Yes we can prove that in the group of more than two people that there are at least two people that have the same number friends given the condition here.
Let us create a variable P. P is an individual called Joe. Now Joes seems to know all at this party. This tells us that all at this party should at least know him.
We have the set {1,2,...n-1} , given that the minimum number of persons that one person knows is 1.
Let us assume we have Harry. Harry is a party crasher who came to the party. Hence it is possible that someone like Joe that knows all at the party may not even know him. Hence the maximum persons that a person would know is given to be n. The set would then be {0, 1,...,n-2}.
There are n elements in the 2 sets that we have above. Given that n people are at this function, and there are n possibilities for the number that one person can know of the participants, then we can say that at least two people can then know equal number of persons at the party.
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