## Exclusive triple solve

First let's restate the basic premise.
Look at all the unsolved cells in a row (or column or region).
For every combination of three of the unsolved values for the row (or column or region)
look for cells that have just two or three possible values and
where all of that cell's possible values occur within the combination's three values.
If there are three such cells then we have an exclusive triple
and all occurrences of this combination's 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.

Our exclusive triple (1,2,5) appears in cells 7, 8 & 9 of the bottom row.
So why does this now preclude 1, 2 & 5 from being solutions to other cells?
Well, suppose 1 was the solution to any of cells 1, 4 or 5 of the bottom row.
Any of these senarios would exclude 1 from being the solution to cells 7 & 9 of the bottom row.
This, in turn, would make 5 the only remaining possible value for cell 7, and
2 the only remaining possible value for cell 9 (bottom line).
This is turn removes 2 & 5 as possible values for cell 8 (bottom line), and leaves this cell
with no possible values, which is clearly a nonsense.

Therefore, you can remove the possible values 1, 2 & 5 from cells 1, 4, 5 & 6
of the bottom line. Because the exclusive triple is also part of the righthand region,
you can also remove 1, 2 & 5 from cell 9, top row and cell 8, middle row.
However, it is rare for an exclusive triple to form the intersection of a row (or column)
and a region (about 1 in 28 times on average).