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(4): Solution, Standing on the shoulders of about.com by tomarken)
tomarken, you CAN win a tiebreaker 76. The margin of 2 only applies to ending a set before 12 games. That aside...
You are correct in saying 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...".
But in the games he loses, and for the loser to make the maximum number of points in the remaining 3 sets but still lose, he must win half (6 games) of the set (40), lose half (6 games) of the set, and lose the tiebreaker of each set only by 1. Thus, for each set he will win 6 (40)games, lose 6 (34) games, and lose the tiebreaker (34). The loser may therefore win only 21 points in the 7 games he loses (the 6 games and the tiebreaker), while the winner will win a minimum of 28 points in each of the 7 games.
Therefore, L – W = 24(x1)/2 + (24+21)(x+1)/2 – 28(x+1)/2
…and simplifying, L  W = (41x 7)/2
For a 5set match, the loser will score (41*5  7)/2 = 99 more points than the winner.
Edited on March 27, 2006, 2:58 pm

Posted by Dej Mar
on 20060327 13:24:59 