Four cells whose candidates span at most four digits. Lock them down and eliminate.
Find four cells in a unit whose combined candidates use at most four digits; each cell may hold two, three or four of them. Those digits are claimed, so remove all four from every other cell in the unit — up to five cells can lose candidates at once. Quads are rare.
A Naked Quad extends the Naked Pair and Naked Triple pattern to four cells. Find four cells in a unit whose combined candidates use at most four distinct digits. Those four digits must go in those four cells, so eliminate them from all other cells in the unit.
Naked Quads are relatively rare. Most puzzles, even Hard ones, don't require them. When they do appear, they tend to involve cells with 2-3 candidates each, where the overlap isn't immediately obvious.
The variety of valid configurations is wide. Four cells could have {1,2}, {2,3}, {3,4}, {1,4} (each with two candidates) or {1,2,3,4}, {1,2}, {3,4}, {2,3} (mixed sizes). As long as the union is four digits across four cells, it's valid.
The logic is identical to Naked Pairs and Triples, scaled up. Four digits in four cells means those digits are fully accounted for within the unit. No other cell in the unit can contain any of the four digits.
Practically, scan for clusters of cells with short candidate lists that share significant overlap. If you find four cells whose combined candidates form a set of exactly four digits, you have a Naked Quad.
After confirming the quad, remove all four digits from every other cell in the shared unit. This can produce significant simplification, as up to five other cells might lose candidates.
Tip: if a unit has nine cells and five of them have candidates that span five digits, then the remaining four cells must form a Naked Quad with the other four digits. Sometimes it's easier to find the complement.
Example 1: Naked Quad in a Row
Look at row 8. Four consecutive empty cells (R8C4, R8C5, R8C6, and R8C7) have candidates drawn from exactly four digits: {2, 3, 4, 6}.
R8C4 has {2, 3, 4}. R8C5 has {2, 3, 4, 6}. R8C6 has {3, 4}. R8C7 has {4, 6}. Each cell's candidates are a subset of {2, 3, 4, 6}. The union across all four is exactly four digits in four cells, a Naked Quad.
Since 2, 3, 4, and 6 must occupy these four cells, eliminate them from all other cells in row 8: remove {2, 6} from R8C1, {2, 3} from R8C2, {2, 4, 6} from R8C8, and {2} from R8C9.
After eliminating, R8C1 drops from {1, 2, 6, 7, 8} to {1, 7, 8}, and R8C8 drops from {1, 2, 4, 6, 8, 9} to {1, 8, 9}. The significantly shorter candidate lists make further progress easier.
Example 2: Naked Quad in a Box
Now look at box 1 (top-left). Four cells (R1C1, R1C3, R2C3, and R3C3) have candidates from the set {2, 4, 5, 7}.
R1C1 has {2, 7}. R1C3 has {2, 4, 5, 7}. R2C3 has {2, 4, 5}. R3C3 has {2, 4}. Each cell is a subset of {2, 4, 5, 7}, a valid Naked Quad. Notice the variety: cells have 2, 3, or 4 of the quad digits.
Eliminate 2, 4, 5, and 7 from all other empty cells in box 1: remove {2} from R1C2, {2} from R2C1, {2} from R2C2, {2} from R3C1, and {2} from R3C2.
R1C2 drops from {2, 8} to just {8}, a Naked Single! Naked Quads in boxes can clear many cells at once since all non-quad cells in the unit are affected.
No. Each cell only needs candidates drawn from the same four digits. {1,2}, {2,3}, {3,4}, {1,4} is a valid Naked Quad, and so is a mixed set like {1,2,3,4}, {1,2}, {3,4}, {2,3}. What matters is that the union across the four cells covers at most four distinct digits.
Start from a cell with a short candidate list, two to four candidates, then look for three more cells in the same row, column or box whose candidates draw from that same pool of digits. If the four cells together span at most four distinct digits, the quad holds. They need not be adjacent or in a line.
In a unit where nine cells are unsolved, if five of them have candidates spanning exactly five digits, the remaining four cells must form a Naked Quad on the other four digits. Spotting that five-cell group is often easier than testing four-cell combinations one by one.
No. A Naked Quad is four cells restricted to four digits; a Hidden Quad is four digits restricted to four cells. They are not automatic complements: a Naked Quad complements to a Hidden Quad only when exactly eight cells in the unit are unsolved. With nine unsolved, it complements to a hidden set of five digits.
Only when you are stuck. Most puzzles, even Hard ones, never require a Naked Quad, so work through pairs, triples and the other intermediate techniques first. The payoff when one does exist is large: the four digits come out of up to five other cells at once, which can reduce one to a single candidate.
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