A puzzle by the Hungarian-Canadian mathematician George Grätzer:
I’m writing an article about a round-robin tennis tournament, in which each player plays each other player once. I decide to pick one player and ask her which players she defeated (in tennis there are no ties). Then I’ll ask each of those players which players they’ve defeated. Is it possible to pick a player so that everyone in the tournament is mentioned in my article?
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Yes. The simplest solution is to choose the tournament’s winner, A. Because she won, we know that no other player won more matches than she did. Now suppose I finish all my interviews and find there’s some player B I haven’t spoken with. By the rules of my own plan, that will mean that B lost neither to A nor to any of the players whom A defeated. But because there are no ties, that would mean that B won all those matches. And that would give B a higher total score than the tournament winner, a contradiction. So A must fulfill the condition.
(From Train Your Brain, 2011.)
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