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)

Ah, but I must again refer you to my earlier post (when I was only stepping on your head - now I'm dancing, too!)

You cannot win a tennis game 4-3.  Another quote from the about.com article (my comments in bold):

"...A wins the next point: "40 - 30." (3-2)

If A wins the next point, she wins the game. (4-2)

If B wins the next point, the score is "40 all," (3-3) which is called "deuce." At deuce, one player must win the next two points to win the game. If, at deuce, A wins the next point, she has the advantage, and the score is called "ad in," which means server's advantage. If B had won that point, the score would have been "ad out." If the player having the advantage wins the following point, he or she wins that game. If the player with the advantage loses the point, the score returns to deuce."

Hmm...this is hilariously embarrassing.  Reading on, I find:

"With traditional scoring, games can go back and forth from deuce to ad over and over. The "No Ad" variation on the scoring within games allows for a game to be won by a margin of one point. Instead of "15," "30," and "40" used to note points, players may use "1," "2," and "3." At "3 all," the receiver may choose whether to receive in the left or right service box. The winner of that point wins the game."

Well, then, I guess we were both right!  Perhaps the problem should have more clearly defined which version of tennis we were playing.  Oddly enough, the author refers us to the about.com article to find the "scoring system in tennis", and yet that very article presents two conflicting versions.  Oh well, obviously I've never heard of the "No Ad" variation, which is the one you so elegantly solved. :)  Deuce!

Posted by tomarken on 2006-03-27 15:42:03