A naked quad is four cells in the same house whose combined candidates make up exactly four digits. Those four digits are locked into those four cells, so they can be eliminated from every other cell in the house.
A naked quad is the four-cell extension of naked pairs and singles. You find four cells that all live in the same house, and when you take the union of their pencil marks, you get exactly four distinct digits.
Because four cells need four digits, those four digits must go into those four cells - in some permutation. They cannot appear elsewhere in the shared house, so you sweep them out of every other cell. Each of the four cells does not need every candidate; one cell may show only two of the four, another all four, etc.
The argument is the same pigeonhole logic that powers every subset technique: n cells with exactly n candidates in total must contain those n digits. With n=4 the calculation gets harder because there are more candidate combinations to track, but the conclusion is just as airtight.
Look for clusters of cells with two-, three-, or four-candidate pencil marks. When four such cells in one house tile a four-digit set, you have a naked quad. The technique is rare in easy and medium puzzles - it shows up in expert and extreme puzzles where simpler subsets have been exhausted.
For practice with smaller subsets first, see naked pairs, naked triples, and the subset entry in the glossary.
It is the same idea with one more cell. Naked triples need three cells whose combined candidates total three digits; naked quads need four cells totalling four digits. The eliminations and the proof generalise directly.
No. Each cell only needs to be a subset of the four. One cell might have just two candidates from the set; another might have all four. The constraint is that no cell in the quad introduces a fifth candidate.
Only after exhausting singles, pairs, triples, and locked candidates. Naked quads are slow to spot, so save them for puzzles that have stalled - usually expert or extreme tier.
Look at four cells in row 1: C1 has [1, 4, 9], C2 has [4, 6, 9], C3 has [1, 6], and C4 has [1, 4, 6, 9].
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