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Um, yeah. Pigeonhole principle. Not exactly news...

http://en.wikipedia.org/wiki/Pigeonhole_principle

Any programmer who does not know this near-instinctively (and also related things like the impossibility of having distinct hash values for all strings) should be ashamed of himself and brush up on basic math.

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Additionally, a compression algorithm need only have a worst case of adding one extra bit in the case that it couldn't compress a file.

This post reminded me about the day when I invented a perfect compression algorithm ( http://www.diovo.com/2010/01/the-perfect-compression-algorit... )

'Near-instinctive' knowledge of this, before being exposed to the basic idea, would make a good marker for high intelligence, and one which I failed at (and I'm no slouch). Ask a few colleagues about it, and prepare to be disappointed!

I did mean "near-instinctive" to apply after having learned about the concepts of surjective, injective and bijective functions. These are so basic and important that I believe you can't be a professional programmer without having been exposed to them, and having them stick at an instinctive level.

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