Suppose one can solve a problem

[mafou]

Six people are in an elevator. Can you demonstrate that it must be the case that either at least three of them are mutual acquaintances or at least three are complete strangers to one another ?

[mafou]

While the solution that is called for is logically difficult, the problem has a readily understood graphical analogue. Let the six people in the elevator be represented by six dots on a piece of paper. (The dots can be positioned in any way,except that no three should be on the same line.) Let a solid line between any two dots represent axquaintances between the people represented by those dots, and let a dashed line indicate that the people are strangers. Now the question is, using either a solid line or a dashed line between any given pair of dots, is it possible to connect every dot with every other dot in such a way that no solid triangles and no dashed triangles appear in the result ?