Sudoku pencil marks: what to write and when to erase it

Sudoku pencil marks are possible digits for an empty cell. Start with 1 to 9, then remove every digit already present in that cell’s row, column or 3×3 box. Update the notes after each placement. A small digit means “still possible”, not “probably the answer”.

You can note one area at a time, but you must know whether a cell’s list is complete. A cell showing only 3 is a naked single only if you have checked that all eight other digits are impossible.

Enter candidates from the grid

In this original puzzle, inspect r4c3: row 4, column 3. The two outlined cells will let us practise both entering notes and removing one.

1. Row 4 contains 2, 1, 6 and 4. Cross these off 1 to 9.
2. Column 3 contains 9, 2, 5, 7 and 1. Cross those off too.
3. The middle-left box contains 2, 9, 5, 6 and 7. Check these as well.

Across all three units, the excluded digits are 1, 2, 4, 5, 6, 7 and 9. Write 3 and 8 in r4c3. Checking only the row would have left 3, 5, 7, 8 and 9, an incomplete check of the constraints.

Make a placement, then clean up

At r4c1, the row excludes 1, 2, 4 and 6; the column excludes 3, 6, 7 and 9; the box excludes 2, 5, 6, 7 and 9. Together they leave only 8. Enter a full-size 8 there and erase that cell’s notes.

Every empty cell sharing r4c1’s row, column or box must now lose 8 from its notes. Here r4c3 changes from 3,8 to just 3, so you can fill in 3 next. Do not erase 8 from an unrelated cell merely because you placed an 8 somewhere on the board.

Incomplete and stale notes are different problems

An omitted candidate can create a false single or false pair. An extra candidate can hide a genuine deduction. If a pattern seems suspiciously convenient, recompute its notes from the givens and your proven placements before using it.

Using notes in Puzzle Lantern

Select an empty cell, turn on pencil mode and tap a digit to add or remove that note. Turn pencil mode off before making a placement. The current app clears notes in the cell you fill; it does not automatically remove that digit from every peer’s notes. Keep checking the affected row, column and box yourself.

Marking one region is a useful place to start, but it is not enough for every technique. A naked pair uses a shared unit; pointing compares a box with a row or column; an X-wing spans two rows and two columns. Complete the relevant candidate information before drawing a conclusion.

Continue with naked versus hidden singles, then pointing versus naked pairs. For the broader solving order, see Sudoku tips when stuck. You can use these checks on a Daily or a More puzzles grid in Puzzle Lantern Sudoku.