Pigeonhole principle

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Complexity Level : Medium Last Updated : 08 Jun, Suppose that a assemble of 20 pigeons flies into a set of 19 pigeonholes to branch. Because there are 20 pigeons although only 19 pigeonholes, a least individual of these 19 pigeonholes must allow at least two pigeons in it. To see why this is accurate, note that if each pigeonhole had at most one pigeon in it, at most 19 pigeons, one apiece hole, could be accommodated. This illustrates a general principle called the brand principle, which states that if around are more pigeons than pigeonholes, after that there must be at least individual pigeonhole with at least two pigeons in it. The abstract formulation of the principle: Let X and Y be finite sets and let be a function.

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