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(7): Solution, dancing atop tomarken by Dej Mar)

Dej Mar, the tie-breaks are played until one of the players reaches 7 points, so it should be W=7, L=6 (or 5, rule dependent) and not W=4, L=3.

I am sticking up my right arm, carrying a long needle.  If anybody wants to get on top, beware!

Posted by Hugo on 2006-03-27 15:19:59