Naked Triple (Obvious Triple)
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 naked triple is three cells in the same row, column or box whose candidates, taken together, are only three digits. Those three cells must hold those three digits, so no other cell in the house can have any of them.
The catch, and the reason it's harder to see than a naked pair, is that the cells don't need to show all three digits. A cell with 7 and 8, one with 1 and 7, and one with 1 and 8 make a triple: none of them lists 1, 7 and 8, but between them those are the only digits they can hold.
An example
In the bottom-left box, look at the three cells of the second column:
- the top one can be 7 or 8,
- the middle one can be 1 or 7,
- the bottom one can be 1 or 8.
Three cells, three digits: 1, 7 and 8. Each cell has to take one of them and no two can match, so the three digits are used up. The rest of the box can't have 1, 7 or 8:
- 7 is struck from the two other cells of the seventh row.
- 1 and 7 are struck from the first cell of the eighth row, and 7 from the third.
None of the other cells had an 8, so nothing more goes. The three cells also share a column, which would lose the same digits, but every other cell in that column is already filled.
How to look for them
- Look in houses with few empty cells left. With four or five empty cells, a triple is easier to see than with eight.
- Count digits, not cells. Pick three cells with two or three candidates each and list every digit that appears. If the list has exactly three, you have a triple.
- Watch for the 2-2-2 shape. Three cells with two candidates each, like the example, are easy to miss, because no single cell looks related to the others.
Why it works
Three cells that share a house need three different digits. If the only digits on offer are three, they take all three, whichever way round. It's the same reasoning as a pair, one size up. The app also looks for quads and quintuples, though they come up rarely: in a house of nine, a large naked set nearly always has a smaller hidden one beside it that is easier to find.
Where it fits
The app's hints call this an "Obvious triple". Like the naked pair, it is a Medium technique. Its mirror image is the hidden triple: three digits that can only go in the same three cells.
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.
- Hidden Single: When a digit fits in only one cell of a row, column or box, it goes there, even if that cell has other candidates.
- 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.
- 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.