## Exclusive pair solve

First let's restate the basic premise.
Look at all the unsolved cells in a row (or column or region).
Look for two of these cells that have exactly the same two possible solutions.
If such a pair is found, then all occurrences of these possible values can be
eliminated from the *other* unsolved cells in the same row / column / region.

Why should this be so?
The simplest way to show this is with an example.
Suppose we have this situation for a set of nine cells.

Our exclusive pair (1,9) appears in cells 1 and 5.
So why does this now preclude 1 and 9 from being solutions to other cells?
Well, suppose 9 was the solution to either cell 8 or cell 9.
Either of these senarios would exclude 9 from being a solution to cells 1 and 5.
This would leave these two cells (1 & 5) with just one possible solution - 1.
Clearly this is a nonsense, as whichever of these cells you choose to put 1 in
leaves the other cell with no possible solution.
A similar situation occurs if you suppose 1 as the solution to either cell 8 or cell 9.

Therefore, you can remove both 1 and 9 as possibles value from cells 8 & 9.
For this particular example this does not immediately solve a cell.
However, you now have another exclusive pair (5,8) in cells 8 and 9
and this may lead to further eliminations in that region.