In a game of tennis, the player who puts in the most effort in a match, and wins the majority of points, does not necessarily win the match as a whole.

Imagine two tennis players compete in a 5-set match, with each set following the scoring system of tennis, and a first to 7 point tie-break takes place if the score in a set is 6 games each. Let the total number of points won by the person who wins the match be represented by W, and let the total number of points won by the person who loses the match be represented by L.

If by the end of the match L-W is equal to a POSITIVE integer, then what is the maximum value this integer can be? Furthermore, develop an equation to determine the integer formed from L-W for a match of x number of sets.

Note: Enough information regarding the scoring system in tennis required to solve the problem, can be found at http://tennis.about.com/cs/beginners/a/beginnerscore.htm

Apparantly, I should do further research before I post.

In the USTA rulebook, the "No-Ad procedure is simply what the name implies; the first player to win four points wins the game, with the seventh point of a game becoming a game point for each player." And, a "tournament electing to use no-ad scoring must announce the election before the start of the tournament"
or "when in the referee's discretion the change is necessary".
 
As the problem states that the "7-point tie-break takes place if the score in a set is 6 games each", the No-Ad variation would not have been implemented. Thus, tomarken is correct.  The maximum difference won by the loser over the winner is 78 points

Posted by Dej Mar on 2006-03-29 20:29:05