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## Homework Statement

Assume that every pair of people are (mutual) friends or enemies.

Show that in a group of 10 people, there are either 3 mutual friends or 4

mutual enemies.

Hint: Fix one person X. Start out by observing that X has either k friends

or 10-k enemies for an appropriately chosen k.

## Homework Equations

N/A

## The Attempt at a Solution

A proof was shown in class for the case where there are 6 people, that involved a K6 graph. Is there any way to do this problem without using a graph since a K10 graph is quite large?

Thanks!