Thread: Interesting Question

I am working on some supplemental math problems and this question has me boggled. Any push in the right direction would be appreciated on how to start this.

Show that in a group of five people (where any two people are mutual friends or enemies) there are not necessarily three mutual friends or three mutual enemies.

Originally Posted by vexiked

I am working on some supplemental math problems and this question has me boggled. Any push in the right direction would be appreciated on how to start this.

Show that in a group of five people (where any two people are mutual friends or enemies) there are not necessarily three mutual friends or three mutual enemies.

You just have to come up with an example that shows this can happen.

Here is an alternative formulation that you may find useful: Suppose you have a graph with 5 nodes, in which every node is connected to every other node. See if you can find a way to color the arcs with two colors (red and blue, say) so that there is no triangle (three nodes and their connecting arcs) with all its arcs the same color.

The 5 nodes correspond to the 5 people and the colors correspond to friendship or its opposite.