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I really liked BruceZ's inclusion-exlusion post... It might not be the most insightful, but I hope that by mentioning it he'll appear like a magic genie and post a link [img]/images/graemlins/smile.gif[/img] (I'm too lazy to search, and too lazy to PM him, so I guess if I never see the post again it'll be my own damn fault)
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The second most beautiful counting method in combinatorics:
Inclusion-Exclusion