Sudoku pencil marks: how to write and update candidates
Learn Sudoku notes on a complete 9×9 puzzle: calculate candidates, update them after two proven moves, then practise the same free puzzle.
What do pencil marks mean?
Pencil marks are the digits that have not yet been ruled out for an empty cell. They record possibilities, not answers. A note of 4, 7, 9 means any of those three digits might still be legal; it does not mean one is more likely than another.
There are two useful styles of notation: recording every candidate in a cell, or marking possible positions for one digit in a box. This guide uses complete cell candidates. Keep the styles distinct, because an incomplete note can look like a single when it is not.
Find candidates with three checks
Start with digits 1–9. Remove every digit already placed in the cell’s row, then its column, then its 3×3 box. Repeated digits in these checks are removed only once. The digits left form the candidate set.
In the example below, the combined exclusions are 1, 2, 3, 5, 6, 8. That leaves 4, 7, 9. This is a local example of the calculation, not a complete puzzle.
| Check | Digits already present |
|---|---|
| Row | 1, 3, 8 |
| Column | 2, 5 |
| Box | 3, 6 |
| Candidates left | 4, 7, 9 |
Try pencil marks on a complete 9×9 puzzle
Here is the starting grid of iPlay Sudoku’s Easy puzzle 1, not an isolated example. R means row and C means column, counted from the top left. Dots are empty cells; ? marks R1C7. Each row, column and 3×3 box must contain 1–9 exactly once. Which notes belong in the marked cell?
| C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | |
|---|---|---|---|---|---|---|---|---|---|
| R1 | 4 | · | 3 | · | 9 | · | ? | 5 | · |
| R2 | · | · | · | · | 3 | · | 7 | · | 4 |
| R3 | 7 | · | 2 | 5 | 4 | 1 | · | 8 | 9 |
| R4 | · | 4 | 6 | · | · | 5 | · | 1 | 3 |
| R5 | · | · | 1 | 3 | · | 9 | · | 4 | 8 |
| R6 | 8 | 3 | 9 | 4 | 1 | 6 | · | · | · |
| R7 | · | · | 7 | 8 | 6 | 3 | · | · | 2 |
| R8 | · | 9 | · | 1 | · | 2 | · | 6 | · |
| R9 | · | 2 | · | 9 | · | 4 | 5 | 3 | 1 |
Why R1C7 has the candidates 1, 2 and 6
Check the actual grid. Row 1 excludes 3, 4, 5 and 9; column 7 also excludes 7; the top-right box also excludes 8. Their combined exclusions are {3, 4, 5, 7, 8, 9}, leaving {1, 2, 6}. These are possibilities, not three interchangeable answers.
| Check | Digits already present |
|---|---|
| Row 1 | 3, 4, 5, 9 |
| Column 7 | 5, 7 |
| Top-right box | 4, 5, 7, 8, 9 |
| Complete notes at R1C7 | 1, 2, 6 |
Watch three notes become one certain answer
First, R1C9 has only candidate 6: its row, column and box together exclude every other digit. Place 6 there. R1C7 shares its row, so its notes shrink from {1, 2, 6} to {1, 2}. It is still unsolved.
Next, R2C8 has only candidate 2. Its row, column and box exclude {1, 3, 4, 5, 6, 7, 8, 9}. Place 2 there. R1C7 is in the same top-right box, so remove 2 from its notes. Only 1 remains: R1C7 = 1. Each placement is proved from the board, not copied from an answer key.
The link selects Easy puzzle 1, the same givens shown above. If you have played it before, this browser may restore your progress. The article always shows the starting position; opening the link does not erase your save.
After placing only the 6 at R1C9, may you already write 1 at R1C7?
Show the explanation
No. Both 1 and 2 are still legal candidates there. The later placement R2C8 = 2 removes the last alternative. A short candidate list is not yet a proof.
Update only what the move affects
After placing a 7, remove 7 from notes in the same row, column and box. A cell outside all three regions is unaffected by that placement. If the example cell sees this new 7, its notes become 4, 9; you still cannot choose either digit.
A candidate can also be removed by a proved pattern such as a naked pair. Keep track of that reason. Rebuilding notes only from placed digits may bring back candidates that you already eliminated logically.
Use Notes on iPlay Sudoku
Select an empty cell, turn on Notes, then press a number to add or remove its small mark. The N key switches Notes on desktop. Turn Notes off before entering a final digit.
The game removes a placed digit from notes in related cells. You remain responsible for initially recording all legal candidates and for pattern-based eliminations. If you undo a move, check that you are reading the restored notes, not remembering the later position.
Check your understanding
Use the combined constraints, rather than checking only the row.
A cell sees 1, 2, 3, 5, 6, 8 and 9 across its row, column and box. What should its complete notes contain? Can you fill it now?
Show the explanation
The candidates are 4 and 7. Neither is forced yet. If a related cell is later filled with 7, this cell becomes a naked single of 4.
When notes seem to disagree
An empty candidate set usually signals a wrong entry or an incorrect elimination. Go back to the last move whose logic you can explain. Do not put an excluded digit back solely to make the cell look possible.
Once your notes are reliable, look for naked singles and hidden singles. Only then scan for pairs. This order keeps your attention on the simplest available deduction.