Question

**My Professor asked us to write ONE paragraph explaining our reasoning/why we chose whichever argument**

New York is one of the largest cities in the world. There has been a debate as to whether you can find two people in New York with the same number of hair on their head.

Take only one of two positions.

1. If you agree that there exists two people with the same number of hair, present a sound argument for this position.

2. If you do not agree that there exists two people with the same number of hair, present a sound argument for this position.

Answer 1

Agree and example given

Proof

First of all we need to make some assumptions, using information which is already available. We need to know how many people there are in London (Around 7.5 million people not counting anyone who is bald.) We also need to know how many hairs people have on their heads. (People have somewhere between 1 and 150,000 hairs on their heads, also ignoring anyone who is completely bald.)

We therefore have up to 150,000 choices for the number of hairs people have on their heads. We have 7.5million people to spread out amongst these options. 7.5 million divided by 150,000 equals 50. There simply isn’t room for everyone to have a unique number of hairs on their head. In fact for at least one of the options, there will be at least 50 people who share that number of hairs!