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.

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## 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.