Notes
Notes — pencil marks, candidates, whichever name you met first — are the digits still legally possible in an empty square, written small inside it. Every technique from here on is a statement about candidates, so this is less a technique than the notation the rest are written in.
The idea
A note is not a guess. If a square carries the marks 2, 4 and 7, that means every other digit has been ruled out by something already on the board: each of 1, 3, 5, 6, 8 and 9 appears somewhere in that square's row, column or box.
Writing them down changes what you can see. Scanning asks where a digit can go; notes let you ask the reverse question, what this square can hold, and comparing the answers across two or three squares is where the pairs techniques live.
A worked example
Box 1 holds 5, 3, 6, 8, 1 and 9, so its three empty squares must take 2, 4 and 7 between them. The two highlighted digits outside the box then do the rest of the work: the 4 in row 1 keeps 4 out of r1c3, and the 4 in column 3 keeps it out of r3c3.
Two conclusions fall out of three sets of pencil marks:
- 4 has only one square left in the box, so r2c2 is 4 — a hidden single, and invisible without the notes.
- r1c3 and r3c3 both read exactly 2 and 7, so between them they use both digits — a naked pair, which clears 2 and 7 out of every other square in column 3.
When to write them
Not at the start. Noting an entire grid before placing anything is slow, and most of what you write is immediately invalidated by the placements that scanning would have given you for free. Scan first, place what the scan yields, and begin noting a region only when it stops producing.
On this site the Notes button switches the number pad to pencil-mark mode, so a digit you tap is written small instead of being entered as an answer.
Common mistakes
Stale marks, and nothing else comes close. Every digit you place has to be erased from the notes of its row, its column and its box straight away. A candidate left behind after an earlier placement is worse than no notes at all, because it quietly hides the deductions the notes were written to expose — a naked single still showing two candidates will never be spotted.
The opposite error is erasing too eagerly and inventing a deduction that is not there. When a conclusion surprises you, re-derive that square's candidates from the board rather than trusting what is written in it.
Common questions
What are notes in Sudoku?
Notes, also called pencil marks or candidates, are the digits still legally possible in an empty square, written small inside it. They are not guesses. Each one is a digit that no square sharing a row, column or box has already taken.
Do I have to use notes to solve Sudoku?
Not for easy puzzles, which can be finished by scanning alone. From medium upwards the techniques that break a stuck grid — naked pairs, hidden pairs, pointing pairs, the X-Wing — are all statements about candidates, so they are invisible until the candidates are written down.
Should I fill in notes for the whole grid at once?
Only when you are stuck. Noting everything early is slow and creates a large amount of writing to keep correct. The usual approach is to scan first, place what scanning gives you, and start noting a region only when it stops yielding.
What goes wrong with notes?
Stale marks. Every digit you place should be erased from the notes of its row, column and box immediately, and the most common way to get stuck for no reason is a candidate left behind after an earlier placement. A note you failed to erase hides the very deductions notes exist to reveal.
Where to go next
The next technique in the order is naked pairs — Two squares, the same two candidates: those digits belong to them, so erase them everywhere else in the unit.
All nine techniques: the techniques index. New to the rules? Start here. Ready to use it? Open a board.