Hidden Singles in Sudoku
Hidden singles are the technique that separates easy solvers from medium solvers. Once you understand them, a large class of previously "impossible" cells becomes immediately solvable. This is one of the most important sudoku techniques to master.
What Is a Hidden Single?
A hidden single occurs when a particular digit can only be placed in one cell within a row, column, or 3×3 box — even though that cell appears to have multiple possible candidates.
The word "hidden" describes the fact that the uniqueness isn't visible when you look at the cell alone. You have to look at the group (the entire row, column, or box) to see that only one cell in it can hold that digit.
Hidden Singles vs. Naked Singles
The difference is the direction of your analysis:
- Naked single: You look at one cell and ask, "What digit can go here?" Only one digit is possible.
- Hidden single: You look at one group and ask, "Where can this digit go?" Only one cell in the group can hold it.
Both produce the same result — a definite digit placement — but they require different thinking.
How to Find Hidden Singles
Pick any digit, say 6. Go through each group (all 9 rows, all 9 columns, all 9 boxes) that doesn't yet contain a 6. For each such group, look at the empty cells and ask: which ones can hold a 6?
A cell cannot hold a 6 if a 6 already exists in the cell's row, column, or box. Apply these constraints to each empty cell in the group. If only one empty cell survives — place the 6 there.
Step-by-step:
- Choose a digit to scan for (start with the most frequent one on the board).
- Find all groups (row, column, or box) that don't already contain that digit.
- Within each incomplete group, identify the empty cells.
- For each empty cell, check: does a copy of the digit exist in this cell's row? Column? Box?
- Cross off any cell where the answer is yes to any of the three checks.
- If exactly one empty cell remains uncrossed in the group — that's a hidden single.
Example: Hidden Single in a Box
Consider the center 3×3 box below. It has four empty cells and you are looking for where 3 can go. Two of the empty cells share a column with an existing 3 elsewhere on the grid — eliminated. A third empty cell shares a row with an existing 3 — eliminated. Only one empty cell remains: that cell must be 3.
From looking at that cell itself, it might appear to have multiple candidates. But from the box perspective, it is the only place 3 can go — making it a hidden single.
Scanning All Three Group Types
Hidden singles can appear in rows, columns, or boxes. Always scan all three:
- Box hidden singles are usually easiest to spot visually.
- Row hidden singles require scanning nine cells horizontally.
- Column hidden singles require scanning nine cells vertically.
Many solvers find box hidden singles first, then switch to row and column scans. Practice all three orientations equally — puzzle designers plant hidden singles in all of them.
Hidden Singles and Pencil Marks
With pencil marks, hidden singles become more visible. Fill in all candidates for every empty cell. Then, for each digit, look through each group. If a digit appears as a pencil mark in only one cell of a group, circle it — that's your hidden single.
This is one of the main reasons experienced solvers always maintain pencil marks on medium and hard puzzles.
After Hidden Singles
Hidden singles solve most medium puzzles. When they run out, you'll need to advance to techniques like naked pairs or pointing pairs.