Hidden Single
Used in Classic 9×9 Sudoku, 6×6 Sudoku, Difference Sudoku, Irregular 6×6 Sudoku, Relational 6×6 Sudoku, Odd/Even Sudoku, Windowed Sudoku, Killer Sudoku, Skyscraper Sudoku 5×5 and Triangle Sudoku.
A hidden single is a digit that has only one place to go in a row, column or box. The cell it lands in may still have several candidates, which is why the single is "hidden": look at the cell alone and nothing stands out. It only shows when you ask the question the other way round. Instead of asking which digits fit in a cell, ask where a digit can go in a house.
An example
The top row already holds 1, 2, 3, 6 and 7, so it still needs 4, 5, 8 and 9. Look at where each of those can go:
- 4 can go in three cells, and 8 and 9 in more than one each.
- 5 is a candidate in only one cell: the third, which also allows 8.
Every row has to contain a 5, and that cell is the only place this row can put it. So the cell is 5, and its 8 doesn't matter.
How to look for them
Pick a digit and a house, and count the cells where that digit can still go. When the count is one, you've found a hidden single. In practice:
- Scan by digit. Take one digit, say 7, and go box by box. For each box, cross out the rows and columns that already have a 7. If one empty cell is left in the box, it is the 7.
- Start with the digits already placed most often. A digit with seven of its nine copies on the board leaves very few places for the other two.
- Check rows and columns as well as boxes. Boxes are easiest to see, but the example above is a hidden single in a row.
Naked or hidden?
A naked single is a cell with one candidate left. A hidden single is a digit with one cell left in a house. Puzzles graded Easy here can be solved with these two techniques alone, so between them they are the whole of the first tier.
When neither turns anything up, the next step is pairs: naked pairs and hidden pairs.
More techniques
- Naked Single (Obvious Single): A cell with only one candidate left must hold it. The first thing to look for in any sudoku, and how to spot it quickly.
- Naked Pair (Obvious Pair): Two cells in a house with the same two candidates take both digits between them, so the rest of the house can't have either.
- Naked Triple (Obvious Triple): Three cells in a house whose candidates use only three digits take all three, even when no cell shows all of them.
- Hidden Pair: Two digits that fit in only the same two cells of a house claim those cells, so every other candidate there can go.
- Hidden Triple: Three digits confined to the same three cells of a house claim them, clearing out every other candidate in those cells.
- Pointing Pairs and Triples: A digit confined to one line inside a box (or to one box along a line) can be removed from the rest of that line or box.