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

(In reply to re(5): Solution, trying to lift tomarken back up by Dej Mar)

How can the winner score only 31 points in the sets he wins?  If he wins the set 7-6, assuming the losing player scores the maximum possible points, you can have these results:

In each of the 6 games the winner loses, he scores nothing.

In the tiebreaker he scores 7 points.

Here's where you're off: In each of the 6 games he wins, he scores 5 points (to win 5-3).  You could say he scores 4 points to win 4-2, BUT if you want to adjust the winner down to 4 points per game won (leading to the 31 solution), you have to also adjust the loser down to 2 points per game lost.  Either way it is a two-point difference, which doesn't change my original solution. 

Posted by tomarken on 2006-03-27 13:35:21