Naked triple practice sheets
Three cells that between them can only hold three digits. You never have to work out which is which.
Three cells, three digits, no order required
A naked triple is the first technique that asks you to stop thinking cell by cell. Three cells in a unit, and between them they can hold only three distinct digits — so those three digits are used up inside those three cells, and they cannot appear anywhere else in the unit.
You do not have to know which digit goes in which cell. That is the point, and it is where people get stuck: they try to resolve the triple first, fail, and conclude there is nothing there. The conclusion is available before the arrangement is.
Spotting one, in order
- Pick a unit and count small candidate lists. You are looking for three cells whose lists are short — two or three digits each. A cell with five candidates can still be part of a triple, but it is rarely the place to start looking.
- Union the three lists. Write down the distinct digits across all three cells. If you get more than three, those cells are not a triple. If you get exactly three, you have one.
- Check it is not already simpler. Three cells holding three digits between them, each with three candidates, is the classic form. But the shape is flexible:
{2,5},{5,9},{2,9}is a triple with no cell showing all three digits. That flexibility is what makes it hard to see. - Clear those three digits from the rest of the unit. Not from the three cells — from everything else in the row, column or box they share.
The trap in step 3 is expecting three copies of the same list. If you wait for that, you will mostly find naked pairs wearing a third cell, and miss the real triples. A triple is defined by the union, not by any single cell.
What the grader guarantees
Every puzzle on this sheet needs at least one naked triple, and nothing on it asks for more than one tier above: the hardest extra step you can meet is an X-Wing or a single-digit colouring. The filter never relaxes to fill a sheet, so if one ever comes up short, press New set.
A word on frequency, because it manages expectations honestly: naked triples are less common than naked pairs. On random boards of this depth the grader meets one roughly once every few dozen puzzles, which is why the sheet takes a moment longer to build than the pair sheets. It is not stuck.
Printing it
Scale 100%. Four puzzles per page gives 78 mm boards; two per page leaves room to write between them; one per page is a single puzzle to live with for an evening.
For this technique Candidate marks are close to mandatory. A triple is a statement about three lists at once, and comparing three lists in your head is where the errors come from. Print with marks on while learning; print a second copy without them later and see whether the scan still works. Answer page adds the solutions at the end, numbered to match.
Where to go next
The full guide to naked triples shows a position where the triple is the only move on the board, and sets it against the hidden triple — the same three cells described from the digits' side instead of the cells' side.
If pairs are still not automatic, the naked pair sheet is the right place to start; triples are the same idea with one more cell. For the version you find by counting digits rather than reading cells, use the hidden triple guide — there is no practice sheet for it, because on random boards of this depth it turns up too rarely to fill one honestly.