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 5set match, with each set following the scoring system of tennis, and a first to 7 point tiebreak 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 LW 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 LW 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: Solution, Standing on the shoulders of giants. by Hugo)
Ah, good call, I must've read it too quickly. It shouldn't be too hard to convert the formula to calculate points instead of games, it's the same idea.
The loser will score 24 points in each of the (x1)/2 sets that he wins 60. In the sets he loses 76, he will score 24 points in the 6 games he wins, 18 points in the games he loses, and 6 points in the tiebreak, for a total of 48 points in each of the (x+1)/2 sets he loses.
The winner will score 38 points in each of the (x+1)/2 sets he wins, and none in the rest.
Therefore, L  W = 24(x1)/2 + 48(x+1)/2  38(x+1)/2
This simplifies to L  W = 12(x1) + 5(x+1) = 17x  7
For a 5set match, the loser will score 48 + 30 = 78 more points than the winner.
Just to clarify where those numbers came from:
When the "loser" wins a set, he wins 6 games to 0, and in each of those 6 games he wins 4 points to 0.
When the "winner" wins a set, he wins 7 games to 6 (the 7th being the tiebreaker). In each of the 6 games he loses, he is outscored 4 points to 0. In each of the 6 games he wins, he wins 5 points to 3. In the tiebreaker, he wins 8 points to 6 (as I believe in tennis, all games/tiebreakers must be won by 2 points).
I think that's right, but I hope somebody checks it. :)

Posted by tomarken
on 20060327 09:51:18 