Problem:
Claudia has coins, each of which is a -cent coin or a -cent coin. There are exactly different values that can be obtained as combinations of one or more of her coins. How many -cent coins does Claudia have?
Answer Choices:
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Solution:
If Claudia only has -cent coins, then she can make different values. Otherwise, suppose that the number of -cent coins is and thus the number of -cent coins is . Then she can make any value that is a multiple of from to . Therefore , and .
The problems on this page are the property of the MAA's American Mathematics Competitions