Exchange gold coins
In a monetary system each coin has an integer number written on it. A coin 'n' can be exchanged in a bank into three coins: n/2, n/3 and n/4. But these numbers are all rounded down.
You can also sell coins for dollars and their exchange rate is 1:1.
You have one gold coin. What is the maximum amount of dollars you can get for it?
for a coin with value 120 you can get 144 dollars.
Suggest an algorithm to solve the problem.