When three cells in a house hold only three digits between them, those three digits belong to those three cells, so every other cell in the house loses them. No single cell has to show all three.
How to spot it
A naked pair is two cells showing the same two candidates. The obvious way to grow it is three cells that each show the same three candidates, and that does happen. It is only one shape of several, though, and a reader who looks only for it walks past the rest.
The rule is about the digits the three cells hold between them. If three cells in one house have only three different digits across all their pencil marks, those digits are spoken for. A cell can show two of the three, or all three. What matters is the total.
So you do not look for three matching cells. You look for cells with two or three candidates, pick three of them in the same house, and count the different digits they show. Three is a triple. Four or more is nothing.
Read row five cell by cell
Row five has six empty cells and is missing six digits. Its first three cells show 5 and 9, 5 and 7, and 7 and 9. No cell is down to one candidate, and no two cells show the same pair, so neither a single nor a naked pair is here.
Count the digits, not the cells
Put the three cells together and they show only three different digits: 5, 7 and 9. Not one of the cells holds all three. Each is missing one, and a different one each time. That is still a naked triple.
Try it both ways round
If the first cell is a 5, the second must be its 7 and the third its 9. If the first cell is a 9, the third must be its 7 and the second its 5. There is no third way. You cannot tell yet which one the puzzle uses, and you do not need to, because both use up the 5, the 7 and the 9 inside these three cells.
Cross the three digits out of the rest of the row
Row five holds one 5, one 7 and one 9, and all three are now accounted for. Three marks go: the 9 from the fourth cell, and the 5 and the 7 from the last cell. The seventh cell shows none of the three and is left alone. So are the three cells of the triple.
Read what the strike left behind
The 9 that came out of the fourth cell of row five was one of only two places column four had for a 9. The other is the cell just above it, the fourth cell of row four. Now it is the only one, so it is a 9: a hidden single, in the column and in box five. Before the strike this grid had no single of either kind anywhere. The triple is what moved it.
Any mix of two and three
The three cells in row five each showed two digits. Other triples mix a cell with all three and cells with two, like 5 7 9, 5 7 and 7 9. Some have all three cells showing all three. The strike is the same every time, because the reasoning never looked inside any one cell. It only counted digits across the three.
Row five shows the all-three case too, after the strike. Its other three empty cells, the fourth, the seventh and the last, now each read 1, 4 and 8. Three cells, three digits, a naked triple. It removes nothing, because the row has no other empty cells left to remove from. A triple only pays when the house has something outside it that carries its digits.
Three short cells are not enough
Row eight has a set of three that looks just like row five's. Its first cell shows 1 and 6, its third shows 4 and 6, and its eighth shows 1 and 8. Three cells, two marks each, sharing digits along the chain.
Count the digits, though, and there are four: 1, 4, 6 and 8. Four digits cannot be locked into three cells, so these three cells claim nothing. Strike their digits from the rest of the row anyway and the only other empty cell, the sixth, loses its 4, its 6 and its 8. That leaves a cell with no candidates at all, which means a mistake has been made somewhere. On this grid that sixth cell is where the 8 goes.
Before you strike, write down every digit the three cells show and count them. The count is the whole test.
5 and 9, 5 and 7, 7 and 9. Three digits. The rest of the row loses them.
1 and 6, 4 and 6, 1 and 8. Four digits. Nothing can be struck.
Four cells and four digits
A naked quad is the same rule once more: four cells in a house holding only four digits between them. Those four digits leave every other cell in the house. The cells can show two, three or four candidates each, in any mix, exactly as with the triple. There is nothing new to learn for it.
Row eight has one. Its four empty cells hold 1, 4, 6 and 8 between them, so they are a naked quad. Like the second triple in row five, it removes nothing, because there is no fifth empty cell in the row. When a quad does have other cells to clear, it clears them exactly the way the triple cleared row five.
Count the digits across all the cells together. What any one cell shows on its own does not decide it. Two cells with two digits between them make a pair, three with three make a triple, four with four make a quad. One digit too many and there is nothing to strike.
Where this sits on the path
Like the naked pair, the triple places nothing. It removes candidates, and the placing is left to the singles. On the grid above the strike placed nothing by itself. It made the 9 in column four a single.
When the three cells share a box as well as a line, check both houses, as with a pair. Row five's triple sits in box four, and the question below is about that box.
The hidden pair reads the same kind of lock from the digits' side, and the hidden triple does the same with three digits. That comes next on the path.
Row five's triple also sits in box four. Which candidates can you strike from the second cell of row six?
Ask which house the three cells share besides row five, and which digits they hold between them.
Recap
- Look for
- Three cells in the same house that show only three different digits between them. Each cell can show two of them or all three.
- Scope
- Any house: box, row or column. Check every house the three cells share.
- Result
- The three digits come out of every other cell in that house. The triple itself is left untouched.
- Tell-tale
- A house with several cells down to two or three candidates. Pick three and count the digits they show.
- If it fails
- If the three cells show four digits between them, they claim nothing. Try a different set of three, or add the fourth cell that carries the extra digit and look for a quad. If no house gives three cells and three digits, read the houses from the digits' side instead, as a hidden pair does.