# Bytelandian gold coins

A nice programming challenge (easy/medium difficulty) comes from http://www.codechef.com/ and it is being called: “Bytelandian gold coins”.

From this exercise I’ve learnt that the most elegant solutions are recursive .

In this challenge our task is to resolve the currency issues in a imaginary country, Byteland:

Each Bytelandian gold 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 (the banks have to make a profit).

You can also sell Bytelandian coins for American dollars. The exchange
rate is 1:1. But you can not buy Bytelandian coins.

You have one gold coin. What is the maximum amount of American dollars
you can get for it?

The input will contain several test cases (not more than 10). Each
testcase is a single line with a number n, 0 <= n <= 1 000 000 000. It is the number written on your coin. For each test case output a single line, containing the maximum amount of American dollars you can make.

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My first attempt (which seemed natural at that point) was working “flawlessly” on my local machine but codechef was insistingly reporting Time Limit Exceed:

Eventually the recursive solution rendered a smile on my face, making me saying: “That wasn’t so hard…”: