1 is 7. 7 has only one place left in the top-left box.
  20. Row 8, column 8 is 1. 1 has only one place left in the bottom-right box.
  21. Row 8, column 7 is 5. 5 has only one place left in the bottom-right box.
  22. Row 6, column 8 is 5. 5 has only one place left in the middle-right box.
  23. Row 4, column 4 is 5. 5 has only one place left in the center box.
  24. Row 9, column 2 is 1. 1 has only one place left in row 9.
  25. Row 3, column 4 is 3. Nothing but 3 is left for this cell.
  26. In the bottom-center box, 7 can only sit in row 7, so it leaves the rest of that row.
  27. Row 8, column 3 is 7. 7 has only one place left in the bottom-left box.
  28. Row 4, column 2 is 7. 7 has only one place left in the middle-left box.
  29. Two cells in row 5 hold only 4 and 7, so no other cell there can.
  30. Row 9, column 1 is 4. 4 has only one place left in column 1.
  31. Row 8, column 9 is 4. 4 has only one place left in the bottom-right box.
  32. Row 6, column 7 is 4. 4 has only one place left in the middle-right box.
  33. Row 4, column 3 is 4. 4 has only one place left in the middle-left box.
  34. Row 5, column 1 is 8. 8 has only one place left in the middle-left box.
  35. Row 2, column 2 is 8. 8 has only one place left in the top-left box.
  36. Row 2, column 1 is 3. 3 has only one place left in the top-left box.
  37. Row 6, column 3 is 3. 3 has only one place left in the middle-left box.
  38. Row 5, column 4 is 4. 4 has only one place left in the center box.
  39. Row 4, column 6 is 8. 8 has only one place left in the center box.
  40. Row 5, column 9 is 7. 7 has only one place left in the middle-right box.
  41. Row 7, column 2 is 3. 3 has only one place left in the bottom-left box.
  42. Row 7, column 3 is 8. 8 has only one place left in the bottom-left box.
  43. Row 8, column 6 is 3. 3 has only one place left in the bottom-center box.
  44. Row 5, column 5 is 3. 3 has only one place left in the center box.
  45. Row 5, column 6 is 6. 6 has only one place left in the center box.
  46. Row 3, column 5 is 6. 6 has only one place left in the top-center box.
  47. Row 3, column 6 is 2. 2 has only one place left in the top-center box.
  48. Row 6, column 5 is 2. 2 has only one place left in the center box.
  49. Row 6, column 4 is 7. 7 has only one place left in the center box.
  50. Row 6, column 6 is 1. 1 has only one place left in the center box.
  51. Row 7, column 4 is 1. 1 has only one place left in the bottom-center box.
  52. Row 7, column 6 is 4. 4 has only one place left in the bottom-center box.
  53. Row 7, column 5 is 7. 7 has only one place left in the bottom-center box.
  54. Row 9, column 9 is 3. 3 has only one place left in the bottom-right box.
  55. Row 9, column 7 is 7. 7 has only one place left in the bottom-right box.

Hard — 26 digits given

Beyond singles, this board asks for a pointing line, a naked pair (2 times) and an XY-wing.

The board

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

The solution

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

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. 59 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 7, column 4 is 3. 3 has only one place left in the bottom-center box.
  3. Row 3, column 9 is 1. 1 has only one place left in row 3.
  4. Row 3, column 6 is 3. 3 has only one place left in row 3.
  5. Row 6, column 5 is 3. 3 has only one place left in the center box.
  6. Row 3, column 8 is 4. 4 has only one place left in row 3.
  7. Row 6, column 3 is 1. 1 has only one place left in row 6.
  8. Row 7, column 1 is 6. 6 has only one place left in row 7.
  9. Row 5, column 3 is 6. 6 has only one place left in the middle-left box.
  10. Row 4, column 2 is 7. 7 has only one place left in the middle-left box.
  11. Row 5, column 5 is 7. 7 has only one place left in the center box.
  12. Row 5, column 4 is 1. 1 has only one place left in the center box.
  13. Row 2, column 5 is 1. 1 has only one place left in the top-center box.
  14. Row 8, column 3 is 7. 7 has only one place left in the bottom-left box.
  15. Row 7, column 9 is 7. 7 has only one place left in the bottom-right box.
  16. Row 6, column 8 is 7. 7 has only one place left in the middle-right box.
  17. Row 4, column 7 is 6. 6 has only one place left in the middle-right box.
  18. Row 6, column 6 is 6. 6 has only one place left in the center box.
  19. Row 7, column 2 is 8. 8 has only one place left in row 7.
  20. Row 8, column 7 is 4. 4 has only one place left in row 8.
  21. Row 5, column 9 is 4. 4 has only one place left in the middle-right box.
  22. Row 4, column 9 is 5. 5 has only one place left in the middle-right box.
  23. Row 5, column 1 is 5. 5 has only one place left in the middle-left box.
  24. Row 9, column 7 is 1. 1 has only one place left in the bottom-right box.
  25. Row 8, column 2 is 1. 1 has only one place left in the bottom-left box.
  26. Row 9, column 2 is 5. 5 has only one place left in the bottom-left box.
  27. Row 9, column 1 is 4. 4 has only one place left in column 1.
  28. Row 9, column 3 is 9. 9 has only one place left in the bottom-left box.
  29. In the bottom-right box, 8 can only sit in column 8, so it leaves the rest of that column.
  30. Two cells in row 2 hold only 2 and 5, so no other cell there can.
  31. Row 2, column 4 is 4. Nothing but 4 is left for this cell.
  32. Row 1, column 3 is 4. 4 has only one place left in the top-left box.
  33. Row 2, column 3 is 8. 8 has only one place left in the top-left box.
  34. Two cells in row 8 hold only 6 and 8, so no other cell there can.
  35. XY-wing: one of its two wings must be 2, so no cell that sees both can be.
  36. Row 9, column 6 is 2. 2 has only one place left in the bottom-center box.
  37. Row 8, column 4 is 8. 8 has only one place left in the bottom-center box.
  38. Row 5, column 6 is 8. 8 has only one place left in the center box.
  39. Row 4, column 5 is 9. 9 has only one place left in the center box.
  40. Row 6, column 1 is 9. 9 has only one place left in the middle-left box.
  41. Row 4, column 1 is 8. 8 has only one place left in the middle-left box.
  42. Row 4, column 4 is 2. 2 has only one place left in the center box.
  43. Row 1, column 5 is 2. 2 has only one place left in the top-center box.
  44. Row 2, column 6 is 5. 5 has only one place left in the top-center box.
  45. Row 1, column 4 is 6. 6 has only one place left in the top-center box.
  46. Row 2, column 8 is 2. 2 has only one place left in the top-right box.
  47. Row 1, column 8 is 5. 5 has only one place left in the top-right box.
  48. Row 6, column 9 is 8. 8 has only one place left in the middle-right box.
  49. Row 1, column 7 is 8. 8 has only one place left in the top-right box.
  50. Row 2, column 7 is 3. 3 has only one place left in the top-right box.
  51. Row 1, column 2 is 3. 3 has only one place left in the top-left box.
  52. Row 2, column 2 is 9. 9 has only one place left in the top-left box.
  53. Row 1, column 9 is 9. 9 has only one place left in the top-right box.
  54. Row 5, column 7 is 9. 9 has only one place left in the middle-right box.
  55. Row 8, column 5 is 5. 5 has only one place left in the bottom-center box.
  56. Row 9, column 5 is 6. 6 has only one place left in the bottom-center box.
  57. Row 8, column 6 is 9. 9 has only one place left in the bottom-center box.
  58. Row 8, column 8 is 6. 6 has only one place left in the bottom-right box.
  59. Row 9, column 8 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.