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MathNet 2026 — Part 03 Question 28

Math Olympiad Vault · MathNet 2026 — Part 03

Question 28

Suppose that $n$ people each know exactly one piece of information, and all $n$ pieces are different. Every time person $A$ phones person $B$, $A$ tells $B$ everything that $A$ knows, while $B$ tells $A$ nothing. What is the minimum number of phone calls between pairs of people needed for everyone to know everything? Prove your answer is a minimum.