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Mathematics

Ramsey Theory and the Party Problem

Quick fact

The party problem guarantees that among any six people, there always exist three who are all mutual acquaintances or three who are all mutual strangers. This is the Ramsey number R(3,3)=6, meaning no matter how you color the edges of a complete graph on six vertices with two colors, you cannot avoid a monochromatic triangle.

Why this is interesting

At any party with just six people, you are guaranteed to find either three mutual acquaintances or three mutual strangers—no matter how the social connections are arranged. How can we be so sure?