title: What is the Entropy of Android's Dot Password System?
body: <p>How many <em>permutations</em> of the androids dot login system are possible?   I know for a fact the solution to this lies in Discrete Math,  specifically <a href="http://www.mathsisfun.com/combinatorics/combinations-permutations.html" rel="noreferrer">Permutations Without Repetition</a>,  If your answer doesn't use permutations or combinations you are incorrect.</p>
  
  <p>The length of passwords is between 4 and 9 dots,  There are a total of 9 dots to permute though.  so my initial equation is:</p>
  
  <pre><code>9P4+9P5+9P6+9P7+9P8+9P9
  </code></pre>
  
  <p>However,  I know this equation is incomplete because it does not take into consideration all of the rules.  Each dot is distinct because of is position so if you assign a number to each dot as follows:</p>
  
  <pre><code>123
  456
  789
  </code></pre>
  
  <p>The password "1397" is impossible,  if you attempt to use this password you will in fact have entered in "1236987" because the numbers in-between are automatically selected.  Another equation needs to be created to account for these limitations and then subtract off from my nPr equation above. </p>
  
  <p>This <a href="http://beust.com/weblog2/archives/000497.html" rel="noreferrer">link</a> has a great video of someone using the android login.  It also goes into greater detail into the rules.  The math on that page is completely incorrect,  he is not even close to a real solution. </p>