Problem 4
Seventeen people correspond by mail with one another, each with all the rest. In their letters only three different topics are discussed, and each pair of correspondents deals with only one topic. Prove that at least three people write to each other about the same topic.
Step 5 of 5: Interpret the triangle
Detailed analysis
A monochromatic triangle is three people whose three correspondence pairs all discuss the same topic. Therefore the required three people exist.