Problem:
Starting with some gold coins and some empty treasure chests, I tried to put gold coins in each treasure chest, but that left treasure chests empty. So instead I put gold coins in each treasure chest, but then I had gold coins left over. How many gold coins did I have?
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Answer Choices:
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Solution:
After putting coins in all but two of the chests, I could take coins out of each chest to leave coins in those chests. Doing this would allow me to fill the remaining chests with coins each, and have another coins left over. So I must have removed coins from each of chests). Thus I initially had put coins into each of chests, making for a total of coins (and chests).
Let be the number of chests. Then . Solving yields , so the number of coins is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions