Sudoku pencil marks: how to write and update candidates
Learn what the small numbers mean, how to find every legal candidate, and when a note can safely be removed.
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 |
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.