How to Count Candidates in a Sudoku Cell
Counting candidates in a Sudoku cell is the process of identifying which digits from 1 to 9 can legally be placed in an empty square. A candidate is any digit that is not already present in that cell's row, column, or 3x3 box. This foundational skill is critical for applying solving techniques like [Naked Singles](/techniques/naked-singles) and [Hidden Singles](/techniques/hidden-singles). Accurate candidate counting prevents errors and is the first step in systematic [candidate elimination](/blog/sudoku-candidate-elimination). Most players get stuck because they miscount possible digits, which leads to incorrect placements and dead ends. This guide provides a reliable, step-by-step method for checking any cell.
What is a candidate in Sudoku?
In Sudoku, a candidate is a potential digit that could legally fill an empty cell. For a digit to be a candidate, it must not appear anywhere else in the cell's row, column, or 3x3 box. Candidates are the possible answers you note as pencil marks before making a final placement. Understanding this definition is key to all logical solving. The entire puzzle is solved by progressively eliminating candidates until only one remains for a cell, which then becomes a placed digit.
What is the fastest, most reliable way to check a cell?
The fastest reliable method is a systematic, unit-by-unit scan. First, look at the cell's row and note all digits already present. Next, scan its column. Finally, examine the 3x3 box that contains the cell. Mentally or on paper, track which digits from 1 to 9 you have seen. The digits you have *not* seen across these three units are the cell's candidates. This three-step scan ensures you never miss a constraint from any of the cell's governing units. Rushing this process by glancing at the whole area often causes players to overlook a digit in a crowded row or box.
- Always scan the row first, then the column, then the box for consistency.
- For speed, try saying the digits 1-9 in your head and marking each one as 'seen' or 'not seen' as you scan.
Why is counting the digits you *cannot* place safer than counting the ones you can?
Counting exclusions is safer because it directly follows the core rule of Sudoku: a digit cannot repeat in a row, column, or box. Your goal is to find digits that are *absent*. If you try to count which digits 'could' go in a cell, you risk accidentally including a digit that is already in a unit, which is a direct violation. The exclusion method is fail-safe. For example, if a cell's row contains 1, 3, and 9, its column contains 2 and 4, and its box contains 5 and 7, you immediately know that 6 and 8 are the only digits not excluded. This logical approach minimizes human error.
How do you keep candidate counts correct after every elimination?
To maintain accurate counts, you must update pencil marks immediately and completely after placing any digit. When you place a digit, it eliminates that digit as a candidate from every empty cell in the same row, column, and box. Go through each affected cell in those three units and remove the newly placed digit from its candidate list if it was present. This ongoing process of candidate elimination is what drives the puzzle forward. A common mistake is to place a digit and then look for the next obvious move without cleaning up the candidate landscape, which leads to missed Naked Singles.
How do you handle a cell with only one candidate?
A cell with only one remaining candidate is called a Naked Single. This is the simplest logical placement in Sudoku. Once you have correctly counted and eliminated all other digits from 1 to 8 for that cell, the 9th digit must be the solution. You can confidently place that digit in the cell. Finding Naked Singles relies entirely on perfect candidate tracking. In many puzzles, including the one provided for this article, a cascade of Naked Singles can solve a large portion of the grid once the candidate landscape is fully developed.
What are common mistakes in candidate counting?
The most frequent error is missing a digit that is already in the cell's row, column, or box, often because of a crowded unit or a quick visual scan. Another mistake is forgetting to check all three governing units—sometimes players check only the row and box but overlook the column. Incorrectly updating pencil marks after a placement is also a major source of error, as it corrupts all future logic. Finally, players sometimes confuse candidate counting with finding a Hidden Single, which requires looking at all candidates for a digit across a unit, not just the candidates for one cell.
- Double-check the column. It's the most commonly forgotten unit.
- If you get stuck, re-scan the candidates for a critical empty cell from scratch.
Key Facts
- ▪A Sudoku candidate is any digit from 1-9 that does not violate the puzzle's rules by appearing in the cell's row, column, or 3x3 box.
- ▪The fastest checking method is to scan the cell's row, then its column, then its 3x3 box, noting all digits already present.
- ▪Counting which digits are forbidden (the exclusion method) is more reliable than trying to list which digits might work.
- ▪You must update all pencil marks in a row, column, and box immediately after placing a new digit to keep candidate counts accurate.
- ▪A cell with only one possible candidate is called a Naked Single and can be placed immediately.
- ▪The most common counting mistake is overlooking a digit already in the cell's column during the initial scan.
- ▪Candidate counting is the essential first step for all advanced Sudoku solving techniques.
- ▪Accurate candidate lists, or pencil marks, are the foundation for systematic logical deduction in Sudoku.
Frequently Asked Questions
What is the difference between a candidate and a pencil mark?
A candidate is a possible digit for a cell. A pencil mark is the physical or digital notation of that candidate inside the cell. All pencil marks represent candidates, but the term 'candidate' refers to the logical possibility itself.
Should I write down all candidates for every cell at the start?
Not necessarily. Many solvers add candidates gradually as needed. Writing all candidates early (full notation) is safe but time-consuming. A hybrid approach is to add candidates only for cells that seem promising or after easier placements are done.
How can I practice counting candidates faster?
Practice the three-step scan (row, column, box) on empty cells without writing anything. Time yourself. The goal is to build a mental process that becomes automatic, reducing the need to double-check constantly.
What if I find two possible candidates for a cell?
That is normal. You note both as pencil marks. Solving progresses by using other techniques to eliminate one of them. A cell with two candidates is not solvable by itself; you need more information from the grid.
Can a cell have zero candidates?
If you correctly follow the rules, a cell should never have zero possible candidates in a valid, solvable puzzle. Finding zero candidates means you made an earlier counting error or placed a digit incorrectly.
Is candidate counting the same as 'cross-hatching'?
They are related. Cross-hatching is a specific visual method for finding Hidden Singles by looking for where a single digit can go in a unit. Candidate counting is the broader process of listing all possible digits for a specific cell.