Sudoku pencil marks: how to use notation properly

1 September 2026 · 7 min read

Pencil marks are the small candidate digits you write into empty cells. Every technique past singles is really a statement about them, so notation is not an optional aid for the careful — past a certain difficulty it is the game.

It is also where most people go wrong, in two opposite directions: marking everything immediately and drowning, or marking nothing and stalling.

What marks are for

A mark is a claim: “this digit is still legal here”. It is not a guess, a preference, or a note-to-self. That precision is what makes marks usable — a naked pair only proves anything if the two cells really do have exactly two legal digits each.

Below is row 8 of a real puzzle with its candidates written in. Two cells hold exactly {5, 7}, and that fact — visible only because the marks are there — eliminates 5 and 7 from the rest of the row.

When to start

The right trigger is behavioural, not a difficulty label: start marking the first time you go all the way round the grid and place nothing.

Before that point, scanning is faster. Marking up a grid takes several minutes and an easy puzzle will be finished before that investment repays itself. After that point, you are looking for patterns your head cannot hold, and no amount of staring will help.

In practice, for the four difficulties on this site:

• Easy — never. Naked singles alone finish these, and a naked single is visible without notation.
• Medium — rarely, and then only in the unit you are stuck on.
• Hard — yes, but not at the start. Scan first, mark when scanning stops paying.
• Expert — yes, and expect to need complete marks, because the patterns these require cannot be seen without them.

How much to write down

There are three approaches, and the middle one is right for most people.

Full marking

Every candidate in every empty cell. Techniques become mechanical — a naked single is a cell with one mark, a hidden single is a digit appearing once in a unit. The cost is the setup time and the upkeep: every digit you place means editing up to 20 cells.

Partial marking (recommended)

Mark only the cells with two or three candidates, and only in the units you are actively working. This is where the useful patterns live — pairs and triples are made of exactly these cells — and it keeps the grid readable.

Cells with six candidates tell you nothing and cost the most to maintain. Skip them until they narrow.

Single-digit marking

Pick one digit and mark every cell it could go in, ignoring all others. Excellent for hunting locked candidates and X-wings, both of which are single-digit patterns. Useless for pairs and triples, which are multi-digit. Worth doing as a targeted sweep rather than a general policy.

Keeping marks honest

A stale mark is worse than no mark, because you will act on it. This is the single largest source of wasted time in hard Sudoku, and the discipline is simple:

1. When you place a digit, immediately clear it from all its peers. Not “in a moment”. The row, the column and the box, right then. Interrupting this to chase the next placement is how marks rot.
2. Erase, don’t annotate. Crossing a candidate out but leaving it visible means re-reading it later and hesitating over whether the strike was yours.
3. Never mark a candidate you have not verified. A speculative mark and a proven one look identical thirty seconds later.
4. If you lose confidence, rebuild the unit from scratch. Recomputing the candidates for one row takes twenty seconds. Reasoning from marks you half-trust can waste twenty minutes and end in an unsolvable grid.

Doing this on paper is genuinely laborious, which is the main argument for solving on screen: this app maintains the consequences for you, keeps every note undoable, and makes an elimination reversible instead of a smudge.

Notes on this site

Notes mode writes pencil marks instead of a digit. Hold Shift with a number to add one without switching modes — worth learning, because switching back and forth is the friction that stops people marking at all. Ctrl/⌘ + Z undoes a note just like a placement, so trying an elimination out costs nothing.

Marks are deliberately not filled in for you, and not auto-cleared when you place a digit. Both would be easy to add, and both would remove the part of the puzzle that actually builds skill — deciding what is possible is the reasoning, not the bookkeeping. If you want the reasoning done instead, Explain next step shows you a real deduction and names it, which teaches the pattern rather than skipping it.

Two habits worth stealing

• Mark a unit, then immediately scan it. Do not mark the whole grid and then start looking. The act of writing candidates into one row is when you notice the pair in it — that attention is most of the value, and it evaporates if you mark for ten minutes first.
• After any elimination, re-sweep for singles before doing anything else. Eliminations exist to create singles. A quick single sweep after each one is what turns a technique into progress instead of a footnote.

Every diagram on this page is a real position from a generated puzzle, and every elimination shown is checked against that puzzle’s unique solution as part of the test suite. Want a move explained on your own board? Play a puzzle.