The party problem, also known as the maximum clique problem, asks to find the minimum number of guests that must be invited so that at least 
will know each other or at least 
will not know each other. The solutions are known as Ramsey
numbers.
Party Problem
See also
Clique, Cocktail Party Graph, Glove Problem, Handshake Problem, Ramsey NumberExplore with Wolfram|Alpha
References
Hoffman, P. The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth. New York: Hyperion, p. 52, 1998.Referenced on Wolfram|Alpha
Party ProblemCite this as:
Weisstein, Eric W. "Party Problem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PartyProblem.html