I'm preparing myself to a combinatorics test. A part of it will concentrate on the pigeonhole principle. Thus, I need some hard to very hard problems in the subject to solve. I would be thankful if you can send me links\books\or just a lone problem.
Show me some pigeonhole problems
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$\begingroup$
combinatorics
problem-solving
big-list
pigeonhole-principle
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2This will be very difficult to answer since "hard to very hard" is not well-defined if we don't know more about your background. To start, have a look at these: http://jan.ucc.nau.edu/~mk84/226/worksheets/pigeonholesol.pdf and http://www.math.utah.edu/mathcircle/notes/pigeon.pdf. Are these too easy? Are they suitable? – 2012-09-11
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0These aren't so taugh.. – 2012-09-13
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0Here's one: http://en.wikipedia.org/wiki/File:TooManyPigeons.jpg – 2014-01-16
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0Duplicate of http://math.stackexchange.com/q/430116/18398 – 2014-01-16