Candidate notes record which digits remain possible in each empty cell under the puzzle's stated row, column, and region constraints. This guide assumes a conventional 9 by 9 Sudoku with digits 1 through 9 appearing once in each row, column, and 3 by 3 box. Those puzzle constraints are not FIDE or Pagat rules, and neither approved reference governs Sudoku.
Who this is for: Sudoku solvers who want auditable pencil marks and deductions instead of untracked guessing or pattern assumptions.
- For Sudoku candidate notes, separate binding rules from practical principles, software conventions, and optional training methods before making a decision.
- Choose an empty cell or a missing digit in a unit, calculate its candidates from all three peer groups, and write only supported digits. After a placement, remove that digit from every peer and rescan affected rows, columns, and boxes before moving elsewhere. Record the position, information, or assumptions so the reasoning can be checked instead of reconstructed from memory.
- Candidate notes can be incomplete, stale, or copied incorrectly. A contradiction may reveal an earlier note or placement error rather than prove the original puzzle invalid. This guide does not claim a solving percentage, universal technique order, or completion timeline. Treat every numeric score, resource count, or probability in this guide as hypothetical unless it comes directly from the stated position or calculation.
Define the problem precisely
Read the puzzle's own instructions because variants add or change constraints. For conventional Sudoku, a candidate belongs in a cell only if the digit is absent from that cell's row, column, and box. Given clues remain fixed; candidate notes are provisional records, not placements.
Derive candidates by elimination and keep the set complete enough for the technique used. A naked single has one candidate in a cell. A hidden single is a digit that can occupy only one cell within a unit even when that cell has other written candidates. Both require current notes.
Use a repeatable process
Choose an empty cell or a missing digit in a unit, calculate its candidates from all three peer groups, and write only supported digits. After a placement, remove that digit from every peer and rescan affected rows, columns, and boxes before moving elsewhere.
Place a digit only when the current constraints force it or when using an explicitly labeled hypothesis method. If no forced move appears, check note accuracy and search for pairs, intersections, or other justified structures rather than selecting the most plausible-looking candidate.
Know what the result means
Candidate notes can be incomplete, stale, or copied incorrectly. A contradiction may reveal an earlier note or placement error rather than prove the original puzzle invalid. This guide does not claim a solving percentage, universal technique order, or completion timeline.
Puzzle rules define valid completions. Candidate sets represent current logical possibilities. Constraint propagation removes values forced out by assignments. Optional pencil-mark styles and hypothesis testing are training or solving methods, not extra rules of Sudoku.
Review and transfer the skill
When stuck or contradicted, return to the last verified placement and recompute affected candidates from the fixed clues. Mark the deduction type beside each placement if training explanation is the goal. Do not erase the evidence that identifies the first unsupported step.
Accurate domains and incremental updates apply to many constraint puzzles. The exact peers and allowed values change with the puzzle, so conventional Sudoku assumptions must not be imported into diagonal, irregular, killer, or other variants without instructions.
Worked example: Sudoku candidate notes
In a hypothetical conventional Sudoku cell r4c7, row 4 already contains 1, 2, 5, and 8; column 7 contains 3, 6, and 9; its box also contains 4. The listed digits cover 1 through 9 except 7.
- Start with the domain {1,2,3,4,5,6,7,8,9} for hypothetical cell r4c7.
- Remove 1, 2, 5, and 8 from the row, then remove 3, 6, and 9 from the column.
- Remove 4 because it is already in the cell's 3 by 3 box, leaving only candidate 7.
- Place 7 as a naked single and remove 7 from candidate notes in all peers of r4c7.
Sudoku candidate notes worksheet
Use this reusable record to make the evidence and decisions behind Sudoku candidate notes visible for later review.
- Puzzle variant, symbols, units, regions, extra constraints, and immutable givens.
- Cell coordinate, row exclusions, column exclusions, region exclusions, and remaining candidates.
- Deduction type, exact supporting unit or peers, placement, and affected cells.
- Candidate removals after each placement and units scheduled for a fresh scan.
- Contradiction found, earliest unsupported step, restored state, and corrected deduction.
Common mistakes
- Treating a candidate as a confirmed digit because it looks likely or appears in a familiar visual pattern.
- Placing a single and failing to remove that digit from every row, column, and box peer.
- Assuming conventional Sudoku constraints govern a variant without reading its additional or altered rules.
Try one
A cell has candidates {2,5}, but digit 5 can appear nowhere else in that cell's row. What justifies placing 5?
Digit 5 is a hidden single in that row because only this cell can contain it under the current candidates. Verify all row candidates and the cell's column and box constraints, then place 5 and update every peer.
Sources
- Chess Programming Wiki: SearchA technical index of game-tree search methods used in chess programming and related engines.
- Pagat card game referenceA reference collection for card games and some related traditional games; it does not govern chess, modern proprietary board games, Sudoku, or escape-room safety.