January 2005

Friends or strangers?

## Party people

Is it possible to hold a party at which no two people have the same number of friends as each other?

If you are stumped by last issue's puzzle, here is the solution.

For some challenging mathematical puzzles, see the NRICH puzzles from this month or last month.

## Comments

## Graph Theory

This is a great question. Without giving away the answer ( if you don't have it yet avert your eyes), the question is solvable using graph theory.

Let each person at the party be a vertex. Form an edge between two people if they are friends. Now think about using the pigeon-hole principle.