Hidden Single Sudoku Technique
The most useful technique in Sudoku, and the one most beginners never learn. Instead of asking what a cell can be, ask where a digit can go.
Also called: only choice, unique candidate, pinned digit.
What a hidden single is
A hidden single is a digit that has exactly one legal cell left within a row, a column, or a box — even though that cell still shows several candidates of its own.
It is hidden because the cell does not look solved. A cell holding four candidates can still be the only place in its box where a 4 will fit, and if so, it is a 4 and the other three candidates are wrong.
This is the difference between scanning by cell and scanning by digit. Naked singles are found by looking at cells; hidden singles are found by looking at units, one digit at a time.
How to spot one
- Take one digit and one unit. Cross out every cell in that unit where the digit is blocked by its row, column or box. If a single cell survives, the digit belongs there.
- Boxes are the most productive unit to scan, because a digit placed in two of the three rows crossing a box confines it to the third.
- Cross-hatching is this technique done systematically: pick a digit, sweep it through all nine boxes, then move to the next digit.
Worked example
| Column 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |
|---|---|---|---|---|---|---|---|---|---|
| Row 2 | 1 | 29 | 3 | 269 | 5 | 46 | 7 | 8 | 269 |
Solid digits are already placed. Small digits are the candidates still available in that cell.
- Ask where the 4 can go rather than what each cell can hold. Three of the four empty cells have had 4 eliminated by their own columns and boxes.
- Only the sixth cell still lists 4, so that cell is a 4 — despite showing two candidates and looking unresolved.
- The 6 that shared the cell disappears, which usually hands you a naked single somewhere in column 6 or box 5.
What it eliminates
Every other candidate in the chosen cell, plus the digit itself from all twenty of that cell’s peers.
When you need it
Constantly, from the very first grid. Easy puzzles are built to be finished with singles alone, and every harder grid still spends most of its moves here between the occasional deeper step.
Difficulty here is set by how many clues are left in the grid: Easy starts from 46, Medium 40 and Hard 34, with Extreme and Insane stripped further still. Fewer clues is what makes the techniques below necessary — the fewer digits you start with, the deeper you have to reason.