Techniques / Singles

Sudoku singles: full house, naked single, hidden single

The three ways a digit can be forced without comparing anything.

3 techniques in this family, introduced at tier 1, 3 with a worked example from a real board. How to read a sudoku grid explains the notation used below.

What these have in common

A single is a placement you can justify by looking at one thing. Not a pattern across the grid, not a chain of consequences, just one cell or one house read carefully. Every sudoku solve is mostly singles, including the hardest ones: the exotic technique breaks the deadlock, and then thirty singles fall out behind it.

Why the logic holds

Two rules generate all three. Every house holds each digit exactly once, and every cell holds exactly one digit. Read the first rule and you get the hidden single, where a digit has only one place left in its house. Read the second and you get the naked single, where a cell has only one digit left. The full house is the degenerate case of both, a house with one empty cell, where the answer is whatever is missing.

When to reach for it

Before anything else, and again after every single placement you make. This is the habit that separates a fast solve from a slow one. A placement changes three houses at once, so it can unlock a digit on the far side of the grid that had nothing to do with the cell you just filled.

How the members differ

Naked and hidden are the same fact approached from opposite ends. Beginners find naked singles first because pencil marks make them visible without effort. Hidden singles are the ones people miss, because spotting one means scanning a house for a digit that is absent rather than reading what is present in a cell. Strong solvers scan for hidden singles deliberately, by digit, and find them far earlier.

The mistake to avoid

Filling one single and then going back to hunting patterns. Almost every single creates another. Work the cascade to exhaustion before you look for anything harder, or you will spend effort finding an X-Wing that a hidden single two moves away would have made unnecessary.

Every technique in this family

• Full HouseA row, column or box has just one empty square left.
• Hidden SingleLook at one digit in one row, column or box.
• Naked SingleA square has only one digit left that fits.