Problem:
In the United States, coins have the following thicknesses: penny, ; nickel, ; dime, ; quarter, . If a stack of these coins is exactly high, how many coins are in the stack?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The height in millimeters of any stack with an odd number of coins has a in the hundredth place. The height of any two coins has an odd digit in the tenth place and a zero in the hundredth place. Therefore any stack with zeros in both its tenth and hundredth places must consist of a number of coins that is a multiple of . The highest stack of coins has a height of , and the shortest stack of coins has a height of , so no number other than can work. Note that a stack of quarters has a height of .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions