1. The problem statement, all variables and given/known data 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. 2. Relevant equations N/A 3. 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!