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Sudoku #20 — the solutions

The three Sudoku boards from October 20, 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 4 | · 1 5
· · 1 | · 3 · | 2 6 ·
· 4 · | 8 · 1 | · 9 3
------+-------+------
· 2 · | 9 · · | · · ·
5 · 7 | 1 · 6 | 3 · 9
· · · | · · 8 | · 7 ·
------+-------+------
9 7 · | 6 · 2 | · 3 ·
· 1 4 | · 8 · | 9 · ·
3 5 · | 4 1 · | · · ·

The solution

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

Medium — 28 digits given

Beyond singles, this board asks for a pointing line.

The board

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

The solution

7 8 6 | 9 3 2 | 5 4 1
1 9 3 | 8 4 5 | 7 2 6
2 5 4 | 6 7 1 | 3 9 8
------+-------+------
9 4 5 | 2 6 3 | 1 8 7
3 6 2 | 7 1 8 | 4 5 9
8 7 1 | 4 5 9 | 2 6 3
------+-------+------
5 3 9 | 1 8 4 | 6 7 2
4 2 7 | 3 9 6 | 8 1 5
6 1 8 | 5 2 7 | 9 3 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. 54 steps; yours need not match, and any order that never guesses ends on the same grid.

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

Hard — 30 digits given

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

The board

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

The solution

7 9 2 | 4 8 5 | 1 6 3
8 1 4 | 9 6 3 | 2 5 7
5 3 6 | 2 1 7 | 4 9 8
------+-------+------
6 8 9 | 1 7 2 | 5 3 4
2 5 7 | 3 4 9 | 6 8 1
1 4 3 | 6 5 8 | 9 7 2
------+-------+------
9 6 1 | 8 3 4 | 7 2 5
3 2 5 | 7 9 1 | 8 4 6
4 7 8 | 5 2 6 | 3 1 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. 54 steps; yours need not match, and any order that never guesses ends on the same grid.

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