title: What is the math program I'm trying to solve in python?
body: <p>I am trying to solve this math problem in python, and I'm not sure what it is called:</p>
  <ul>
  <li>The answer X is always 100</li>
  <li>Given a list of 5 integers, their sum would equal X</li>
  <li>Each integer has to be between 1 and 25</li>
  <li>The integers can appear one or more times in the list</li>
  </ul>
  <p>I want to find all the possible unique lists of 5 integers that match.</p>
  <p>These would match:</p>
  <ul>
  <li>20,20,20,20,20</li>
  <li>25,25,25,20,5</li>
  <li>10,25,19,21,25</li>
  </ul>
  <p>along with many more.</p>
  <p>I looked at itertools.permutations, but I don't think that handles duplicate integers in the list. I'm thinking there must be a standard math algorithm for this, but my search queries must be poor.</p>
  <p>Only other thing to mention is if it matters that the list size could change from 10 integers to some other length (6, 24, etc).</p>