Naked single

Pick a cell and cross out every digit that cannot go there. Sometimes only one is left. That digit is the answer. In the end, every sudoku solve fills its cells this way.

Why it works

By the rule, a cell's digit cannot repeat any digit in its row, its column or its box. On a 9×9 board a cell touches 8 cells in its row, 8 in its column and 4 more in its box: 20 cells in all. If eight of the digits 1 to 9 are already among those 20 cells, the last digit is the only one that fits.

On a real board

This is the starting position of a 9×9 · Easy board. Let's find the digit for row 9, column 7.

1. Look at row 9. It already holds 2, 4 and 9. Cross those out.
2. Look at column 7. It adds 3 and 7.
3. Look at box 9. It adds 5, 6 and 8.
4. That is eight digits crossed out. Of 1 to 9, only 1 is left, so row 9, column 7 is 1.

The row alone or the column alone is not enough. Only all three together rule out eight digits. That is what this technique means by looking in three directions from one cell.

Finding them faster

• Start with cells where a full row meets a full column or box. If the row has seven digits and the column six, the cell where they cross is nearly decided.
• Count 1 to 9 in your head and tick off each one: “there, there, missing…”. You will not skip any. One missing digit and you are done.
• After filling a cell, look again at the other empty cells in that row, column and box. The digit you just placed often turns a neighbour into a naked single. Easy boards fall to this chain reaction alone.

Where you need it

Everywhere. 4×4 Tutorial, 6×6 Easy and 9×9 Easy boards were chosen to be solvable with naked singles alone, so start there if you are new. On 12×12 and 16×16 boards a cell touches 28 to 39 other cells, and pencil marks become more reliable than counting in your head.

When no naked single is left, turn the question around and look at digits instead of cells: that is the hidden single.