Volodymyr Sakhan  ·  March 26, 2026  ·  Updated March 29, 2026

Notes — also called pencil marks or candidates — are small numbers written inside an empty cell to record every digit that could legally go there. A digit is a valid candidate if it does not already appear in the cell's row, column, or 3×3 box.

Pencil marks transform the puzzle from a visual scan into a structured elimination game. Once candidates are written in, patterns like naked singles, hidden singles, and naked pairs become visible at a glance. Enable Notes mode with the pencil icon in the OnSudoku app to start using them.

How to write candidates for a cell

For each empty cell, check its row, column, and box. Any digit already present in those three groups cannot go in that cell. Whatever digits remain are the candidates — write them as small marks inside the cell.

• Look at the cell's row — cross off every digit that already appears there.
• Look at the cell's column — cross off any additional digits found there.
• Look at the cell's 3×3 box — cross off any remaining digits found there.

Whatever digits are not crossed off are the candidates. Write them as small marks in the cell. By checking just three groups — row, column, box — you can always determine exactly which digits are still possible.

When to start using pencil marks

Not every puzzle requires notes from the start. A good rule of thumb:

• Easy puzzles — work through Last Free Cell, Last Remaining Cell, and Last Possible Number first. Notes are usually not needed.
• Medium and hard puzzles — switch to notes as soon as you cannot find any direct placement by eye.
• Expert puzzles — fill in full pencil marks for every empty cell before looking for patterns.

Example: finding candidates for cell E5

Cell E5 is empty. To find its candidates, check which digits are already placed in its row, column, and box.

Work through the three constraint groups one by one:

1. Row 5 contains 1, 6, 5, 4, 2, 8, 9 — seven digits are already ruled out.
2. Column E adds no new eliminations — all its digits are already in the row.
3. The center box (rows 4–6, cols D–F) contains 8, 1, 4, 2, 9 — again no new eliminations.
4. Digits 3 and 7 are the only ones absent from all three groups.
5. Write 3 and 7 as small marks inside E5 — those are its candidates.

The blue cells are the constraints that eliminate candidates. The green cell is where you write the surviving candidates: {3, 7}.

Reading candidates to find a placement

Once candidates are filled in, look for any cell that has only one candidate left — that digit must go there. This is called a naked single.

1. Box 1 (top-left) already contains 6, 9, 2, 4, 5, 8, 1, 3 — eight of nine digits placed.
2. Row 3 is also nearly complete, covering the same set of digits in the other eight cells.
3. Column A contains no 7 anywhere.
4. The only digit missing from all three constraint groups is 7.
5. Write 7 as the sole candidate in A3 — this cell is solved.

When a cell's candidates reduce to exactly one number, you have found a naked single — place it immediately.

Updating candidates after a placement

Every time you place a digit, erase it as a candidate from every other empty cell in the same row, column, and box. This cascading elimination often triggers further placements.

• When you confirm a digit for a cell, remove it from candidates in its row, column, and box.
• This can create new naked singles in those groups, which you then place — triggering another round of eliminations.
• Always update candidates immediately after each placement to keep the board current.

In the OnSudoku app, Notes mode updates candidates automatically when you place a digit — so the board always reflects the current state.

Full pencil marks vs. selective notes

There are two approaches to using pencil marks — choose the one that fits your solving style.

• Full pencil marks — fill in candidates for every empty cell before solving. Gives a complete picture and is recommended for beginners learning patterns like naked pairs and hidden singles.
• Selective notes — only annotate cells you are actively analyzing. Faster to start but risks missing patterns in other parts of the grid.

Tip: use a consistent layout for your marks — write 1–3 in the top row of the mini-marks, 4–6 in the middle, 7–9 at the bottom. A uniform layout makes patterns like naked pairs much easier to spot.

Practice with pencil marks

The best way to get comfortable with pencil marks is to use them on real puzzles. Start with an easy puzzle and try filling in candidates for just a few cells — you will quickly see how constraints narrow the options.

Pencil marks are the essential foundation for all advanced sudoku techniques. Once you are comfortable writing and updating candidates, you will be ready to tackle naked pairs, hidden singles, and beyond.