Sudoku candidates
A Sudoku candidate is a digit not ruled out for an empty cell. To make basic pencil marks, start with 1–9 and remove every digit already present in that cell’s row, column or 3 × 3 box. A candidate is a possibility, not a promise that the whole puzzle can be completed with it.
The worked example
Coordinates start at the top left: r = row, c = column. Small digits are candidates; outlined cells are discussed below.
Check this exampleView puzzle text
Read left to right across each row, then top to bottom. A 0 means a blank.
003056789056789123789023456234567891567891234891234567345678912678912345902345678Find the candidates for r1c1
Coordinates count from the top left: r1c1 means row 1, column 1. A box is one of the nine regions bounded by the thicker lines. In this teaching position, row 1 has three empty cells. Do not fill any of them just because a digit is missing from the row.
| Constraint | Digits already present | Still possible for r1c1 |
|---|---|---|
| Start | None considered yet | 1, 2, 3, 4, 5, 6, 7, 8, 9 |
| Row 1 | 3, 5, 6, 7, 8, 9 | 1, 2, 4 |
| Column 1 | 7, 2, 5, 8, 3, 6, 9 | 1, 4 |
| Top-left box | 3, 5, 6, 7, 8, 9 | 1, 4 |
Use fixed positions for small digits
Place candidates in a miniature 3 × 3 layout: 1–3 across the top, 4–6 in the middle, and 7–9 along the bottom. In r1c1, the 1 belongs at the top left and the 4 at the middle left. Keeping this layout consistent makes repeated possibilities easier to spot.
Write all basic candidates while learning. A note containing only one digit is useful evidence only if you have systematically checked the alternatives. If you use a shorthand such as noting only two possible positions in a box, an unmarked cell does not mean that no candidate fits there.
Why 4 is legal here but still wrong
At first, writing 4 in r1c1 would create no immediate duplicate. That is all the basic candidate calculation establishes. Look one row down: r2c1 is the only empty cell in row 2, so it must be 4. That placement removes 4 from r1c1, leaving 1.
A conflict check finds repeated digits. A solution check determines whether the whole grid can be completed.
Step 1. Before making a move, confirm that its supporting entries are givens or proven placements.
Step 2. Place r2c1 = 4 because row 2 contains every other digit.
Step 3. Remove 4 from the notes of every empty cell sharing row 2, column 1 or the top-left box.
Step 4. Recheck r1c1. Its only remaining candidate is 1, so that placement is now justified.
Keep notes accurate
Keep placed digits and notes visually distinct. A large 4 claims an answer; a small 4 records a possibility. After undoing a placement, rebuild any notes you removed because of it. Otherwise an old elimination can create a false single.
More advanced techniques can remove candidates that pass the three basic constraints. If you have made such a deduction, record its reason. Recomputing only the basic candidates will add that digit back; this does not invalidate the deduction, but it loses the work you already proved.
Check your understanding
Before placing anything, can r1c2 contain 1? Does that make 1 the answer?
Show the reasoning
Its basic candidates are 1 and 2, so 1 is locally allowed. But column 2 already contains every digit except 1 and 2, and r9c2 is forced to be 1 by row 9. Therefore r1c2 must eventually be 2. A candidate list is the beginning of the reasoning, not the end.
About this example
This teaching board keeps many givens to make the deduction clear and has no difficulty rating. Diagnosis examples deliberately include the stated conflicts or ambiguity.
Rules and terminology
- Nikoli: Sudoku rules
The standard row, column and 3 × 3 box rules used in these examples. The board and worked explanation on this page were created separately.
- Andrew Stuart: Naked Candidates
Established terminology for naked singles and their relationship to hidden singles. The board and worked explanation on this page were created separately.