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 Lazy Tennis (Posted on 2006-03-27)
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

 No Solution Yet Submitted by Chris, PhD Rating: 4.3333 (6 votes)

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 This IS the solution!!! | Comment 22 of 24 |
This is very easy!!!
Here it is:

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 45-40 (4-3 points) and every game the Loser wins is won 45-0 (4-0 points).

In total:
Winner = 3*(6*4+7) = 93 points
Loser = 3*(6*4+5) + 3*(6*4) + 2*(6*4) = 207

Result: L-W = 114 and the formula for X sets is: 23*X-1.

 Posted by TheKPAXian on 2009-10-05 12:09:10

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