Thursday, December 23, 2010

Problems with Friends

A is a friend of B if and only if B is a friend of A.

Problem 1:
There are N people in the world, N > 1. Is it possible for everyone to have a unique number of friends?

A person is popular if none of his friends have more friends than him.
A person is a loner if none of his friends have less friends than him.

Problem 2:
In general, are there more loners or popular people?

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