Pencil marks are small notations used to track which digits are still possible in each cell, unlocking intermediate and advanced strategies.
Pencil marks are small numbers written inside Sudoku cells to indicate which digits could potentially be placed there. They represent the candidates for each cell - the digits that have not yet been eliminated by the row, column, and box constraints. On paper, solvers write them lightly in pencil so they can be erased; in digital apps, there is usually a dedicated notes or pencil mark mode.
Pencil marks are purely a solver's tool and are not part of the puzzle itself. The puzzle designer provides only the givens; everything else, including pencil marks, is work done by the solver. For more solving tips, visit our Sudoku tips page.
To create pencil marks for a cell, check which digits from 1 through 9 are already present in that cell's row, column, and box. Any digit not found in any of these three groups is a valid candidate and should be noted. As you solve cells and apply techniques, update the pencil marks by removing eliminated candidates.
Pencil marks enable strategies like naked pairs, where you need to see that two cells share exactly the same two candidates. Without pencil marks, spotting these patterns is nearly impossible in complex puzzles. Accurate pencil marks are also key to getting faster at Sudoku.
Most solvers can handle easy puzzles without pencil marks, relying on crosshatching and mental tracking. The transition to pencil marks typically happens when you encounter medium-difficulty puzzles where basic scanning is no longer sufficient to make progress.
A good rule of thumb: if you find yourself stuck on a puzzle and cannot find any more digits through scanning alone, it is time to add pencil marks. Start by filling in candidates for the cells with the fewest possibilities, then expand to the rest of the grid. You do not always need to pencil mark every cell - strategic partial marking can be very effective.
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Pencil marks are small notations written in cells to track which candidates (possible digits) remain for that cell. They are a solving tool used by the solver, not part of the puzzle rules. Pencil marks are essential for applying intermediate and advanced solving techniques.
For easy puzzles, many solvers can work without pencil marks using mental tracking and crosshatching. However, for medium and harder puzzles, pencil marks become essential. Most intermediate strategies like naked pairs and hidden singles require knowing the exact candidates in each cell.
The most common approach is to write small digits in a consistent grid pattern within each cell. Many solvers place candidates in positions corresponding to a 3x3 mini-grid: 1 in the top-left, 2 in the top-center, 3 in the top-right, and so on. This makes it easy to scan for specific digits.
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