Prove:
- Every collection of 6 people contains a group of 3 friends or a group of 3 strangers.
- The shortest closed walk is a cycle.
(Don't have any idea how I will solve the first statement. For the second statement I just say that if there is a closed walk keep removing repeated edges. For example if $r----r$ was repeated in between the walk then keep removing it and you'll end up with a shorter closed walk - Till a point where it can't become any shorter. The end result is a cycle.)