Naked Singles and Hidden Singles Explained

What a single is

A single is a cell where you can prove exactly one value belongs. Singles are the backbone of Sudoku. Most of the moves you make, even in hard puzzles, come down to finding one kind of single or another.

Naked singles

A naked single is a cell that has only one candidate left. You look at its row, column and box, cross off every value that already appears in them, and a single possibility remains. Because nothing else can fit, that value is the answer. Naked singles are easiest to see when you keep good notes, since the cell literally shows one mark.

To find them, scan for cells that are hemmed in by lots of filled neighbors. A nearly complete row that crosses a nearly complete box often creates a cell with just one option.

Hidden singles

A hidden single is trickier and more powerful. Here a cell might look like it could hold several values, but when you check a whole group, one value has nowhere else to go. Pick a value, look across a single box, and rule out every cell that already sees that value in its row or column. If only one cell survives, that value must go there, even though the cell had other candidates too.

The reason it is called hidden is that the answer is disguised by extra candidates. You are not proving the cell has one option. You are proving the value has one home.

How to hunt for them efficiently

• Work box by box. For each value, ask where it can go inside that box.
• Use the values that already appear several times on the board. They are the easiest to pin down.
• Keep your notes current so naked singles reveal themselves as cells with one candidate.
• Alternate between the two. Placing a hidden single often creates a naked single nearby.

Practice makes them automatic

At first you will search hard for each single. With practice your eye learns the shapes of a forced move and you spot them instantly. That speed is exactly what separates a slow solve from a fast one. Try a Medium board in Shapedoku, look only for singles, and see how far pure logic carries you.