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?
Solution
