Techniques / Subsets

Naked Quad

Also called Naked Quadruple, Disjoint Subset of size 4.

New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.

What it means

Four squares in one group share the same four digits between them. Those digits fill those squares, so rub them out of the rest of the group.

The exact rule, for stronger players

The rule, stated exactly: For a house H, if four cells of H have candidate sets whose union has cardinality four, those four digits may be eliminated from every other cell of H.

What it removes: Remove all four digits from all cells of H outside the quad.

Why it works: Identical to the triple argument, extended by one. Four cells confined to four digits consume all four.

Worked examples

These come from real Proven Sudoku boards. Nobody drew them by hand to make the pattern look neat. Each one is checked first, so the board is one you could really meet, the pattern is really there, and every digit it rules out is really wrong.

Sudoku grid showing Naked Quad. r1c2, r1c3, r1c4, r1c6 in r1 hold only 2, 4, 7, 8 between them, so those 4 digits fill those cells and appear nowhere else in r1. — r1c2, r1c3, r1c4, r1c6 in r1 hold only 2, 4, 7, 8 between them, so those 4 digits fill those cells and appear nowhere else in r1.

Sudoku grid showing Naked Quad. r2c2, r2c4, r2c5, r2c7 in r2 hold only 3, 6, 7, 8 between them, so those 4 digits fill those cells and appear nowhere else in r2. — r2c2, r2c4, r2c5, r2c7 in r2 hold only 3, 6, 7, 8 between them, so those 4 digits fill those cells and appear nowhere else in r2.

Learn these first

Naked TripleThree squares in one group share the same three digits between them.

Related subsets

Naked Subset (general form)Find some squares in one row, column or box.
Hidden PairTwo digits in one group can only go in the same two squares.
Hidden QuadFour digits in a group can only go in the same four squares.
Hidden Subset (general form)Some numbers in a group have only a few homes left.
Hidden TripleThree digits in a group can only go in the same three squares.

How often does it come up?

Our rough estimate: uncommon. In a nine-cell house a naked quad implies a hidden pair among the remaining cells, which is usually easier to see.

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