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
The original solution proposed by tomarken is defenitely correct. For the first two sets won by the loser, these are 6-0, giving the loser of the match a total of a 48 point lead after the first two sets. In the third, fourth and fifth set, the score is 6-7. For the six games won by the loser, he gains 24 points. For the 6 games won by the winner, he will win by the closest possible margin, which is 2 points ahead of the loser. He can also win the tie-break by the smallest possible margin, which is 2 points. Hence a lead of 14 points, from the games won by the winner in each set the winner wins. The difference between the winners lead and the losers lead in the third, fourth and fifth set is 24-14, which is equal to 10. Three sets are in this format, hence 10*3 = 30. This means that the loser can have a lead of 30 points from the last three sets, plus a lead of 48 points from the first two sets. 48+30=78.
Therefore the loser of the match can win 78 more points than the winner.
Edited on March 28, 2006, 4:47 am