Naked Singles in Sudoku: How to Find Them Fast

A naked single is a cell where only one digit is still possible. Look at the cell's row, its column, and its 3x3 box. If eight different digits already appear across those three groups, the ninth digit is the only one left, and it goes in the cell. It is the first technique almost every solver learns, and on easy puzzles it does a large share of the work.

How a naked single works

Every cell sees 20 other cells: eight in its row, eight in its column, and four more in its box that are not already in the same row or column. The digits placed in those 20 cells are ruled out for the cell you are looking at. When the ruled-out set covers eight digits, one candidate remains.

Take the cell in row 5, column 5 (R5C5). Say row 5 contains 1, 3, and 8. Column 5 contains 2, 3, 6, and 9. The center box contains 4, 6, and 8. Combine them and you get 1, 2, 3, 4, 6, 8, and 9. That is seven digits, so R5C5 could be 5 or 7. Not a single yet. If a 7 turns up anywhere in row 5 later, the only candidate left is 5, and R5C5 becomes a naked single.

The word "naked" means the answer is visible from the cell itself. You only have to look at one cell and its three groups. That is the difference from a hidden single, where you look at one digit across a whole row, column, or box.

Full house: the easiest naked single

A full house (also called the last remaining cell) is a row, column, or box with exactly one empty cell. Eight digits are placed, so the missing one goes in the gap. You do not need to check anything else. Full houses are the fastest placements on the board, and good solvers grab them the moment a group reaches eight.

A full house is technically both a naked single and a hidden single, which is why most solving guides list it separately. Our full house guide covers how to spot them at a glance.

How to find naked singles quickly

Start with the busiest cells

A naked single needs eight digits in the cell's combined row, column, and box. Cells sitting where a crowded row crosses a crowded column are the likeliest candidates. Before counting anything, glance for rows and columns with six or more digits, then check the empty cells where they meet.

Count what is missing, not what is there

Counting eight present digits is slow. Instead, pick the group with the most digits (usually the row or column) and list what it is missing. If a row is missing 2, 5, and 7, you only need to check those three digits against the cell's column and box. When two of them are ruled out, you have your single.

Recheck after every placement

Each digit you place removes a candidate from up to 20 cells. The cells in the same row, column, and box as your last placement are where new naked singles appear. Checking those first is much faster than rescanning the whole grid, and it is how solvers chain placements together on easy puzzles.

Naked singles with pencil marks

On harder puzzles you will fill in pencil marks (the small candidate digits in each cell). With full marks, a naked single is any cell showing a single candidate. The catch is that marks go stale: when you place a digit, you have to remove it from every cell that sees it. A missed removal hides a naked single, or worse, makes you think one exists when it does not.

A good app removes the stale marks for you. When you place a digit in Sudoku Royale, that digit is cleared from the notes of every cell in the same row, column, and box, so a naked single shows up as a cell with one small digit left.

Naked single vs hidden single

Both techniques place one digit in one cell. They differ in what you look at.

• Naked single: fix one cell, check all nine digits. "This cell can only be 5."
• Hidden single: fix one digit, check every cell of one group. "In this box, 5 can only go here."

Hidden singles usually show up earlier and more often in a fresh puzzle, because most cells still have several candidates. Naked singles take over later, when the grid is crowded. You need both, and switching between them is most of what solving an easy or medium puzzle looks like. The full order of techniques is in our sudoku techniques guide.

Common mistakes

• Forgetting the box. Beginners often check the row and column and skip the box. A digit in the box rules out the cell just as firmly.
• Trusting old pencil marks. If your marks are out of date, a "single" candidate may be wrong. Recheck the three groups before you commit.
• Counting the same digit twice. A 3 in the row and a 3 in the column is still one digit. Count distinct digits, not placements.

What to learn next

Once naked singles feel automatic, learn hidden singles if you have not already, then move to pointing pairs and naked pairs. Those four techniques together solve most medium puzzles. For a start-to-finish method, read how to solve sudoku step by step.