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

(In reply to This IS the solution!!! by TheKPAXian)

So, i can see the wrongs in my solution and that is: Every game the winner wins is won 45-30 (4-2 points) or any other posible score after the 40-40 (3-3) - deuce.

The solution should be:

The Winner of the match has to win 3 Sets all of them in Tie-Break 7-5.
The Loser of the match wins 2 Sets, all of them 6-0.

Every game the Winner wins is won 45-30 (4-2 points) and every game the Loser wins is won 45-0 (4-0 points).

For a 5 sets match(with Tie-Break in fifth set)
Winner = 3*(6*4)+3*(7) = 93 points
Loser = 3*(6*2)+3*(5) + 3*(6*4) + 2*(6*4) = 171

Result: L-W = 78 and the formula for X sets is: 17*X-7.

Posted by TheKPAXian on 2010-01-20 16:26:45