In the June/July issue of 1958, the American Mathematical Monthly has such a topic:?

"prove that at any party of six people, or three people have known each other before, or three people have not known each other before." ?

This problem can be proved simply and clearly in the following ways:?

On the plane, six points, A, B, C, D, E and F, respectively represent any six people attending the meeting. If two people have known each other before, then connect a red line between the two points representing them; Otherwise, connect a blue line. Consider the AF between five connecting lines AB, AC, ..., A and other points, with no more than two colors. According to the pigeon hole principle, at least three lines have the same color, so let AB, AC and AD be red. If a line in BC, BD and CD3 is also red, then the triangle ABC is a red triangle, and the three people represented by A, B and C have known each other before; If the lines BC, BD and CD3 are all blue, then the triangle BCD is a blue triangle, and the three people represented by B, C and D have never known each other before. No matter what happens, it is consistent with the conclusion of the problem.