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Sudoku #12 — the solutions

The three Sudoku boards from October 12, 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

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

The solution

4 7 2 | 9 5 6 | 3 8 1
3 9 8 | 2 7 1 | 4 6 5
1 5 6 | 3 8 4 | 9 2 7
------+-------+------
8 4 1 | 7 2 3 | 6 5 9
2 3 5 | 4 6 9 | 7 1 8
9 6 7 | 5 1 8 | 2 4 3
------+-------+------
7 2 9 | 8 4 5 | 1 3 6
5 1 4 | 6 3 7 | 8 9 2
6 8 3 | 1 9 2 | 5 7 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. 45 steps; yours need not match, and any order that never guesses ends on the same grid.

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

Medium — 29 digits given

Beyond singles, this board asks for a pointing line (7 times).

The board

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

The solution

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

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

The board

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

The solution

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

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

Previous: Sudoku #11 (Sun, Oct 11)

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.