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Sudoku #4 — the solutions

The three Sudoku boards from October 4, 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

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

The solution

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

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

The board

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

The solution

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

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

The board

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

The solution

2 9 4 | 7 6 1 | 5 3 8
6 8 7 | 3 2 5 | 1 4 9
5 3 1 | 9 4 8 | 2 6 7
------+-------+------
3 5 8 | 1 9 7 | 6 2 4
1 7 2 | 6 3 4 | 8 9 5
9 4 6 | 8 5 2 | 3 7 1
------+-------+------
8 6 3 | 4 1 9 | 7 5 2
7 2 9 | 5 8 6 | 4 1 3
4 1 5 | 2 7 3 | 9 8 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. 59 steps; yours need not match, and any order that never guesses ends on the same grid.

  1. Row 6, column 2 is 4. 4 has only one place left in the middle-left box.
  2. Row 5, column 2 is 7. 7 has only one place left in the middle-left box.
  3. Row 5, column 8 is 9. 9 has only one place left in the middle-right box.
  4. Row 7, column 2 is 6. 6 has only one place left in the bottom-left box.
  5. Row 2, column 8 is 4. 4 has only one place left in row 2.
  6. Row 4, column 9 is 4. 4 has only one place left in the middle-right box.
  7. Row 5, column 3 is 2. 2 has only one place left in row 5.
  8. Row 8, column 2 is 2. 2 has only one place left in the bottom-left box.
  9. Row 5, column 7 is 8. 8 has only one place left in row 5.
  10. Row 5, column 5 is 3. 3 has only one place left in row 5.
  11. Row 9, column 6 is 3. 3 has only one place left in the bottom-center box.
  12. Row 9, column 5 is 7. 7 has only one place left in row 9.
  13. Row 7, column 5 is 1. 1 has only one place left in column 5.
  14. Row 7, column 4 is 4. 4 has only one place left in the bottom-center box.
  15. Row 3, column 5 is 4. 4 has only one place left in the top-center box.
  16. Row 1, column 5 is 6. 6 has only one place left in the top-center box.
  17. Row 3, column 8 is 6. 6 has only one place left in the top-right box.
  18. In the top-left box, 5 can only sit in row 3, so it leaves the rest of that row.
  19. In the top-right box, 3 can only sit in row 1, so it leaves the rest of that row.
  20. Row 3, column 2 is 3. 3 has only one place left in column 2.
  21. Row 1, column 2 is 9. 9 has only one place left in column 2.
  22. In the bottom-right box, 1 can only sit in column 8, so it leaves the rest of that column.
  23. Three cells in row 6 hold only 1, 2 and 8 between them, so no other cell there can.
  24. In the middle-left box, 8 can only sit in row 4, so it leaves the rest of that row.
  25. XY-wing: one of its two wings must be 7, so no cell that sees both can be.
  26. Row 3, column 9 is 7. 7 has only one place left in the top-right box.
  27. Row 1, column 4 is 7. 7 has only one place left in the top-center box.
  28. Row 2, column 6 is 5. 5 has only one place left in the top-center box.
  29. Row 2, column 7 is 1. 1 has only one place left in the top-right box.
  30. Row 3, column 3 is 1. 1 has only one place left in the top-left box.
  31. Row 3, column 1 is 5. 5 has only one place left in the top-left box.
  32. Row 2, column 2 is 8. 8 has only one place left in the top-left box.
  33. Row 4, column 6 is 7. 7 has only one place left in the center box.
  34. Row 6, column 6 is 2. 2 has only one place left in the center box.
  35. Row 6, column 4 is 8. 8 has only one place left in the center box.
  36. Row 3, column 6 is 8. 8 has only one place left in the top-center box.
  37. Row 3, column 4 is 9. 9 has only one place left in the top-center box.
  38. Row 4, column 4 is 1. 1 has only one place left in the center box.
  39. Row 6, column 9 is 1. 1 has only one place left in the middle-right box.
  40. Row 4, column 8 is 2. 2 has only one place left in the middle-right box.
  41. Row 9, column 2 is 1. 1 has only one place left in the bottom-left box.
  42. Row 8, column 4 is 5. 5 has only one place left in the bottom-center box.
  43. Row 9, column 3 is 5. 5 has only one place left in the bottom-left box.
  44. Row 7, column 1 is 8. 8 has only one place left in the bottom-left box.
  45. Row 4, column 3 is 8. 8 has only one place left in the middle-left box.
  46. Row 6, column 3 is 6. 6 has only one place left in the middle-left box.
  47. Row 6, column 1 is 9. 9 has only one place left in the middle-left box.
  48. Row 4, column 1 is 3. 3 has only one place left in the middle-left box.
  49. Row 6, column 7 is 3. 3 has only one place left in the middle-right box.
  50. Row 1, column 8 is 3. 3 has only one place left in the top-right box.
  51. Row 1, column 7 is 5. 5 has only one place left in the top-right box.
  52. Row 4, column 7 is 6. 6 has only one place left in the middle-right box.
  53. Row 8, column 3 is 9. 9 has only one place left in the bottom-left box.
  54. Row 7, column 6 is 9. 9 has only one place left in the bottom-center box.
  55. Row 8, column 8 is 1. 1 has only one place left in the bottom-right box.
  56. Row 7, column 9 is 2. 2 has only one place left in the bottom-right box.
  57. Row 7, column 8 is 5. 5 has only one place left in the bottom-right box.
  58. Row 7, column 7 is 7. 7 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.

Previous: Sudoku #3 (Sat, Oct 3)

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.