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Subset Exclusion

The name Subset Exclusion is not commonly used in the Sudoku community. This article is created as a bridge between Aligned Pair Exclusion and Death Blossom.

Aligned Pair Exclusion can be extended to Aligned Triple Exclusion and so on. In fact, the set of cells to be enumerated does not need to be aligned at all. Lacking a better name, let us call the resultant technique Subset Exclusion.

Example

image:SubsetExclusion.png

We can enumerate the possible combinations of the blue cells as in Aligned Pair Exclusion. The following list shows the possible combinations, from top to bottom:

5+2+4
5+2+6
5+6+4
5+7+4*
5+7+6*
5+9+4*
5+9+6*
7+2+4
7+2+6
7+6+4
7+9+4
7+9+6

The starred combinations are those that causes any of the yellow cells to have no candidates at all, so these combinations can be removed from the list. As a result, we find that 7 can be eliminated from r2c4.

Death Blossom

The Death Blossom technique is actually an instance of Subset Exclusion where all but one of the cells to be enumerated falls neatly into Almost Locked Sets.

This page was last modified 11:08, 25 November 2006.