The Naked Quad Technique identifies four candidates that appear across four cells within the same row, column, or block. These four candidates, in some combination, are confined to these four cells, meaning they cannot appear elsewhere in that house.
- Row-based Naked Quad: If four candidates appear only across four specific cells of a row, they can be eliminated from other cells in the same row.
- Column-based Naked Quad: If four candidates are distributed across four cells of a column, these candidates can be removed from other cells in that column.
- Block-based Naked Quad: If four candidates appear across four cells in a block, any instance of these candidates in other cells of the block can be eliminated.
In this puzzle, a Block-based Naked Quad occurs where the numbers 1, 2, 5, and 7 are distributed across four cells in block 4. Therefore, these numbers must appear only in those four cells, and any other instance of these candidates in the block can be eliminated.
This puzzle combines Hidden and Naked Singles with the Naked Quad technique for a more advanced challenge.
How to spot it
Find four cells in one unit whose combined candidates use only four distinct digits. The four digits are locked into those four cells.
When to use it
Quads are rare; check for one when pairs and triples leave a unit only partly resolved.
Common mistakes
- Miscounting the union of candidates; a true Naked Quad has exactly four digits across the four cells.
- Overlooking it because the four cells rarely show identical candidates.
Frequently asked questions
- What is a Naked Quad in Sudoku?
- A Naked Quad is four cells in the same unit that together contain only four candidate digits. Those digits can be eliminated from every other cell in the unit.
- How common is a Naked Quad?
- It is uncommon. Because a unit has nine cells, a Naked Quad and the rest of the unit divide it neatly, but the pattern appears far less often than pairs or triples.
- Do the four cells need identical candidates?
- No. Each cell can contain any two, three, or four of the digits, as long as the four cells together contain exactly four distinct candidates.