At least two participants in a meeting received the same number of phone numbers The question is: there are $n$ participants in a meeting ($n \geq 2$). During this meeting, people exchanged phone numbers with each other. Prove that at least $2$ participants received the same number of phone numbers.
I was thinking of solving it using contradiction. So somehow prove that at least $2$ participants doesn't receive the same number of phone numbers, or no one received the same number of phone numbers. Would that work?

How many numbers can a person get? Anywhere from $0$ to $n-1$ numbers.
If they all get a different number of numbers, then somebody must get $0$ numbers and somebody must get $n-1$ numbers. (Why?) Is that possible?
