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Thursday, September 06, 2007




New approach to the topology/combinatorics problem:

Suppose we have two sets: (x1, x2, ... , xm) and (y1, y2, ... , yn) where m, n are positive integers, and we have a collection P of ordered pairs of the form (xj, yk) where 1 <= j <= m, 1 <= k <=n.

There are m*n possible ordered pairs of this form, and therefore 2^(m*n) possible collections. But suppose we add the following restriction: For any k between 1 and n, there exists j between 1 and m such that (xj, yk) is an element of P. In other words, every element of the second set has to be used in at least one ordered pair.

How many possible collections are there that satisfy this stipulation?

Saturday, September 01, 2007




This evening I caught a praying mantis. Now I must feed it things.

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