Question

Show that in any group of people, two of them have the same number of friends in the group. (Some important assumptions here: no one is a friend of him- or herself, and friendship is symmetrical—if x is a friend of y then y is a friend of x.)

Answer 1

Answer:

Step-by-step explanation:

Let us assume there are n people in the group.  If possible let each have different number of friends.

Number of friends can vary from 0 to n-1 only since no one is a friend of him- or herself, and friendship is symmetrical—if x is a friend of y then y is a friend of x.)

Now n people have friends as 0,1,2...n-1 such that each has distinct number of friends.

But say if A has 0 friends, it means A has no friend,

but there is one B who has n-1 friends i.e. all the others in the party are friends to him including A

This is a contradiction.  So it follows in any group of people, two of them have the same number of friends in the group.