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Tennis Balls (Posted on 2008-01-29) Difficulty: 3 of 5
In tennis a set is won by the first player to win 6 games unless the score reaches 5-5, in which case the set is won 7-5 or 7-6.

At Wimbledon the first batch of tennis balls is used for the warmup and the first 7 games. Each subsequent batch of balls is used for 9 games. As a result of these rules, there are certain scores during the course of play of the second set, that, if this procedure is followed, a new batch of balls would never be called in upon being reached.

Dick was officiating at a match which he called for a new batch of balls in the second set at three points among these occasions when supposedly a new batch of balls could never be appropriate, as described in the preceding paragraph.

The two competitors were Tom and Harry, and the number of games that Tom had won in the second set was the same at the times of the second and third of these three "impossible" calls for new balls.

What was the score at each of the times that Dick called for new balls when in theory he should never call for them at such scores?

See The Solution Submitted by Charlie    
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Hints/Tips re: Solution | Comment 2 of 3 |
(In reply to Solution by Dej Mar)

Since the calls for balls are supposed to occur at the end of 7, 16 and 25 games, if there were 6 games in the first set there could legitimately be a call for balls after the 10th game of the second set, so a score of 5-5 is not a theoretically impossible score on which to call new balls.

Likewise if there were 13 games in the first set, there could legitimately be a call for balls after the 12th game of the second set, as when the score is 6-6.

Are you sure that every number of games from 6 to 13 is possible for a complete first set?

  Posted by Charlie on 2008-01-30 15:53:30
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