Naked Quadruple
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Naked Quadruple is a size-4 subset.
How to spot it
- Examine each house (row, column, and box) in turn. Consider groups of four unfilled cells (with no given or entered digit) and examine their candidates.
- If the candidates across those four cells consist of exactly four distinct digits,
a,b,c, andd, eliminate those candidates from the other cells in the house.
The cells do not all need to contain all four candidates. Only the combined set of candidates across the four cells needs to be exactly a, b, c, and d.
How it works
- Those four cells can contain only
a,b,c, andd. Because digits cannot repeat within a house, the cells must contain those four digits, one in each cell, although their exact arrangement is not yet known. - Therefore, no other cell in the house can contain any of those four digits, so those candidates can be eliminated from the other cells.
Examples
A naked quadruple can appear in a row. For example, in row 1 below, cells R1C5, R1C7, R1C8, and R1C9 contain only candidates 2, 4, 6, and 8, so those candidates can be eliminated from the other cells in the row.
A naked quadruple can also appear in a column. For example, in column 7 below, cells R1C7, R2C7, R3C7, and R6C7 contain only candidates 1, 5, 6, and 7, so those candidates can be eliminated from the other cells in the column.
A naked quadruple can also appear in a box. For example, in box 3 below, cells R1C8, R2C8, R2C9, and R3C8 contain only candidates 1, 2, 3, and 9, so those candidates can be eliminated from the other cells in the box.