A candidate is a digit that has not been ruled out for an empty cell. Pencil notes make those possibilities visible so you can compare cells without repeatedly doing the same mental work. Good notes support deductions; incomplete or stale notes can suggest a move that has no valid proof.
Calculate the basic candidate set
Begin with digits 1–9. Remove every digit already placed in the cell’s row, column and 3 × 3 box. Use all three groups, including their filled cells beyond the immediate neighbors. Each digit left is a basic candidate: it respects the current placed numbers, but might still be eliminated by a later logical deduction.
Do not eliminate a candidate simply because another empty cell has that digit written as a note. Several cells can allow the same digit. Notes are possibilities, not placed numbers, and choosing one arbitrarily does not make it correct.
A two-candidate cell, step by step
This original teaching example is separate from Daily puzzles. Row 1 starts with two blanks followed by 3–9. Focus on the first blank, r1c1. Its column, in rows 2–9, contains 4, 7, an empty cell, 5, 8, 3, 6 and 9. The top-left box contains the two row-1 blanks and the placed digits 3–9.
- Check the row. Digits 3–9 are present, leaving 1 and 2.
- Check the column. Its placed digits are 3–9 as well. Neither 1 nor 2 is blocked.
- Check the box. It also contains 3–9, so both possibilities remain legal.
- Write both notes. The complete basic candidate set for r1c1 is {1, 2}. This calculation does not prove either digit belongs there.
The givens are compatible with a completed Sudoku. For example, rows of the completion can start 1–9, 4–9 then 1–3, and 7–9 then 1–6, with the usual shifted rows continuing below. The example’s point is to calculate possibilities, not to certify a unique puzzle or reveal a Daily answer.
Update notes after a confirmed placement
Suppose a separate, valid deduction later proves that r4c1 is 2. That proof is an assumption for this update example, not something the row diagram establishes. Because r4c1 shares column 1 with r1c1, remove 2 from r1c1’s notes. Its list is now {1}, giving a naked single.
For each confirmed placement, review the empty cells in its row, column and box. Remove the placed digit from their notes; do not remove it from unrelated cells. Also check for a hidden single: a missing digit might now have only one possible location in a group even if that cell has other notes.
If you have used more advanced logic to eliminate a candidate, a fresh row-column-box calculation may include it again. Preserve the reason for that logical elimination. Distinguish a complete basic candidate list from a smaller list that has been reduced by proven deductions.
Use Notes in Puzzuno
Select an empty cell, turn Notes on, and enter its possibilities. Turn Notes off before placing a confirmed number. Puzzuno records the notes you enter; it does not automatically fill every cell with a complete candidate set. Placing a number clears that cell’s notes and removes the same candidate from other cells sharing its row, column or box. Undo restores those notes along with the previous number.
Automatic removal cannot repair an omitted candidate or an earlier mistaken assumption. If you change an entry directly, revisit affected notes: removing an old number can make possibilities legal again. See the Sudoku How to Play guide for Notes, keyboard controls and Undo.
A manageable note-taking routine
- Start with a crowded row, column or box and calculate the complete candidates of its empty cells.
- Use notes where memory is becoming unreliable; you do not need to annotate the entire board before making an obvious deduction.
- Before treating a lone note as a forced answer, check that you have not omitted another legal candidate.
- After placing a number, inspect the affected groups for new singles and update their notes.
- If you return after a break, verify a few important lists before building a deduction on them.
Common mistakes
- Writing only a favorite digit. One written note is not proof that other digits are impossible.
- Forgetting the box. A digit can be absent from a row and column but still blocked by its 3 × 3 box.
- Using notes as blockers. Only placed digits, or a valid logical argument, justify eliminating possibilities.
- Keeping notes after changing assumptions. A corrected entry may require restoring candidates as well as deleting them.
- Ignoring an empty list. Zero legal candidates signals a contradiction in the entries or reasoning. Review the board instead of guessing a number.
Frequently asked questions
Does a candidate mean the digit occurs in a solution?
No. A basic candidate merely passes the immediate row, column and box checks. It may lead to a contradiction once more constraints are considered.
Should every cell have pencil notes?
Not necessarily. Complete lists in the area you are analyzing may be enough. Be especially careful with hidden singles: checking where a digit can go requires considering every empty cell in the chosen group, not just annotated cells.
Are two candidates a reason to guess?
No. They tell you the cell is unresolved. Look elsewhere or use another deduction before committing.
Practice making one list complete
Open Sudoku practice, choose an empty cell, and explain each digit you exclude. Then use the list to look for a single. Visit Daily Challenges when you want to try the routine on a shared puzzle.