Hidden Triple
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Hidden Triple is a size-3 subset.
How to spot it
- Examine each house (row, column, and box) in turn. Choose three distinct digits that have not yet been placed in the house,
a,b, andc, and examine their candidate positions. - If all possible positions for those three digits in the house together occupy exactly three unfilled cells, and at least one of those cells contains other candidates, eliminate all candidates other than
a,b, andcfrom those three cells.
A digit does not have to be a candidate in every one of the three cells. Only the combined set of possible positions for those digits in the house needs to be exactly those three cells.
How it works
- Each of
a,b, andcmust appear exactly once in the house. Because they can appear only in those three cells, they must occupy all three cells, one digit in each. - Placing any other digit in one of those cells would leave too few cells for
a,b, andc. Therefore, all other candidates can be eliminated from those three cells.
Examples
A hidden triple can appear in a row. For example, in row 7 below, digits 4, 7, and 9 can appear only in R7C2, R7C3, and R7C7, so all other candidates can be eliminated from those three cells.
A hidden triple can also appear in a column. For example, in column 5 below, digits 1, 3, and 7 can appear only in R4C5, R6C5, and R8C5, so all other candidates can be eliminated from those three cells.
A hidden triple can also appear in a box. For example, in box 3 below, digits 1, 2, and 8 can appear only in R1C7, R1C8, and R2C8, so all other candidates can be eliminated from those three cells.