A Three-Topic Ramsey Minimum

★ 8/10combinatorics Graph Theory Pigeonhole Casework

Problem

In a seminar of $n$ students, three problems $A$ , $B$ , $C$ are discussed. Every pair of students discusses exactly one of the three problems. Find the minimum value of $n$ that guarantees there exist at least $3$ students who pairwise discussed the same problem, and prove your answer.

Answer

Solution

Difficulty	8/10
Topics	combinatorics, Graph Theory, Pigeonhole, Casework

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