I recently had an assignment and got this question wrong, was wondering what I left out.
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. Be sure to use the variable "n" when writing your answer.
n >= 2 Case1: another person comes to the party, but doesn't know either of the first two. So the original two still only know the same number of people. Case2: another person comes, and knows one out of the original 2, so therefore the >newcommer, and the one that doesnt know the newcommer both know the same number of people. Case 3: another person comes and knows both of them, implying that they all know each >other, and therefore they all know the same number of people.
So therefore if n>=2, where n and n-1 know each other, in either case whether n+1 joins, >there will be at least two people who know the same amount of people.
Many thanks in advance. Have a test coming up.