A box contains three pairs of socks colored red, blue, and white, respectively. Suppose I take out the socks without looking at them. How many socks must I take out to be sure that they will include a matching pair?
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Consider a flock of pigeons nestled in a set of nn pigeonholes. If there are nn pigeons, then it is possible for all of the pigeons to rest happily in separate pigeonholes. However, if at least one more pigeon arrives, making a total of more than nn pigeons, then at least one of the pigeonholes, inevitably, will end up with more than one pigeon.
The idea that having more pigeons than pigeonholes requires a pigeonhole with more than one pigeon is seemingly trivial, but it turns out
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