Lesson 2 of 8
Hidden single
A hidden single is a digit with one home left. The cell holding it still looks busy, with two or three candidates written in it, but the digit you're chasing can go nowhere else in that row, column or box. So the cell must be that digit, and its other candidates are wrong.
- Level
- Beginner
The pattern
What it does.
The single candidate reads one cell and counts digits. The hidden single turns that around: pick one digit, and count the cells in a unit that can still take it.
If exactly one cell in the unit allows the digit, that cell is the digit. Nothing else has to be decided first, and no other candidate in that cell can be true.
Example
A worked example.
Pick a unit
Choose a row, a column or a box, and prefer one that already holds a lot of digits. The more of the unit is filled, the fewer cells you have to check.
Pick a digit
Take one digit that isn't placed in that unit yet. You're asking a question about that digit alone, not about any particular cell.
Count its homes
Go through the empty cells of the unit and ask of each one whether the digit is already in its row, its column or its box. Any cell where it's already present is ruled out.
One home means placed
If a single cell survives, write the digit into it and clear the other candidates from that cell. If two or three survive, there's no hidden single here for that digit; move to the next digit or the next unit.
Spotting it
How to spot it.
- Work digit by digit rather than cell by cell. The pattern is invisible from a single cell, which is exactly what makes it "hidden".
- Boxes and rows that are missing just one or two digits are the quickest places to find one.
- After a placement, re-check the digit you placed in the other two units that cross it: one placement removes three homes at once.
Where it stops working
The count has to cover the whole unit. A cell that allows three different digits can still be a hidden single for one of them, so don't skip a cell because it looks busy. And if your candidate list is incomplete, the count will say two homes where there's only one, and the move will be missed rather than made wrongly.
Keep going
Related topics.
New to sudoku? The rules take two minutes to read, and the first-puzzle walkthrough covers the basics that come before any of these.
Practice it in Sudoku Mori.
Hidden single is lesson 2 in the game, with a worked example and three practice puzzles. Lesson puzzles are separate from your daily ones, and you can redo any lesson whenever you like.