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Sudoku #16 — the solutions

The three Sudoku boards from October 16, 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 · 7 | 2 4 ·
· 7 · | 6 · 8 | 3 · 1
· 5 · | · 1 · | · 8 ·
------+-------+------
· · 4 | · 8 · | 7 1 ·
8 · 5 | · · · | 6 · 4
· 6 9 | · 3 · | 5 · ·
------+-------+------
· 4 · | · 2 · | · 7 ·
2 · 1 | 8 · 5 | · 6 ·
· 3 7 | 1 · 4 | · · ·

The solution

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

The board

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

The solution

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

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

Hard — 26 digits given

Beyond singles, this board asks for an XY-wing.

The board

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

The solution

3 6 8 | 4 1 2 | 9 7 5
9 4 7 | 6 8 5 | 1 2 3
2 5 1 | 9 3 7 | 8 4 6
------+-------+------
4 1 9 | 3 5 6 | 7 8 2
6 8 2 | 1 7 4 | 3 5 9
5 7 3 | 2 9 8 | 4 6 1
------+-------+------
1 2 6 | 8 4 9 | 5 3 7
7 9 4 | 5 6 3 | 2 1 8
8 3 5 | 7 2 1 | 6 9 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. 56 steps; yours need not match, and any order that never guesses ends on the same grid.

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