title: 2d array permutation proof
body: <p>I want to know if it's possible to get any possible combination of a 4x4 integer array given three rules:</p>
  
  <ul>
  <li>you may shift any column up or down</li>
  <li>you may shift any row left or right</li>
  <li>you may shift the entire array left, right, up, or down</li>
  </ul>
  
  <p>That is, you can transform:</p>
  
  <pre><code>[1]  [2]  [3]  [4]
  [5]  [6]  [7]  [8]
  [9]  [10] [11] [12]
  [13] [14] [15] [16]
  </code></pre>
  
  <p>into any possible combination of a 4x4 array of the same 16 values, given those three rules.</p>
  
  <p>Basically, I just want to know if there are impossible combinations.</p>