Question

Is this what they want for both parts of The nugget problem? This code solves the beginning and end easily.
http://codepad.org/RPPITqX4

Answer 1

This is just for problem number one.

Answer 2

This is a good solution for solving the diophantine equation, but isn't the first part basically pen & paper? At least, your program should add the test cases for 50...55, then show how one can find a solution for 56...65 given the solution for 50...55, i.e. "In other words, show how, given solutions for 50-55, one can derive solutions for 56-65."