Naked triples
What it is
A naked triple is the bigger sibling of the naked pair. It is three cells, all in the same row, column or box, whose candidates between them include only three different digits.
Those three cells must hold those three digits, one each. So no other cell in that row, column or box can hold any of the three. You can remove all three digits from the notes of every other cell in the unit.
The important point is that each cell does not need all three candidates. What matters is that, put together, the three cells use only three digits.
How to spot it
You need full pencil marks. Look for a row, column or box with several cells that have only two or three candidates each. Pick three of them and list every digit that appears in any of them. If the list has exactly three digits, you have a naked triple.
The patterns can look like this:
- {4, 8, 9}, {4, 8, 9}, {4, 8, 9}: all three cells show the same three digits.
- {4, 8, 9}, {4, 8}, {8, 9}: one full set and two smaller ones.
- {4, 8}, {4, 9}, {8, 9}: no cell has all three. This form is the easiest to miss.
A worked example
Look at row 3. Among its empty cells:
- Row 3, column 1 has candidates 4 and 8.
- Row 3, column 5 has candidates 4 and 9.
- Row 3, column 8 has candidates 8 and 9.
Put together, these three cells use only 4, 8 and 9. So they must hold the 4, the 8 and the 9 of row 3, in some order. Notice that no single cell has all three, and none of the three pairs matches, so you would not spot this by looking for naked pairs.
Now look at the other empty cells in row 3:
- Row 3, column 3 has candidates 1, 4 and 6. Remove the 4, leaving 1 and 6.
- Row 3, column 6 has candidates 2, 8 and 9. Remove the 8 and 9, leaving only 2.
Row 3, column 6 is now a naked single. Place the 2.
Why it works
Three cells, three digits. Each cell must take one of those digits, and since they share a row, they must all be different. So all three digits are used up by these three cells, and none is left for anywhere else in row 3.
A common mistake
The most common mistake is thinking every cell must show all three digits. As the example shows, the {4, 8}, {4, 9}, {8, 9} pattern is a perfectly good naked triple, and it is the one most players walk past.
The opposite mistake is counting four digits as three. If any of the three cells has a fourth candidate, such as 4, 8 and 9 plus a 2, the triple does not hold. Check each cell carefully.
Finally, all three cells must be in the same unit. If one of them is in a different row, the logic only holds for a unit all three share, such as a box.
When you will need it
Naked triples are part of the Hard toolkit on sudoku.ie, alongside hidden triples, quads and the X-wing. You will meet them on Thursday and Friday puzzles, and on Saturday’s Expert puzzle.