**change_diophantine**,
a Python code which
sets up a Diophantine equation to solve the change making problem,
which counts the number of ways a given sum can be formed
using coins of various denominations.

The change making problem is given a target value C and a set of N coin denominations with value W. The task is to determine the minimum number of coins needed to form the given value.

In the unbounded change making problem, there are a limitless supply of coins of each denomination. In the bounded change making problem, each denomination is available only up to some given limit.

For some sets of denominations, there will be target values that cannot be formed. (This relates to Frobenius's problem.)

The computer code and data files described and made available on this web page are distributed under the MIT license

**change_diophantine** is available in
a MATLAB version and
an Octave version and
a Python version.

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- change_diophantine.py, the source code.
- change_diophantine.sh, runs all the tests.
- change_diophantine.txt, the output file.