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(6): Solution, stepping on Dej Mar's head :) by tomarken)

Again I posted without fully confirming my own figures....You are right, the winner does not score 31, but 28...but the loser scores 45 not 48...(I was in the middle of correcting my posting when you apparently posted).  But here is a breakdown of the match as I see it....

Set 1, Game  1: W=0, L=4
Set 1, Game  2: W=0, L=4
Set 1, Game  3: W=0, L=4
Set 1, Game  4: W=0, L=4
Set 1, Game  5: W=0, L=4
Set 1, Game  6: W=0, L=4
 
Set 2, Game  1: W=0, L=4
Set 2, Game  2: W=0, L=4
Set 2, Game  3: W=0, L=4
Set 2, Game  4: W=0, L=4
Set 2, Game  5: W=0, L=4
Set 2, Game  6: W=0, L=4
 
Set 3, Game  1: W=0, L=4
Set 3, Game  2: W=4, L=3
Set 3, Game  3: W=0, L=4
Set 3, Game  4: W=4, L=3
Set 3, Game  5: W=0, L=4
Set 3, Game  6: W=4, L=3
Set 3, Game  7: W=0, L=4
Set 3, Game  8: W=4, L=3
Set 3, Game  9: W=0, L=4
Set 3, Game 10: W=4, L=3
Set 3, Game 11: W=0, L=4
Set 3, Game 12: W=4, L=3
Set 3, Tie-Bkr: W=4, L=3
 
Set 4, Game  1: W=0, L=4
Set 4, Game  2: W=4, L=3
Set 4, Game  3: W=0, L=4
Set 4, Game  4: W=4, L=3
Set 4, Game  5: W=0, L=4
Set 4, Game  6: W=4, L=3
Set 4, Game  7: W=0, L=4
Set 4, Game  8: W=4, L=3
Set 4, Game  9: W=0, L=4
Set 4, Game 10: W=4, L=3
Set 4, Game 11: W=0, L=4
Set 4, Game 12: W=4, L=4
Set 4, Tie-Bkr: W=4, L=3
 
Set 5, Game  1: W=0, L=4
Set 5, Game  2: W=4, L=3
Set 5, Game  3: W=0, L=4
Set 5, Game  4: W=4, L=3
Set 5, Game  5: W=0, L=4
Set 5, Game  6: W=4, L=3
Set 5, Game  7: W=0, L=4
Set 5, Game  8: W=4, L=3
Set 5, Game  9: W=0, L=4
Set 5, Game 10: W=4, L=3
Set 5, Game 11: W=0, L=4
Set 5, Game 12: W=4, L=3
Set 5, Tie-Bkr: W=4, L=3
========================
Match Total   :W=84 L=183
 
L - W = 183 - 84 = 99

Edited on March 27, 2006, 3:24 pm

Posted by Dej Mar on 2006-03-27 15:14:06