Problem:
Ten tiles numbered through are turned face down. One tile is turned up at random, and a die is rolled. What is the probability that the product of the numbers on the tile and the die will be a square?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
There are possible pairs. The squares less than are and . The possible pairs with products equal to the given squares are , , , , , , , , , and . So the probability is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions