olymmath

KURSCHAK 1954 Problem 3

    A tournament is arranged amongst a finite number of people. Every person plays every other person just once and each game results in a win to one of the players (there are no draws). Show that there must a person XX such that, given any other person YY in the tournament, either XX beat YY , or XX beat ZZ and ZZ beat YY for some ZZ .

    Dataset text AI-MO AoPS. Quoted with source.

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