Aligned Pair Exclusion

The Aligned Pair Exclusion technique applies to a pair of cells lying at the intersection of a box and a column, or a box and a row. In this technique, all combinations of candidates for a pair are checked. If there is a cell that sees the both cells of the pair and which have exactly two candidates that the pair might have, then this combination for this pair is not allowed. If for a certain digit in one cell of the pair all combinations are not allowed, this candidate is eliminated from this cell.

In the following sudoku diagram for the pair R8C3 and R9C3 all possible combinations of candidates are:

• 1-2
• 1-6
• 1-7
• 2-2 (invalid)
• 2-6 (conflicted with R1C3)
• 2-7 (conflicted with R9C1)

The pair 2-2 is not allowed for obvious reasons. If the pair were set to 2-6, all possible candidates would be eliminated from the R1C3 cell. A similar situation occurs with pair 2-7 and the cell R9C1. As we can see, all combinations with the digit 2 in the R8C3 cell have been eliminated. Thus, we can eliminate the digit 2 from this cell. After this elimination, only the digit 1 can be placed in the R8C3 cell.