A naked quad is the counting argument at full stretch: four cells in one house whose candidates, pooled together, come to exactly four digits. Those four cells must absorb all four digits between them, so every other cell in the house drops the lot from its pencil marks.
Like the naked triple, no cell has to show all four digits — and in practice almost none do. Cells of {4,6,8}, {6,8}, {4,6,7}, and {4,7,8} pool to {4,6,7,8}: four cells, four digits, quad. Each cell looks unremarkable on its own, which is what makes quads hard to see; scan houses for clusters of small cells drawing on the same short list.
It works because four cells restricted to four digits soak all of them up. If any of those digits sat elsewhere in the house, the quad’s cells would be left sharing three digits across four cells — and one of them would end up with nothing legal to hold.
On the board
In the centre box of this board, four cells draw on the same four digits: R4C4 shows {4,6,8}, R4C6 {6,8}, R5C4 {4,6,7}, and R6C4 {4,7,8}. Pooled, that is exactly {4,6,7,8} across four cells, so the box’s other cells surrender those digits: R5C5 loses its 6, R5C6 its 6 and 7, R6C5 its 8, and R6C6 its 7 and 8 — six eliminations from a single count.
This is the exact board the app's interactive Naked Quad demo uses — step 18 of its 69-step walkthrough, drawn here with its live pencil marks.
