title: Ensuring only a single formula could ever apply to 4 random elements
body: <p>I have a list of formulae for combining elements:</p>
  
  <pre><code>A + B + C = X
  D + E + F = Y
  G + H + I = Z
  </code></pre>
  
  <p>I want to ensure that given any random 4 elements, there will never be more than 1 applicable formula. For example the formulae below should not be allowed as if I get elements A, B, C and D then both are applicable:</p>
  
  <pre><code>A + B + C = X
  B + C + D = Y
  </code></pre>
  
  <p>Every formula will consist of 3 elements on the LHS and it's the LHS that I want to enforce the rule on.  
  The elements are sortable, if that helps.</p>
  
  <hr>
  
  <p>An alternative, equivalent problem:</p>
  
  <p>I have a list of an array of 3 elements: <code>List&lt;Element[3]&gt;</code> How do I ensure that no 2 elements appear in more than one array.</p>
  
  <hr>
  
  <p>What would be a reasonably efficient (runtime speed) way of doing this for a large number of elements and a large number for formulae (beyond brute forcing)?</p>