Pigeonhole Principle
According to the Wikipedia, the Pigeonhole principle is...
In mathematics, the pigeonhole principle states that if n items are put into m containers, with n > m, then at least one container must contain more than one item. [^1] For example, if one has three gloves (and none is ambidextrous/reversible), then there must be at least two right-handed gloves, or at least two left-handed gloves, because there are 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.
Birthday Problem
The birthday problem is a special case of the pigeonhole principle. It states that in a set of n randomly chosen people, the probability that two of them will have the same birthday is more than half, provided n is more than 23.
This unexpected result can be explained by the pigeonhole principle,
which asserts that if n items are put into m containers,
with
References
Web Links
- Pigeon hole principle (from Wikipedia, the free encyclopedia)
- Birthday Problem (from Wikipedia, the free encyclopedia)
Note Links
Textual References
[^1]: Herstein, I. N. (1964), Topics In Algebra, Waltham: Blaisdell Publishing Company, ISBN 978-1114541016