Problem:
Boris has an incredible coin changing machine. When he puts in a quarter, it returns five nickels; when he puts in a nickel, it returns five pennies; and when he puts in a penny, it returns five quarters. Boris starts with just one penny. Which of the following amounts could Boris have after using the machine repeatedly?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Neither of the exchanges quarter five nickels nor nickel five pennies changes the total value of Boris's coins. The exchange penny five quarters increase the total value of Boris's coins by . Hence, Boris must have after uses of the last exchange. Only option D is of this form: . In cents, option A is more than a multiple of , is more than a multiple of is more than a multiple of , and is more than a multiple of .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions