Problem:
The Tigers beat the Sharks 2 out of the first 3 times they played. They then played more times, and the Sharks ended up winning at least of all the games played. What is the minimum possible value for ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
If the Sharks win the next games, then they win of the games. Therefore , so . Therefore .
OR
If the Tigers win no more games, then their 2 wins should be no more than , or , of the games played. So the minimum number of games played must be at least 40 , and .
The problems on this page are the property of the MAA's American Mathematics Competitions