Problem:
Lola, Lolo, Tiya, and Tiyo participated in a ping pong tournament. Each player competed against each of the other three players exactly twice. Shown below are the win-loss records for the players. The numbers and represent a win or loss, respectively. For example, Lola won five matches and lost the fourth match. What was Tiyo's win-loss record?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
There are exactly wins and losses in each round. Summing the scores for each round for Lola, Lolo, and Tiya gives . Therefore Tiyo must have won the fourth and sixth games for a record of .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions