What are candidates in Sudoku?
Candidates are the numbers that could legally fill an empty square. Begin with 1 to 9, then remove every number already in its row, column or 3×3 box. A candidate is a possibility, not a promise that the number belongs there.
Use the three checks together. A number absent from the row can still be ruled out by the column. In the practice grid below, rows run left to right and columns run top to bottom; both are numbered 1 to 9.
Technique 1: find a naked single
A naked single is an empty square with exactly one candidate. Look at row 1, column 6, marked with a question mark in the grid.
- Row 1 is missing 5, 8 and 9.
- Column 6 already contains 8, so 8 is ruled out. It also contains 5, so 5 is ruled out.
- The top-middle box allows 9. The row, column and box therefore agree: place 9 in row 1, column 6.
You did not need to try a number and hope. Every alternative was eliminated by something already on the board.
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 7 | – | 2 | 3 | 1 | ? | 6 | 4 | – |
| 2 | 5 | – | 4 | 7 | – | 8 | 9 | – | – |
| 3 | – | – | – | – | 4 | – | 8 | 2 | 7 |
| 4 | – | – | – | – | 7 | – | 2 | – | – |
| 5 | 9 | – | – | – | – | – | 4 | – | 8 |
| 6 | 8 | 4 | 7 | – | – | 2 | – | 5 | – |
| 7 | – | – | – | – | – | – | – | 6 | – |
| 8 | 1 | – | 6 | – | 8 | 5 | – | – | – |
| 9 | 2 | 7 | – | 1 | – | – | 5 | 8 | – |
What should you do after every placement?
- Check the three affected groups. A new number changes its row, column and box. Remove that number from notes in those groups.
- Scan nearly complete groups. A row with one blank is a useful starting point, but always check its column and box before entering the answer.
- Scan one number across boxes. Pick a number and use the rows and columns already containing it to rule out squares in another box.
- Repeat before learning more techniques. Several easy placements can unlock one another. After a move, an old group may have a new single.
What if singles stop working?
First check whether a note is missing or an old candidate should have been removed. If there are genuinely no singles, the puzzle may need another technique, such as pairs or interactions between a box and a row. Singles are a starting method, not a guarantee that every Sudoku can be finished this way.
Avoid treating repeated wrong entries as a solving strategy. In our game a wrong answer costs one of three hearts. Use Notes to keep possibilities separate from confirmed numbers, and try an Easy puzzle while learning.
Practise in our Sudoku game
Our Sudoku has Easy, Medium and Hard puzzles, Notes and a daily puzzle. The teaching board above is a separate worked example; opening the game starts its own puzzle.
Open Sudoku, choose Easy and look for one justified placement before you touch the number buttons. For offline play, the Android app includes the game; browser play needs a connection to load.
Questions
- Do I need maths to solve Sudoku? You need logical elimination rather than arithmetic. The digits are labels: each must appear once in every row, column and box.
- Can a square have several candidates? Yes. Keep them as notes until another placement or a stronger deduction removes the alternatives.
- Should beginners guess? For these techniques, place a number only when you can explain why it is forced. If you get stuck, review the notes or choose an easier puzzle.
