Naked Quad
A Naked Quad appears when four cells in the same house — a row, column, or 3×3 box — together hold only four distinct candidate digits between them. Those four digits must fill those four cells, so every other cell in the house can have all four crossed off its pencil marks.
What is a Naked Quad?
A Naked Quad is the four-cell version of a Naked Pair, and it comes in more than one shape. The four cells don't each need the same four candidates — what matters is that across all four cells, only four distinct digits appear. So one cell might have {1, 4}, another {4, 5, 8}, a third {1, 8}, and the fourth {5, 8}: between them that's still just 1, 4, 5 and 8. Whatever the split, those four digits are locked into those four cells, and the rest of the house is cleared of them. It's the hardest naked subset to spot because the candidates are spread across four cells, but the logic is identical to a pair or triplet.
How to spot it
Scan each house for four cells whose combined candidates total four digits or fewer. With pencil marks on, look for clusters of cells that draw from a small shared pool — if four cells only mention four digits between them, that's your quad. The candidates don't have to match cell-for-cell, which is what trips people up: the test is on the union of candidates, not on each cell individually. Naked Quads are rare and show up only in the hardest puzzles once pairs, triplets, and fish have thinned the field.
The logic
Every house places each digit 1–9 exactly once. If four cells in a house between them can only hold four specific digits, those four digits must be distributed across those four cells — one digit per cell — because there's nowhere else in the house any of them can land. That uses up all four digits inside the quad, so no other cell in the house can contain any of them. The same reasoning with two cells gives a Naked Pair, with three a Naked Triplet, and with four it's the Naked Quad.