Naked Pair - Breaking Through with Mutual Candidate Elimination

A Naked Pair occurs when two cells in the same row, column, or block have exactly the same two candidate digits and no others. For example, if two cells in a row both have only candidates {3, 7}, then 3 and 7 must go in these two cells (though which goes where is undetermined). The crucial insight is that these two digits cannot appear in any other cell in the same row. Therefore, 3 and 7 can be eliminated from the candidates of all other cells in that row.

Finding Naked Pairs requires accurate pencil marks as a prerequisite. The procedure is: (1) Identify all cells that have exactly two candidates. (2) Check whether any two cells in the same unit (row, column, or block) share the same candidate pair. (3) If a pair is found, eliminate those two digits from all other cells in the same unit. This elimination often reduces another cell to a single candidate (triggering a Naked Single), leading to a chain of further progress.

The Naked Pair concept extends to three cells. A Naked Triple occurs when three cells in the same unit have candidates that are subsets of the same three digits. For example, if three cells have candidates {2,5}, {2,8}, and {5,8} respectively, they form a Naked Triple of {2,5,8}. These three digits cannot appear in any other cell in that unit.

The right time to look for Naked Pairs is after Naked Singles and Hidden Singles have been exhausted. When every cell has 2 or more candidates remaining and no cell can be confirmed, Naked Pair elimination becomes the breakthrough. Units with many cells having exactly two candidates are particularly likely to contain Naked Pairs.