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I think the first paragraph just clouds the principle behind this analysis. The second paragraph is in some sense the "dual" of the first, but does much more clearly illustrate the point. In fact, I think the second paragraph could be phrased as a general rule, as follows:

Rule: If there are two numbers that can only go in (the same) two locations, all other numbers can be eliminated as possibilities in these two locations.

Example: The numbers {1,9} in locations (3,9) in the above example.

Generalization: If there are N numbers that can only go in (the same) N locations, all other numbers can be eliminated as possibilities in these N locations.

One could call this a "pigeonhole principle" of sorts, which would be an analogy with the term used in mathematics about one-to-one functions over finite sets. Derkire (talk) 20:27, 9 February 2008 (UTC)