title: Trying to calculate the state space of a board with 5 numbers on
body: <p>I have a 5x5 board with 1..5 numbers in the top row of the board.</p>
  
  <p>Every number can ultimately end up in any position so long as it is not on top of another number. </p>
  
  <p>Every number can move one up,down,left or right in a single move, however I don't believe this makes a difference to the state space since ultimately every number can end up anywhere given an unlimited amount of moves.</p>
  
  <p>Because every number can ultimately be anywhere at any point except on top of another number I'm assuming that a number can be in 1/21 positions at any one time? i.e. the board space (25) minus the numbers that it cannot be ontop of (4).</p>
  
  <p>My original calculation was ((n*n)-(n-1))^n because I was trying to take into account that a number could not be ontop of another number however I found the following calculation:</p>
  
  <p>I found this on a wiki page as a way of calculating the state space of a go game board.</p>
  
  <p>Each space can have 6 different possible vales (1..5 and empty) and the board has 25 squares, so the equation would be (n+1)^(n*n) = 6^25 = 2.843x10^19</p>
  
  <p>Is this correct? Does the fact that a single number can only be in 21 spaces out of the 25 at any single moment not affect it?</p>
  
  <p>If it's incorrect could you please inform me why or/and offer a working solution.</p>
  
  <p>Thanks a lot! :)</p>