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

After considering the no-ad variation of the game, i have concluded that a more appropriate answer will be that the loser can win 96 more points than the winner.

Positive values indicate lead of loser. Negative values indicate lead of winner.

Set 1: +24

Set 2: +24

Set 3: This can be calculated as follows:

For the six games won by loser, he will gain 24 points. In a no-ad version, you can win a game by 1 point, hence the winner after his six games won will have a lead of 6 points. The winner wins the tie-break, which must be won by two points regardless of the no-add or add variations, hence giving him a lead of 8 points. From this the total lead for the third set is 24-8 = 16.

The last three sets are all in this format hence the total point lead by the loser:

24*2+16*3

=96 points

Equation for x number of sets, when x is an odd integer:

24(x-1)/2+16(x+1)/2

=12(x-1)+8(x+1)

=12x - 12 + 8x 8

=20x - 4

With your solution Dej Mar, you assumed there could be a lead of only 1 point to win a tie-break. Due to the ambiguity of the question, your answer may also be considered to be correct.

For a Dej Mar solution, the equation would be as follows:

24(x-1)/2 + 17(x+1)/2

=12(x-1) + 8.5(x+1)

=12x - 12 + 8.5x + 8.5

=20.5x - 3.5

*Edited on ***March 29, 2006, 3:17 am**