A unique tennis match

Algebra Level 2

The sport of men's tennis has the following scoring system:

The first player to win three sets wins the match. So there can be a maximum of five sets in a match.

To win a set, you have to reach six games and win by at least 2. If the set goes to 5-5, two more games are played. If someone does not win 7-5, a tiebreaker is played. This counts as a game, and the winner of the tiebreaker wins the set 7-6.

If a match goes to a fifth set, a tiebreaker is not played in that set.. The first player to reach at least 6 games and win by at least 2 wins the set and the match. (The longest fifth set ever played went to 70-68.)

Player A and Player B played a match that meets the following conditions.

1) Player A won the first set, and did not need a tiebreak.

2) Player B won the second and third sets.

3) Player A won the fourth and fifth sets, winning the match 3 sets to 2.

4) If you add up all the games won in the match by Player A, the total is equal to the number of games won in the match by Player B. (In other words, let A1, A2, A3, A4 and A5 be the number of games won by Player A in the 1st, 2nd, 3rd, 4th and 5th sets respectively, and B1, B2, B3, B4 and B5 be the number of games won by Player B in those sets. A1 + A2 + A3 + A4 + A5 = B1 + B2 + B3 + B4 + B5.)

5) A1 * A2 * A3 * A4 * A5 = B1 * B2 * B3 * B4 * B5

What is the total number of games played in the 5th set (i.e., what is A5 + B5)?


The answer is 16.

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1 solution

Denton Young
Jan 18, 2018

Player A won the match 6-1, 2-6, 2-6, 7-6, 9-7. 9 + 7 = 16.

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