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Sudoku Naked Triple

Three cells' candidates total three digits → erase those three from the rest of the unit.

Technique 8 in the order the hint searches · difficulty Very hard · up to intersections and triples

The naked pair with one more cell. If the candidates written across three cells of the same unit come to only 1, 4 and 9 between them, those three cells share out the 1, 4 and 9.

Put together, the notes in the first three cells of row 9 come to just 1, 2 and 3, and no cell has to carry all three. The three digits fill those three cells, so the fourth cell loses 1, 2 and 3 and keeps only the 4.

Look for a combination whose union is three

This is where people go wrong most often: the three cells do not each need to hold 1, 4 and 9. Two apiece, like 1·4 / 4·9 / 1·9, still unions to three and still works. Restricting yourself to cells with two or three candidates makes the combinations manageable.

How the hint says it

The three cells r7c7, r7c9 and r9c9 in the bottom-right box can hold only 1, 3 and 4. Three digits fill three cells, so 3 comes off the other cells in the same box.

Three cells use up all three digits

In that unit, the homes for 6, 7 and 9 are settled inside these three cells. If another cell in the line took one of the three, one of the trio would have nowhere to go. It's exactly the pair's logic stretched by one cell.

It belongs to Very hard, but puzzles where it is genuinely the deciding move are rare. Across 300 generated puzzles it came up five times.

Puzzles that need this technique

Four puzzles with a spot where nothing moves until you use Naked Triple. Press a number to play it.