# Among Six People, Either Three Know Each Other or Three Are Strangers to Each Other

Among Six People, Either Three Know Each Other or Three Are Strangers to Each Other

Represent the six people as the vertices of a regular hexagon. Draw a blue segment between a pair of vertices if the corresponding pair of people know each other and otherwise draw a red segment. A triangle with all three sides of the same color is called monochromatic; fill in such triangles with the appropriate color. There is always a monochromatic triangle! Moreover, there are always two monochromatic triangles!