Naked Triple
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Naked Triple is a size-3 subset.
How to spot it
- Examine each house (row, column, and box) in turn. Consider groups of three unfilled cells (with no given or entered digit) and examine their candidates.
- If the candidates across those three cells consist of exactly three distinct digits,
a,b, andc, eliminate those candidates from the other cells in the house.
The cells do not all need to contain all three candidates. Only the combined set of candidates across the three cells needs to be exactly a, b, and c.
How it works
- Those three cells can contain only
a,b, andc. Because digits cannot repeat within a house, the cells must contain those three 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 three digits, so those candidates can be eliminated from the other cells.
Examples
A naked triple can appear in a row. For example, in row 5 below, cells R5C1, R5C5, and R5C6 contain only candidates 1, 4, and 8, so those candidates can be eliminated from the other cells in the row.
A naked triple can also appear in a column. For example, in column 8 below, cells R2C8, R3C8, and R7C8 contain only candidates 1, 3, and 9, so those candidates can be eliminated from the other cells in the column.
A naked triple can also appear in a box. For example, in box 4 below, cells R4C3, R6C1, and R6C2 contain only candidates 1, 3, and 4, so those candidates can be eliminated from the other cells in the box.