# A little bit of math…

I was in my Linear Algebra class today and my most favorite theorem/principle happened to come in class for a brief moment. It is called The Pigeon Hole Principle. Now, for you who are not familiar with it, here is a simple approach to understanding it (although, once you work with it a couple times it sticks like glue):

Let’s assume that n is the number of pigeons and m is the number of holes, hence the “Pigeon Hole” part of the title. Now, as long as m < n, meaning there are less holes than pigeons, then we know that there must be at least two pigeons in one hole.

For example, we have six pigeons and five holes. If five of the pigeons fill up all five holes, there is still one pigeon left over, correct? Then that one must buddy up and share a hole with someone else.

The main reason I love this is because you can know that in a room of 500 people, there are at least two people who share the same birthday. You can also know that in NYC alone, there are at least two people who have the same number of hairs on their heads. The human head has around 140,000 hairs, but there are around 8.5 million people living in NYC. Taking the number of hairs as “holes” and the human heads as “pigeons” we see there are way more pigeons than holes. Therefore, without even counting a single hair on a single head, we can already determine this to be true. Amazing, right?!

I just thought I would share this little mathematical tidbit with you since I thought it was pretty cool. You can even dazzle your kids’ minds with telling them the NYC/hair fact!

Until next time…

~ Kristen

Posted on October 29, 2014, in Math, Uncategorized and tagged math, pigeon hole, principle, The Pigeon Hole Principle, theorem. Bookmark the permalink. Leave a comment.

## Leave a comment

## Comments 0