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My first proof employing the pigeonhole principle / dirichlet's box principle - very simple theorem on real numbers. Please mark/grade.

What do you think about my first proof employing the pigeonhole principle? What mark/grade would you give me? Besides, I am curious about whether you like the style. Theorem Among three elements ...
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Pigeonhole: Practical Applications in Computer Science

Most of the problems I've seen involving the pigeonhole principle have so far seemed fairly artificial. As I'm studying CompSci I'm interested what kind of practical, real world problems in CompSci ...