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Sudoku #21 — the solutions

The three Sudoku boards from October 21, 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 | 9 · 3 | 2 · 8
· · · | · 6 · | · · ·
4 · · | 1 8 7 | 5 6 ·
------+-------+------
3 · 6 | · · 8 | · · 2
· · 9 | 5 · 6 | 3 · ·
2 · · | 3 · · | 1 · 6
------+-------+------
· 9 7 | 8 3 2 | · · 5
· · · | · 7 · | · · ·
1 · 3 | 4 · 5 | 6 · ·

The solution

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

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

The board

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

The solution

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

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

Hard — 28 digits given

Beyond singles, this board asks for a pointing line (4 times), a claimed box, a naked pair and an XY-wing.

The board

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

The solution

2 9 4 | 5 3 8 | 6 1 7
7 3 1 | 6 4 9 | 5 2 8
6 5 8 | 2 7 1 | 9 3 4
------+-------+------
5 7 2 | 8 9 6 | 3 4 1
1 8 3 | 7 5 4 | 2 9 6
9 4 6 | 1 2 3 | 7 8 5
------+-------+------
4 2 5 | 9 8 7 | 1 6 3
3 6 9 | 4 1 5 | 8 7 2
8 1 7 | 3 6 2 | 4 5 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. 60 steps; yours need not match, and any order that never guesses ends on the same grid.

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