Explain why there may not be $3$ people with same car.

Question

I don't really understand how to apply Ramsey Theory or the Pigeonhole Principal, so I can't see why this is true:

There are $100$ people at a party.

Assume each person has an even number of cars, possibly zero but no more than $98$ (super rich people).

Can anyone explain why there may not be three people with the same number of cars?

Answer 1

There are $50$ possible numbers of cars. If each number applies to $2$ people, that's $100$ people accounted for.