Question 1182758: The sport of bingbong involves two players. Each match consists of a number of rounds and each round consists of a number of points. The first player to win four points in a round wins the round. The first player to win six rounds in a match wins the match.
Suppose that after a match of bingbong, the winner has won W points while the loser has won L points. What is the largest possible value of L-W?
Answer by robertb(5830)   (Show Source):
You can put this solution on YOUR website! Suppose there are two players A and B, and assume that A has won the game.
It is quite apparent that the maximum number of rounds the game could have taken was 11, with A winning 6 of those rounds and B winning the other five, with A
winning the 11th and final round. To maximize the value of L-W, we determine the scenario where A has won by the slimmest of margins, i.e., 4 - 3 (in 6 games), and
lost by the widest of margins, i.e., 0 - 4 (in 5 games).
The largest value of L-W would then be 6*3 + 5*4 - (6*4 + 5*0) = 18 + 20 - 24 = 14.
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