Naked single: the cell with only one possible digit

What is a naked single?

Every empty cell belongs to three units: its row, its column and its 3×3 box. Together these units contain 20 other cells, called the cell’s peers. Any digit that already appears among the peers cannot go in the cell, because sudoku forbids repeating a digit inside a row, column or box.

The digits that remain are the cell’s candidates. When a cell has exactly one candidate left, that candidate is called a naked single. It is “naked” because it is visible from the cell itself: you do not need to compare it with other cells, you only need to look at what surrounds it.

Why it always works

A valid sudoku has exactly one solution, and in that solution every cell holds some digit from 1 to 9. If eight digits are ruled out by the peers, no other digit is legal in that cell, so the remaining one is forced. There is no guessing involved: a naked single is a certainty, and you can fill it in ink. That is also why Quietdoku’s Easy puzzles can be solved using only naked singles and hidden singles.

How to find naked singles

Start with the busiest areas. A row, column or box that already has six or seven digits leaves few options for its empty cells, so naked singles tend to appear there first. Pick an empty cell in such an area and count the distinct digits in its row, column and box together.

Count digits, not cells. The same digit can appear in both the row and the box, so it only counts once. A practical method is to run through 1 to 9 in order and ask for each digit whether it appears among the peers. If you reach the end with exactly one digit unaccounted for, you have found a naked single.

On harder puzzles, write pencil marks: small candidates in every empty cell. Then a naked single is simply a cell with one pencil mark left. Every time you place a digit, remove it from the pencil marks of its peers, because that is exactly how new naked singles appear.

Worked example

In the example board, look at R4C1 (row 4, column 1), the cell marked with the gold digit. Its row already contains 3, 1, 4, 7 and 5, in R4C2, R4C5, R4C6, R4C7 and R4C8. Its column adds 9 in R3C1, 7 in R5C1 and 6 in R6C1. Its box, the middle-left box, adds 4 in R5C2 and 2 in R6C3. These are the highlighted cells.

Collecting the distinct digits gives 1, 2, 3, 4, 5, 6, 7 and 9. Only 8 is missing, so R4C1 must be 8. Notice that 7 and 4 each appear twice among the peers; that does not matter, each digit only needs to appear once to be ruled out.

This naked single is not a hidden single: in row 4, 8 could also go in R4C3, R4C4 or R4C9, and in column 1 it could also go in R7C1, R8C1 or R9C1. You can only find it by looking at the cell itself. It is also the only naked single on this board right now, which is typical of real puzzles: the next step is often one specific cell, not many.

Common mistakes

Checking only the row and column. Forgetting the box is the most frequent error. Many naked singles depend on one or two digits that appear only inside the 3×3 box, as 2 does in the example.

Counting cells instead of digits. If a digit appears in both the row and the box, it is still only one digit ruled out. Counting it twice makes a cell look solved when it still has two candidates.

Stale pencil marks. If you keep candidates but forget to erase a digit after placing it nearby, a real naked single stays hidden behind an outdated mark. Update the peers every time you fill a cell.

When to use it and what comes next

Look for naked singles after every placement, because each new digit removes candidates from 20 peers. On easy puzzles you can alternate naked singles and hidden singles until the grid is full.

When no cell has a single candidate left, move on to hidden singles, which look at a digit instead of a cell. After that come locked candidates and naked pairs, which remove candidates so that new naked singles appear. If you get stuck, a Quietdoku hint shows the next logical step and names the technique it uses.