A puzzle by Polish mathematician Paul Vaderlind:
Andre Agassi and Boris Becker are playing tennis. Agassi wins the first set 6-3. If there were 5 service breaks in the set, did Becker serve the first game?
(Service changes with each new game in the 9-game set. A service break is a game won by the non-server.)
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If there were 9 games in the set, then one player served 4 games and one served 5. Suppose Agassi served 4 games and Becker had k service breaks. That would mean that Agassi won 4-k of the games in which he served, and 5-k of the games in which Becker served (because there were 5 service breaks altogether). Then Agassi would have won a total of (4-k) + (5-k) = 9-2k games, an odd number. But we know that Agassi won 6 games, so this is a contradiction. Hence Agassi must really have served 5 rather than 4 games, and therefore he served the first game.
From The Inquisitive Problem Solver, 2002.
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