**From New Scientist #2633, 8th December 2007**

In tennis a set is won by the first player to win 6 games unless the score reaches 5-5; in that case the set is won 7-5 or 7-6.

At Wimbledon the first batch of tennis balls is used for the warm-up and the first seven games; each subsequent batch of balls is used for nine games.

This means that during the second set there are certain scores at which it is impossible for a new batch of balls to be required, whatever the score in the first set may have been.

Dick wants to be a Wimbledon umpire and practiced by umpiring the match between Harry and Tom. But three times during the second set he called for new balls at scores at which it is impossible for them to be required.

The number of games that Tom had won in the second set was the same when Dick made the third of those calls as when Dick made the second of them.

What was the score in the second set at the time of (a) the first wrong call, (b) the third wrong call? Give each answer in the form *x*–*y*, Harry’s score first.

[enigma1472]

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The following Python program runs in 40ms.

Solution:The scores are: (a) 0-2; (b) 6-5.