MathDB
Tennis tournament

Source: KJMO 2023 P4

November 4, 2023
combinatorics

Problem Statement

20232023 players participated in a tennis tournament, and any two players played exactly one match. There was no draw in any match, and no player won all the other players. If a player AA satisfies the following condition, let AA be "skilled player".
(Condition) For each player BB who won AA, there is a player CC who won BB and lost to AA.
It turned out there are exactly N(≥0)N(\geq 0) skilled player. Find the minimum value of NN.
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