Sudoku Notes (Pencil Marks): When and How to Use Them

Sudoku notes, or pencil marks, are small digits you write in an empty square to record which candidates are still possible there. Use them when a grid is too hard to hold in your head: on most 9x9 puzzles once the easy singles run out, and always for techniques such as pairs and X-Wings. There are two main ways to take them: full notes, every candidate in every square, and partial notes, only the ones that matter. This guide is for solvers moving from easy grids to harder ones.

What sudoku notes are for

Sudoku notes are a memory aid: they store the result of checking a square, so you do not have to check it again. A note "3 7" in a square means you have looked along its row, column and box and found that only 3 and 7 are still possible.

Notes do three jobs:

They find naked singles. A square whose notes shrink to one digit is solved.
They show patterns. Pairs, triples, X-Wings and wings are patterns in the notes, and nearly impossible to see without them. The whole ladder is in sudoku strategies.
They let you stop and come back. A grid with good notes can be picked up again tomorrow.

On paper they are pencil marks, written small and erased as you go. In apps they are a notes mode: in Puzzle Picnic you tap a square and pick a number, and Notes mode pencils in candidates instead of placing the digit.

Full notes: every candidate in every square

Full notes mean writing every possible digit in every empty square. They are slow to set up and busy to read, but they are complete, and complete notes are what advanced techniques need.

Here is one box of a 9x9 puzzle at the start of a solve: the bottom-middle box (rows 7 to 9, columns 4 to 6), with clues 7 and 5. R8C5 means row 8, column 5. The table shows its full notes, and the partial marks you would write in the two-square style described in the next section.

Square	Full notes	Two-square marks
R7C4	2 3 4 9	4
R7C5	clue 7
R7C6	1 3 4 6 9	1 4 6
R8C4	3 9	none
R8C5	3	none
R8C6	3 6 9	6
R9C4	2 3 8 9	8
R9C5	1 2 3 8	1 8
R9C6	clue 5

The full notes give something away at once: R8C5 has only one candidate, 3. Its row already holds 1, 2, 4 and 8, its column 6, 7 and 9, and its box 5 and 7, so 3 is the only digit left. Place it and the box falls quickly:

R8C5 is 3, so R8C4 loses its 3 and is left with 9.
With 3 and 9 now in row 8, R8C6 is left with 6.

Three digits from one box, all found because the notes were complete.

How to fill in full notes quickly

Fill notes digit by digit, not square by square. Take the 1s: for each box, cross-hatch for 1 as you would for a hidden single, and write a small 1 in every square that survives. Then the 2s, and so on. This is quicker than staring at each square in turn and asking which of nine digits fit, and you will often find a hidden single on the way, because a digit with one surviving square is simply placed.

Partial notes and the two-square rule

Partial notes mean writing only the candidates most likely to lead somewhere. The best-known style is to mark a digit in a box only when it has exactly two possible squares there. Many solvers call this Snyder notation, after Thomas Snyder, who won the World Sudoku Championship in 2007, 2008 and 2011 (Wikipedia: Thomas Snyder).

Look back at the table. In the two-square style the box shows four marks:

4 in R7C4 and R7C6: both in row 7, so the box's 4 is in row 7. That is pointing: no other square in row 7 can be 4.
1 in R7C6 and R9C5.
6 in R7C6 and R8C6: both in column 6, so no other square in column 6 can be 6.
8 in R9C4 and R9C5: both in row 9, so 8 is out of the rest of row 9.

That is 8 small digits instead of the 23 in the full notes, and every mark is useful: when one of the two squares is ruled out, the other is solved. Marks that line up give pointing for free. Two digits marked in the same two squares are a hidden pair, explained in naked and hidden pairs.

What the two-square style misses is just as clear: it shows nothing in R8C5, the square that was already solved. Partial notes find hidden singles and pointing; they do not show naked singles or naked pairs. That is the trade.

Style	What you write	Good at finding	Misses
No notes	Nothing	Full houses, hidden singles by cross-hatching	Anything that needs memory
Two-square marks	A digit with exactly two spots in a box, in both spots	Hidden singles, pointing, hidden pairs	Naked singles, naked pairs, most advanced patterns
Full notes	Every candidate in every square	Everything on the technique ladder	Nothing, but slow to set up and easy to let go stale

Many solvers combine them: two-square marks for most of the solve, then full notes for the last stubborn part, or for one digit when they are looking for an X-Wing.

Corner marks and centre marks

Some apps and many online puzzle tools offer two kinds of pencil mark. Corner marks are small digits placed around the edge of a square; centre marks are small digits in the middle. SudokuPad, a browser-based solver, has both as separate modes, with Shift plus a digit for a corner mark and Ctrl plus a digit for a centre mark (SudokuPad).

A common convention gives each its own meaning:

Corner marks say where a digit can go in a box: "the 4 in this box is in one of these squares". They are the natural home for two-square marks.
Centre marks say what a square can be: "this square is 3 or 9". They are the natural home for full notes on a square, and for naked pairs.

Keeping the two meanings apart lets you read the grid at a glance. A square with corner marks 1, 4 and 6 is not limited to those digits; a square with centre marks 1, 4 and 6 is. If an app offers only one notes mode, treat every note as a centre mark, a full list of what the square can be, and keep two-square marks for paper.

When notes waste time

Notes are a tool, and on some grids they cost more than they save. Leave them out:

On easy grids. An easy 6x6 or 9x9 sudoku can usually be solved with full houses, hidden singles and naked singles. Writing notes for every square takes longer than just solving. Puzzle Picnic's Easy and Medium levels, for example, are 6x6 grids solvable with singles.
At the start of a hard grid. The first few minutes of most grids are hidden singles. Cross-hatch digit by digit first, and only start notes when a full pass finds nothing.
In squares you will not use. If you are working on one box, note that box. Notes in the far corner of the grid will be out of date by the time you look at them.

And use them when:

A full cross-hatching pass of all nine digits finds nothing.
You are about to look for pairs, triples, fish or wings.
You want to stop and come back later.

Keeping notes tidy and correct

Notes are only useful while they are true, and a stale note is one of the easiest ways to break a sudoku. One rule covers most of it: every time you place a digit, erase it from the notes of every square in its row, its column and its box. Do it straight away, before you look for the next move.

Habits that keep notes honest:

Note only what you have checked. A note you are not sure of is worse than no note, because you will trust it later.
Never note a guess. Notes are facts about the grid, not possibilities you are exploring.
Write digits in fixed places. On paper, put each digit in the same spot in every square, 1 top left to 9 bottom right, like a phone keypad. A gap then shows at a glance which digit is missing.
Recheck a square before you rely on it. Before a pair or an X-Wing, glance along the row, column and box of each square in the pattern.
If a square runs out of candidates, stop. Something is wrong. Go back to the last move you are sure of rather than patching forward.

Frequently asked questions

Are pencil marks cheating in sudoku?

No. Pencil marks only record what you have already worked out; they do not tell you anything new. Competitive solvers use them, and most sudoku apps include a notes mode for exactly that reason.

Should I write every candidate in every square?

Only when you need to. Full notes are slow to set up but necessary for pairs, X-Wings and other advanced techniques. For most of a solve, cross-hatching plus two-square marks is faster. A good rule: start without notes, switch to two-square marks when singles dry up, and fill in full notes only for the part of the grid where you are stuck.

What is Snyder notation?

It is the name many solvers give to the habit of marking a digit in a box only when it has exactly two possible squares there, and marking both. It is named after Thomas Snyder, a three-time World Sudoku Champion. It finds hidden singles and pointing quickly but does not show naked singles.

What is the difference between corner and centre marks?

In tools that offer both, corner marks usually say where a digit can go within a box, and centre marks say which digits a square can still be. A square with centre marks 3 and 9 must be 3 or 9; a square with corner marks 3 and 9 might still be something else.

Your notes routine

A routine you can use on any 9x9 grid:

Cross-hatch all nine digits with no notes. Place every single you find.
When a full pass finds nothing, add two-square marks box by box.
When those stop helping, fill in full notes for the busiest box or row, digit by digit.
Look for naked and hidden pairs in those notes, then for fish such as the X-Wing and Swordfish.
Every time you place a digit, clean its row, column and box.

If you are still learning the rules, start with how to play sudoku. To practise taking notes, the Hard and Expert levels of Puzzle Picnic's sudoku are classic 9x9 grids where notes start to pay off, and a hint explains the next logical step when you are stuck. More guides are on the sudoku topic page.