Naked Quadruple

A naked quadruple occurs when, in a house (row, column, or box), four cells contain only four candidates, and those four candidates are confined to those four cells. In that case, those four candidates can be eliminated from every other cell in the house. No matter how the digits are arranged, they must occupy those four cells.

Naked Quadruple is a size-$4$ subset.

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.