One popular demonstration of this is the fact that there are at least two people in New York City with the exact same number of hairs on their heads.

This isn’t some wishy-washy “they probably have the same number of hairs” or “there is a 99.99% chance that they do.” This is a cold hard fact: I know that there are at least two people in NYC that have the same number of hairs on their heads.

How am I so certain?

Think of the possible number of hairs on your head as boxes that we will place people in. If you have 1 hair on your head, you get placed on one box with all the other single-haired people. If you have 2 hairs on your head, you get placed in a box with all the other 2-haired people, and if you have 87,693 hairs on your head, you get placed in a box with all the other 87,693-haired people

How many boxes do we have? Depending on who you ask, the average number of human head-hairs is somewhere between 100,000 and 150,000. Given this, I think it is reasonable to establish 1,000,000 as a hard upper bound. So we have a million boxes.

And how many people do we have? The population of NYC is roughly 8.5 million.

So We are going to hypothetically place 8,500,000 people into 1,000,000 boxes.

# of people > # of boxes, so there must be at least one box with more than one person in it. Hence, there are at least two3 people in NYC with the exact same number of hairs on their heads.