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" for the total number of people at the party when writing your answer.

Question

Mathematics

Aditya Sims

5 November, 23:10

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" for the total number of people at the party when writing your answer.

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Answers (1)

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Raelynn Preston · Answer 1

Step-by-step explanation:

Given that at a party there are at least two people.

We have to prove that there are two people who know the same number of other people there

Let n>2 be the no of people there

If possible let us assume each person knows different number of persons

The number of persons any one knows can vary from 0 to n-1

Hence these n people will have 0,1,2 ... n-1 persons known.

Consider the last person who knows n-1 people this means that he knows everyone in the party. So there cannot be any one who does not know any one or with known persons number as 0.

Thus we get a contradiction.

So there must be atleast two people who know the same number of people