Enigma 1678: Tennis tournament
21 December 2011
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From New Scientist #2844, 24th December 2011 [link]
My tennis club held a knockout tournament, in which eight players competed. The two losers of the semi-finals played a match to decide 3rd and 4th places. Matches were decided by the best of five sets, with the match ending once a player had won three sets. Two matches had to be abandoned due to poor weather. When this happened the winner was the player who had won the most completed sets when the match was abandoned – luckily this didn’t lead to a draw on either occasion.
At the end of the tournament no two players had played the same number of sets, and all players except the winner had lost more sets than they had won.
How many sets were played overall?