Naked Quad
Four cells in a unit share only four candidates.
A naked quad is four cells sitting in one house — a row, column or box — whose pencil marks between them draw on only four different digits. Because those four digits have nowhere else in the house to live, they claim those four cells for themselves, which means you can rub them out of every other cell in that unit. Learning the naked quad sudoku technique simply extends the locked-set logic you already use for naked pairs and triples up to a group of four, and it often cracks a grid that singles and smaller subsets have stalled on.
Worked example
Look along row 1: R1C1 holds {1,2}, R1C2 holds {2,3}, R1C3 holds {3,4} and R1C4 holds {1,4}. Pool those four candidate sets together and you get exactly {1,2,3,4} — four cells drawing on four digits, and notice no single cell shows all four. Those digits are now locked inside those four cells, so no other cell in row 1 may use them. R1C6, which read {1,9}, therefore loses its 1 and resolves to R1C6=9.
When to use it
Reach for a naked quad only after singles, naked and hidden pairs, and triples have all dried up and a unit is still jammed with two-, three- and four-candidate cells. Scan one house at a time for four cells whose combined candidates come to just four digits — the cells need not each carry all four, so {1,2}, {2,3}, {3,4}, {1,4} still counts. The reward is the eliminations it forces on every other cell in that unit.
How to use it
- Find four linked cells. Find four cells in one row, column, or box whose candidates are all drawn from the same four digits.
- Confirm the quad. Those four digits must fill those four cells in some order, so they cannot appear anywhere else in the unit.
- Eliminate across the unit. Remove the four digits from every other cell in the unit.
Frequently asked questions
What is a Naked Quad in Sudoku?
A naked quad is a set of four cells in one row, column or box whose candidates, taken all together, use only four distinct digits. Those four digits are forced to fill those four cells in some order, so they can be eliminated from every other cell in the unit. In the row-1 example, the cells {1,2}, {2,3}, {3,4} and {1,4} form a quad locked onto {1,2,3,4}.
How do I spot a Naked Quad on the grid?
First exhaust singles, pairs and triples, then look at a crowded house and hunt for four cells whose pencil marks union to exactly four digits. The cells do not have to be identical — {1,2}, {2,3}, {3,4} and {1,4} qualify because together they cover {1,2,3,4}. Once you find one, strike those four digits from the other cells; that is how R1C6={1,9} collapses to R1C6=9.
What is the difference between a naked quad and a hidden quad?
A naked quad is four cells confined to four candidates, and you eliminate those digits from the other cells of the unit. A hidden quad is the mirror image: four digits confined to four cells, and you instead eliminate all the OTHER candidates from those four cells. The row-1 example is naked because the four cells R1C1 through R1C4 are pinned to just {1,2,3,4}, freeing the rest of the row.