title: 8-puzzle: hamming and manahttan heuristic consider "blank space"?
body: <p>I've a very simple question.</p>
  
  <p>I'm working on 8-puzzle (8 numbers(from 1 to 8) + blank(=0) )</p>
  
  <p>When calculating hamming distance (numbers in wrong position) and manhattan distance (distance horizontal+vertical between start and final position) should I consider "blank" space to calculate the result ?</p>
  
  <p>For example..</p>
  
  <pre><code> |7 2 4|
   |5 _ 6|
   |8 3 1|
  </code></pre>
  
  <p>with goal state</p>
  
  <pre><code> |_ 1 2|
   |3 4 5|
   |6 7 8|
  </code></pre>
  
  <p>What's correct?</p>
  
  <ul>
  <li>Hamming distance = 8 (every number not in place) or 9 (also 0 = blank is considered)</li>
  <li>Manhattan distance (distance(7),distance(2),distance(4),...) = 3 (=1+2) + 1 (=1+0) + 2 (1+1) + 2 (2+0) + 0 (blank) + 3 (1+2) + 2 (2+0) + 3 (1+2) + 3 (2+1)
  --> without considering blank is 18 , with blank (+2) is 20. What's correct?</li>
  </ul>
  
  <p>Thank you</p>