Naked Triples and Quads in Sudoku Explained

How a naked triple works

A naked triple appears when three cells in one row, column, or 3 by 3 box contain candidates drawn from the same set of three symbols. The cells do not all need to show all three candidates. You might find one cell with heart and circle, another with circle and crescent, and a third with heart and crescent. Together, those three cells can contain only the heart, circle, and crescent. Since the unit must use each symbol once, those three symbols are locked into those three cells in some order. They can therefore be removed from every other unsolved cell in the unit. The important word is together. No individual cell is solved, and no pair alone creates the deduction. The restriction comes from comparing the combined candidate set with the number of cells. In Shapedoku, full Notes are useful here because the pattern can be spread across a row or box rather than sitting in one obvious cluster.

How a naked quad extends the same idea

A naked quad uses four cells whose combined candidates contain exactly four symbols. For example, four cells might use only triangle, diamond, square, and lotus, even though each cell shows two or three of them. Those four symbols must fill those four cells, so they can be eliminated from the rest of the unit. Quads are harder to notice because the candidate combinations look less tidy and the unit may contain many notes. Start by looking for four cells with small candidate counts rather than trying every possible group. A quad can also hide in plain sight when one of its candidates appears only once inside the four cells. That does not invalidate the pattern, as long as the union of all candidates is exactly four symbols. Before removing anything, count both sides of the relationship: four selected cells and four combined candidates. If you accidentally include a fifth candidate, the set is not locked and the eliminations are unsafe.

A reliable way to search for larger naked sets

Search the most constrained units first. A row with five empty cells is easier to analyze than one with eight. Within that unit, identify cells holding two or three candidates and compare their combined sets. For triples, begin with a bivalue cell and look for two nearby cells that use the same three-symbol pool. For quads, look for a cluster of four low-candidate cells, then count the union carefully. Once you find a valid set, remove its symbols only from other cells in the same unit. A triple in a box does not automatically justify eliminations from a crossing row unless an additional locked-candidate pattern is present. After each elimination, let Shapedoku's smart cleanup handle candidates affected by final placements, then rescan for singles and pairs before hunting another large set. The purpose of a triple or quad is usually not to finish the puzzle directly. It is to make one or two outside cells simpler enough for an easier technique to take over.

1. Choose a row, column, or box with several low-candidate cells.
2. Select three cells for a triple or four cells for a quad.
3. Combine every candidate from the selected cells into one set.
4. Confirm that the candidate count matches the selected cell count.
5. Remove those candidates only from the other cells in the same unit.
6. Rescan the affected unit for singles, pairs, and locked candidates.