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

I would guess that for a five-set match, the max value of L-W would be 9, if the scoring went as follows:

Set 1: Player L wins 6-0
Set 2: Player L wins 6-0
Set 3: Player L loses 7-6
Set 4: Player L loses 7-6
Set 5: Player L loses 7-6

Player L won 30 games to the other player's 21, but still lost the match.

In general, this value could be found by:

x = number of sets in the match

L - W = 6x - 7(x+1)/2

This would give the losing player 6 games in every set.  The winning player gets 7 games in the majority of sets (just enough to win the match) and 0 games in the rest.  Of course, this formula assumes that there are an odd number of sets in the match, it wouldn't really make sense if it were even...

Posted by tomarken on 2006-03-27 07:49:33