How can we try to prove that among any 9 people thare are 3 people who are familiar with each other or 4 who are not familiar with each other?
My approach:
I try to convert this to graph theory. So I have a graph with 9 vertices which is clique. Now we try to point the graph edges into 2 colors. When we show that there always exist 3-clique or 4-clique in the same color in this graph then the statement will be proved. But how to start considering the graph?