Math Trivia:The Pigeonhole Principle & Understanding The World
Here’s a light-hearted trivia post for the Thanksgiving holiday. Click Here To Read About The Remaining Trivia.
Article Introduction (Via Mind Your Decisions)
The pigeonhole principle is a powerful tool used in combinatorial math. But the idea is simple and can be explained by the following peculiar problem.
Imagine that 3 pigeons need to be placed into 2 pigeonholes. Can it be done? The answer is yes, but there is one catch. The catch is that no matter how the pigeons are placed, one of the pigeonholes must contain more than one pigeon.
The logic can be generalized for larger numbers. The pigeonhole principle states that if more than n pigeons are placed into n pigeonholes, some pigeonhole must contain more than one pigeon. While the principle is evident, its implications are astounding. The reason is that the principle proves the existence (or impossibility) of a particular phenomenon.
Article Summary (Via Mind Your Decisions)
1. For every 27 word sequence in the US constitution, at least two words will start will the same letter.
2. In New York City, there are two non-bald people who have the same number of hairs on their head.
3. Imagine a certain college has 6,000 American students, at least one from each of the 50 states. Then there must be a group of 120 students coming from same state.
4. In any cocktail party with two or more people, there must be at least two people who have the same number of friends.
