Question

Prove that at a party where there are at least two people, there are two people who know the same number of other people there.

Answer 1

OK, there are 2 people and each does not know the other

Answer 2

why u can prove it

Answer 3

Can't be proved, because it is NOT TRUE.
Line up the people in a row, and imagine that everybody knows everyone to their right and doesn't know anybody to their left. Then no two people know the same number of people.

Answer 4

If you assumed that everybody at the party knows at least one other person, then you can prove it by the pigeon hole principle:
Let N be the number of people at the party. The number of people a person knows is a number from 1 to N-1. Since there are more people than there are possible numbers of acquaintances, there must be two people who have the same number of acquaintances.

Answer 5

pigeon hole for this one'
oh, what @abayomi12 said, assuming that if person x knows person y then person y knows person x

Answer 6

also it is possible that one person knows no one, so you have to be a little careful
but if person x knows no one, then we assume no one knows person x, in which case the number of people a person can know at the party are 0 to n - 2, and the principle still applies