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Sudoku #7 — the solutions

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

The solution

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

Medium — 29 digits given

Beyond singles, this board asks for a pointing line (2 times), a claimed box and a naked pair.

The board

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

The solution

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

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

The board

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

The solution

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

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. 57 steps; yours need not match, and any order that never guesses ends on the same grid.

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

Previous: Sudoku #6 (Tue, Oct 6)

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.