Pigeon Principle

In mathematics and computer science, the pigeonhole principle states that if n items are put into m pigeonholes with n > m, then at least one pigeonhole must contain more than one item. This theorem is exemplified in real-life by truisms like "there must be at least two left gloves or two right gloves in a group of three gloves". It is an example of a counting argument, and despite seeming intuitive it can be used to demonstrate possibly unexpected results; for example, that two people in London have the same number of hairs on their heads (see below).

Hair-counting
One can demonstrate there must be at least two people in London with the same number of hairs on their heads as follows.[9] Since a typical human head has an average of around 150,000 hairs, it is reasonable to assume (as an upper bound) that no one has more than 1,000,000 hairs on their head (m = 1 million holes). There are more than 1,000,000 people in London (n is bigger than 1 million items). Assigning a pigeonhole to each number of hairs on a person's head, and assign people to pigeonholes according to the number of hairs on their head, there must be at least two people assigned to the same pigeonhole by the 1,000,001st assignment (because they have the same number of hairs on their heads) (or, n > m). For the average case (m = 150,000) with the constraint: fewest overlaps, there will be at most one person assigned to every pigeonhole and the 150,001st person assigned to the same pigeonhole as someone else. In the absence of this constraint, there may be empty pigeonholes because the "collision" happens before the 150,001st person. The principle just proves the existence of an overlap; it says nothing of the number of overlaps (which falls under the subject of probability distribution).

There is a passing, satirical, allusion in English to this version of the principle in A History of the Athenian Society, prefixed to "A Supplement to the Athenian Oracle: Being a Collection of the Remaining Questions and Answers in the Old Athenian Mercuries", (Printed for Andrew Bell, London, 1710).[10] It seems that the question whether there were any two persons in the World that have an equal number of hairs on their head? had been raised in The Athenian Mercury before 1704.[11][12]

Perhaps the first written reference to the pigeonhole principle appears in 1622 in a short sentence of the Latin work Selectæ Propositiones, by the French Jesuit Jean Leurechon,[2] where he wrote "It is necessary that two men have the same number of hairs, écus, or other things, as each other."[13] The full principle was spelled out two years later, with additional examples, in another book that has often been attributed to Leurechon, but may have been written by one of his students.[2]

link:https://blog.csdn.net/rauber_hotzenplotz/article/details/7072475
https://en.wikipedia.org/wiki/Pigeonhole_principle#Hair-counting