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Sudoku #18 — the solutions

The three Sudoku boards from October 18, 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 · | 4 6 ·
· 4 · | · · 2 | 3 · 5
3 9 1 | · · 6 | · · ·
------+-------+------
6 1 · | · · 8 | · 7 ·
4 7 2 | · · · | 8 1 9
· 3 · | 7 · · | · 4 6
------+-------+------
· · · | 9 · · | 6 3 8
1 · 3 | 8 · · | · 5 ·
· 8 7 | · 3 · | · · ·

The solution

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

The board

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

The solution

9 1 5 | 3 2 4 | 7 6 8
8 7 6 | 1 9 5 | 3 4 2
3 2 4 | 8 6 7 | 5 1 9
------+-------+------
6 3 7 | 9 8 2 | 4 5 1
4 9 1 | 6 5 3 | 2 8 7
5 8 2 | 4 7 1 | 9 3 6
------+-------+------
1 6 3 | 7 4 9 | 8 2 5
2 4 9 | 5 1 8 | 6 7 3
7 5 8 | 2 3 6 | 1 9 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. 57 steps; yours need not match, and any order that never guesses ends on the same grid.

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

Hard — 26 digits given

Beyond singles, this board asks for a pointing line (5 times) and an XY-wing.

The board

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

The solution

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

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

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