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(8): Solution, my legs are getting tired too, I'm second in line by Hugo)

Hugo,

At first I, too, took it to mean that the tie-breaking game was to be played to 7-points.  But in this problem, the limit imposed is a 13th game  -- 7th winning game for the winner of the set. 

I guess if the 7-point limit was imposed on EACH game and not the set, tomarken's calculations as to the point difference would be correct.

I will point out the title to this problem is Lazy Tennis.  The title suggest that the game is played with the "No Ad" variation of the game.  Following the rules of tennis for this variation, each game is played to 4 points (a win can be by 1 point).

Edited on March 27, 2006, 5:27 pm

Posted by Dej Mar on 2006-03-27 16:45:14