Hidden Quadruple
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Hidden Quadruple is a size-4 subset.
How to spot it
- Examine each house (row, column, and box) in turn. Choose four distinct digits that have not yet been placed in the house,
a,b,c, andd, and examine their candidate positions. - If all possible positions for those four digits in the house together occupy exactly four unfilled cells, and at least one of those cells contains other candidates, eliminate all candidates other than
a,b,c, anddfrom those four cells.
A digit does not have to be a candidate in every one of the four cells. Only the combined set of possible positions for those digits in the house needs to be exactly those four cells.
How it works
- Each of
a,b,c, anddmust appear exactly once in the house. Because they can appear only in those four cells, they must occupy all four cells, one digit in each. - Placing any other digit in one of those cells would leave too few cells for
a,b,c, andd. Therefore, all other candidates can be eliminated from those four cells.
Examples
A hidden quadruple can appear in a row. For example, in row 5 below, digits 3, 7, 8, and 9 can appear only in R5C4, R5C5, R5C6, and R5C9, so all other candidates can be eliminated from those four cells.
A hidden quadruple can also appear in a column. For example, in column 3 below, digits 2, 3, 8, and 9 can appear only in R4C3, R5C3, R6C3, and R9C3, so all other candidates can be eliminated from those four cells.
A hidden quadruple can also appear in a box. For example, in box 3 below, digits 1, 3, 7, and 8 can appear only in R1C7, R1C9, R2C7, and R2C9, so all other candidates can be eliminated from those four cells.