Hidden Single: learn the sudoku technique step by step at Sudokuen

See the technique in practice

Work through the examples step by step. Each step explains what you see in the puzzle and why the conclusion is valid.

Example:

We look at row 3. The question we ask is simple: in which of the empty cells can digit 5 go?
Digit 5 already appears in some of the surrounding cells. Their colors show how they block it. Blue cells block through their own row or column, so the empty cell they cross in row 3 can no longer take the digit. Orange cells block through their own box, so the empty cells sharing a box with them cannot take the digit either. This leaves only the circled cell.
Only one cell remains, namely row 3, column 7.
Digit 5 must go somewhere in row 3. Since only this cell can take it, it must go here. This is called a Hidden Single.

We look at row 1. The question we ask is simple: in which of the empty cells can digit 8 go?
Digit 8 already appears in some of the surrounding cells. Their colors show how they block it. Blue cells block through their own row or column, so the empty cell they cross in row 1 can no longer take the digit. Orange cells block through their own box, so the empty cells sharing a box with them cannot take the digit either. This leaves only the circled cell.
Only one cell remains, namely row 1, column 4.
Digit 8 must go somewhere in row 1. Since only this cell can take it, it must go here. This is called a Hidden Single.

We look at row 3. The question we ask is simple: in which of the empty cells can digit 1 go?
Digit 1 already appears in some of the surrounding cells. Their colors show how they block it. Blue cells block through their own row or column, so the empty cell they cross in row 3 can no longer take the digit. Orange cells block through their own box, so the empty cells sharing a box with them cannot take the digit either. This leaves only the circled cell.
Only one cell remains, namely row 3, column 2.
Digit 1 must go somewhere in row 3. Since only this cell can take it, it must go here. This is called a Hidden Single.

We look at row 2. The question we ask is simple: in which of the empty cells can digit 8 go?
Digit 8 already appears in some of the surrounding cells. Their colors show how they block it. Orange cells block through their own box, so the empty cells sharing a box with them cannot take the digit either. This leaves only the circled cell.
Only one cell remains, namely row 2, column 1.
Digit 8 must go somewhere in row 2. Since only this cell can take it, it must go here. This is called a Hidden Single.

We look at row 3. The question we ask is simple: in which of the empty cells can digit 5 go?
Digit 5 already appears in some of the surrounding cells. Their colors show how they block it. Blue cells block through their own row or column, so the empty cell they cross in row 3 can no longer take the digit. Orange cells block through their own box, so the empty cells sharing a box with them cannot take the digit either. This leaves only the circled cell.
Only one cell remains, namely row 3, column 8.
Digit 5 must go somewhere in row 3. Since only this cell can take it, it must go here. This is called a Hidden Single.

A Hidden Single is harder to spot than a Naked Single, because the cell often has several candidates. The key is to switch perspective: instead of asking what can go in a cell, you ask where a specific digit can go in a unit. When the answer is only one cell, you have found a Hidden Single.

Systematically look for digits that already appear many times in the puzzle. If a digit appears seven or eight times, its remaining positions are often forced. Boxes are the best place to start because they are compact and quick to scan.

Choose a digit that already appears many times in the puzzle.
Choose a box, row or column that is missing the digit.
Mark which empty cells in the unit can take the digit, that is, the cells that are not blocked by the same digit in their own row, column or box.
If only one possible cell remains, the digit must go there. Write it in.

Rejecting a cell because it has many candidates. A Hidden Single does not require the cell to have only one possible digit, just that the digit does not fit anywhere else in the unit.
Checking only rows. Hidden Singles show up equally often in columns and boxes, so vary which unit you scan.
Missing a blocking occurrence. One missed occurrence of the digit in a crossing row or column can make you find two possible cells when there is really only one.

The easiest Sudoku puzzles can be solved with two techniques based on the same rule: each digit can appear only once in each row, column and box. Learn both techniques, and you can solve every puzzle at the Easy level.

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Hidden Single

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