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, Standing on the shoulders ofTomarken, who is standing on the shoulders of about.com, who is... by Hugo)

For the sake of completeness, assuming the problem intended a first to 7 tiebreaker without the requirement that you win by two, it would seem to change the solution to:

L - W = 17.5x - 6.5

Since x is always odd, those ugly .5's will disappear when it is solved. :)

In the case of the 5-set match the solution would now be 81 (the earlier solution was 78), which shows the difference when the winning player wins the 3 tiebreakers 7-6 as opposed to 8-6 as I first assumed.

Posted by tomarken on 2006-03-27 11:48:18