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Sudoku technique

Naked triples

Three cells that between them can only hold three digits. The trap is that no single cell has to show all three — which is exactly why triples get walked past.

What a naked triple is

A naked triple is three cells in one row, column or box whose candidates, taken together, amount to exactly three digits. Those three digits are then locked into those three cells and can be removed from every other cell in the unit.

It is the direct extension of the naked pair, and the logic is identical: three cells that must consume three digits leave none of them for anyone else.

The mistake everyone makes

Looking for three cells that each show the same three candidates. That is a naked triple, but it is the rarest form of one and waiting for it means missing nearly all of them.

Cells holding 1,4, 4,7 and 1,7 are a perfectly good triple on 1, 4 and 7. So are 1,4,7, 1,4 and 4,7. What matters is the union of the three candidate sets, not what any one cell looks like. No cell has to contain all three digits, and usually none does.

Is it worth the effort?

Less often than people expect. A naked triple takes real work to spot and frequently eliminates less than a well-chosen pointing pair, which takes seconds. Check the box and line interactions first; come back to triples when they have run dry.

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Step 1 of 4

A real position

Candidates marked, singles and pairs already taken. Somewhere in this grid three cells have quietly locked up three digits.

A real position from a generated puzzle. Every elimination shown here was checked against that puzzle's actual solution.

A method that actually works

Restrict yourself to cells with two or three candidates — a cell with four cannot be part of a triple. In most units that leaves three or four cells to consider, which is a small enough set to check exhaustively.

Then take them three at a time and union the candidates. If the union has three digits, you have one. It sounds laborious and it takes about ten seconds per unit in practice, because the shortlist is always short.

Hidden triples

The mirror image exists: three digits that between them have only three homes in a unit, which strips those three cells of every other candidate. Same relationship as hidden pairs have to naked pairs.

Hidden triples are genuinely hard to see and rarely necessary. If a board seems to require one, it is worth a second sweep for something simpler first — the usual culprit is a hidden single that was missed several moves ago.

Other techniques

Try it on a real board

The free board on the home page has a notes mode, which is what every technique past hidden singles needs. Then take the same eye into a live match.