How to use pencil marks
Pencil marks, also called notes or candidates, are small digits you write in an empty cell to record which numbers could still go there. Use them when scanning in your head stops being enough, which on this site is usually from Medium puzzles upward.
Fill them in once, keep them in step with the board as you place digits, and read patterns off them: a cell with one mark, a digit with one home in a row, or two cells sharing the same two marks.
What exactly is a pencil mark?
An empty cell is not a blank. At any moment some digits are still possible there and others are ruled out by the digits already in its row, column and box. Pencil marks are your written record of the possible ones. A cell with the marks 2, 4 and 7 is saying: “the answer is one of these three.” When a mark is crossed out, you have decided that digit cannot go in that cell.
In this game a cell holds either a value or a set of notes, never both. Entering a value clears that cell’s notes, and erasing a cell clears both. Notes mode is switched on with the Notes button or the N key. While it is on, tapping a digit toggles that digit as a note in the selected cell, so tapping the same digit twice adds it and then removes it. A screen reader announces such a cell along the lines of “row 3, column 5, empty, notes 2 4 7”.
When do you need them?
Not always. Easy puzzles are defined on this site as ones that need only naked singles and hidden singles, and both can be found by scanning without writing anything. The guided first puzzle is solved that way.
Medium is where marks start to pay off. Pointing pairs, box/line reduction and the pair techniques all work on candidates, so you cannot see them unless the candidates are visible. The technique-frequency data shows how common they are: in the committed sample of 1,000 classic Medium puzzles, pointing pairs were used by 952 and naked pairs by 285. See the frequency guide for the full table. If you are stuck on a Medium puzzle and have no notes on the board, writing them is the most useful thing you can do next.
Which style of marking should you use?
Players use two broad styles, and neither is the official one.
- Full marking. Write every possible candidate into every empty cell at the start, then cross marks out as the board fills. It takes longer up front, but all the information is in one place and every technique is available.
- Selective marking. Write marks only where they help: in cells that have two or three candidates, or in the one row, column or box you are working on. It is faster and keeps the board uncluttered, but you can miss a pattern that needed a mark you never wrote.
A reasonable approach is to begin without marks, place every single you can find, and switch to full marking when the singles run out. By then the board is more filled in, so each cell has fewer candidates and fewer marks to write.
How do the game’s notes tools work?
Auto-notes
The Auto-notes button fills the candidates for every empty cell in one step. For each cell, it starts with all the digits and removes every digit that already appears in a placed value in the cell’s row, column or box. What remains becomes the cell’s notes.
One detail catches people out. Auto-notes works only from the placed digits, and it sets every empty cell to exactly that result. If you have crossed out candidates by reasoning, for example with a pointing pair, pressing Auto-notes again puts them back, because the placed digits alone do not justify the removal. It is best used once, at the point where you decide to start marking, and not again after you have made eliminations. If you press it by accident, undo it.
Automatic removal when you place a digit
There is a setting called “Remove notes automatically when placing a digit”, and it is on by default. When you place a value, that digit is removed from the notes of every cell that shares a row, column or box with it. This does the most tedious clean-up for you. It does not add notes, and it only affects notes that already exist.
It has one consequence to remember. If you place a wrong digit, the game removes that digit’s correct notes from the neighbors. Undo restores them, because the removal is stored as part of the same step, so undoing a wrong placement puts both the cell and the notes back.
Undo, erase and hints
- Undo and redo cover notes as well as values, so a bad round of marking can be reversed one step at a time.
- Erase on a cell removes its value and all its notes. If you want to keep the notes and only change the value, enter the new value over the old one instead.
- Hints are computed from the placed digits and ignore your notes, so a hint cannot be confused by a mistake in your marking. If you accept a hint that is an elimination, the game applies it to the notes: a cell without notes first receives its full candidate set, and then the digit is removed, all as one undoable step.
How do you read patterns off the notes?
Once candidates are on the board, each technique has a recognizable look. The table below links what you see to the lesson that explains the deduction.
| What you see | Technique | What you do |
|---|---|---|
| A cell with exactly one mark | Naked single | Place that digit |
| A digit marked in only one cell of a row, column or box | Hidden single | Place that digit in that cell |
| Two cells in one house with the same two marks | Naked pair | Remove those two digits from the rest of the house |
| Two digits that each appear in only the same two cells of a house | Hidden pair | Remove all other marks from those two cells |
| A digit marked in one box only along a single row or column | Pointing pair | Remove that digit from the rest of the line |
| A digit marked in one line only inside a single box | Box/line reduction | Remove that digit from the rest of the box |
Scanning for these in a fixed order, singles first, matches how the site’s own solver works. The grading guide lists the order.
A small example of reading marks
This is a constructed illustration, not a position from a stored puzzle. Suppose four empty cells in one row carry these notes: the first cell has 2 5, the second has 2 5, the third has 2 5 7 and the fourth has 1 2 5 9. The first two cells carry the same two marks and nothing else, so together they use up the digits 2 and 5 between them. That is a naked pair. Neither the third nor the fourth cell can hold a 2 or a 5, so cross those marks out. The third cell is left with just 7, which is a naked single, and the fourth is left with 1 and 9.
Notice the order of events: you wrote down candidates, spotted two identical cells, removed marks, and then a single appeared. That sequence repeats through most Medium and Hard solves. The marks make the pair visible, and the removals produce a new single.
What habits keep notes trustworthy?
- Update after every placement. A mark for a digit that is already in the same row, column or box is wrong. Leave automatic removal on to handle this, and check that it has done so.
- Mark in a consistent place. Digits should always sit in the same position inside the cell, as on a phone keypad, so you can compare two cells at a glance.
- Re-check before a big deduction. Before acting on a pair, an X-Wing or any removal that deletes several marks, confirm that the marks involved match the board. One missing mark can make a pattern look valid when it is not.
- Remove, don’t overwrite. When you rule out a candidate, delete just that mark. Starting a cell’s notes again throws away reasoning you already did.
- Stop when a cell has no marks left. A cell with no candidates means something earlier was wrong. Use undo to go back and find it, rather than patching the cell.
What mistakes do notes cause?
- Notes mode left on. If you think you are entering values but notes mode is on, each digit you tap becomes a small mark. The button reads “Notes: on” when it is active, and the game announces the change, so check it when a tap does not behave as expected.
- Over-marking. Marking every cell on a crowded board produces a wall of digits that is hard to read. If the board is cluttered, switch to selective marking for the area you are working on.
- Stale marks after an elimination. Pressing Auto-notes after you have reasoned out removals restores the candidates you deleted, as described above.
- Trusting a wrong placement. A mistake in a value spreads into the notes through automatic removal. If candidates vanish that you expected to remain, look for a recent wrong digit.
What changes in expert mode?
The expert mode page describes a stricter setup: no hints, no auto-notes and no mistake feedback. Notes work, but you build and maintain them yourself, so the habits above matter more. A mistaken mark has no safety net, since the game will not flag it.
A simple practice plan
Try a Medium puzzle from the home page and place every single before you write any marks. When no single is left, switch to Notes, press Auto-notes once, and look for a pointing pair. Fix any pair or line you find, remove the marks it eliminates, and scan for new singles. The strategy guide for each difficulty describes what to learn at each level, the controls page lists the keys and settings, and the guides hub has the rest of the tutorials.