Pigeonhole principle

In mathematics, the pigeonhole principle states that if  items are put into  containers, with , then at least one container must contain more than one item. For example, if one has three gloves, then one must have at least two right-hand gloves, or at least two left-hand gloves, because one has three objects, but only two categories of handedness to put them into. This seemingly obvious statement, a type of counting argument, can be used to demonstrate possibly unexpected results. For example, given that the population of London is greater than the maximum number of hairs that can be present on a human's head, then the pigeonhole principle requires that there must be at least two people in London who have the same number of hairs on their heads.


In mathematics, the pigeonhole principle states that if items are put into containers, with , then at least one container must contain more than one item. For example, if one has three gloves, then one must have at least two right-hand gloves, or at least two left-hand gloves, because one has three objects, but only two categories of handedness to put them into. This seemingly obvious statement, a type of counting argument, can be used to demonstrate possibly unexpected results. For example, given that the population of London is greater than the maximum number of hairs that can be present on a human's head, then the pigeonhole principle requires that there must be at least two people in London who have the same number of hairs on their heads.
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