Sudoku pencil marks: what to write when the next move is unclear
An empty square does not always need a number immediately. Sometimes it needs a short list of possibilities. Pencil marks help you keep that list visible while you work out what the puzzle permits.
A pencil mark means “this number has not been ruled out yet.” It is not a confirmed answer.
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |
|---|---|---|---|---|---|---|---|---|---|
| A | 1 | 6 | 3 | 2 | 5 | 4 | · | 8 | 9 |
| B | · | 5 | · | · | · | 9 | 4 | 6 | · |
| C | · | · | 9 | 7 | · | · | 3 | 5 | 2 |
| D | 7 | 3 | 1 | · | · | 8 | 9 | · | 5 |
| E | · | · | 6 | 1 | 2 | · | 8 | 7 | · |
| F | 5 | 2 | 8 | 9 | 7 | 3 | 1 | 4 | 6 |
| G | · | 1 | · | · | 9 | · | 2 | · | · |
| H | 9 | 7 | · | 8 | 3 | · | 5 | 1 | 4 |
| I | · | 8 | · | 4 | 1 | 2 | 6 | · | 7 |
Start with the right square
In this classic 9×9 example, rows A–I run from top to bottom. Columns 1–9 run from left to right. B1 means the second row, first column. Each box contains 3×3 squares.
Before adding notes to an empty square, check three things: its row, its column and its box. Any number already entered in one of those places cannot go in the square.
A worked example: why B1 needs two notes
In our example, row B is:
_ 5 _ _ _ 9 4 6 _
The missing numbers are 1, 2, 3, 7 and 8. That is the starting list, not the final list.
Column 1 already contains 1, 7, 5 and 9. This removes 1 and 7 from B1’s list, leaving 2, 3 and 8.
Now check the top-left box. Its entered numbers are 1, 6, 3, 5 and 9. The 3 is already present, so it cannot go in B1. The remaining candidates are 2 and 8.
Write small 2 and 8 notes in B1. Do not enter either as the answer yet: the checks allow both. A different deduction is needed to choose between them, and a simple move may exist elsewhere on the board.
Manual notes or Auto Pencil?
Manual notes let you practise those checks yourself. Turn on pencil-mark mode, select B1 and add 2 and 8 as notes. Return to normal number entry before placing a confirmed answer. Auto Pencil can help establish the candidates allowed by the current entries. In either case, review the notes against the board.
Auto Pencil is not a promise that the puzzle will solve itself. A list containing several candidates still needs reasoning. If your notes show no candidates for a square, pause and check for an incorrect entry or a missing note.
After placing a confirmed number, check the notes in its row, column and box again. Remove candidates that now conflict with that number.
When AI Coach finds no basic move
Treat that message as a prompt to review the available information, not as proof that the puzzle is impossible.
First, check your entries. Next, inspect the candidates. Look for a square with only one candidate, or a row, column or box where one number has only one possible position. These are different ways of narrowing the choice.
If neither is available, filling a complete set of notes may make the position easier to inspect, but it does not guarantee that the Coach will find another supported step. Some positions need a different technique. Repeatedly requesting the same analysis does not create a new deduction.
Try the checks yourself
Practise checking a square’s row, column and box in the browser starter edition:
https://smartpuzzles.github.io/play/sudoku/
It may resume your saved puzzle rather than open the example above. You can apply the same checks to any empty square.
For native app features and Coach access details, see Smart Sudoku:
https://smartpuzzles.github.io/sudoku/