Enigma 1501: Five sets at Wimbledon
22 October 2012
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From New Scientist #2663, 5th July 2008
A men’s singles match at Wimbledon is won by the first player to win three sets. A set is won by the first player to win six games unless the score reaches 5-5; in that case, in the first four sets the set will be won 7-5 or 7-6 (but no set in our match was won 7-6), and in the fifth set play goes on until one player is two games ahead. The longest fifth set in Wimbledon history was won 28-26. Players serve in alternate games.
Our Wimbledon match went to five sets. The number of games in each set was different; the number of games won by the server in each set was different; the percentage of games won by the server in each set was different but was always an integer. Over the whole match exactly half of the games were won by the server.
What was the score in the final set, and how many games in that set were won by the server?
Note: In Wimbledon 2010 the Isner-Mahout match went to 70-68 in the final set (and broke the scoreboard).