2000 AMC 10 Problem 17
Problem 17 of 25IntermediateAlgebraNumber Theory
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
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Solution
Trading a quarter for five nickels or a nickel for five pennies does not change the total value. Only trading a penny for five quarters changes it, adding cents.
Starting from cent, Boris always has cents for some nonnegative integer
Only has this form, since
Thus, the correct answer is D.