February 26th, 2013, 01:48 PM  #1 
Newbie Joined: Feb 2013 Posts: 2 Thanks: 0  Permutation
I am going through some permutation tutorials, one of them has an exercise asking in a 15puzzle, if we assume the top right corner is 2, how many configurations satisfy this? I think the answer is 14! Am I right? My sincere thanks 
February 26th, 2013, 01:52 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,946 Thanks: 1137 Math Focus: Elementary mathematics and beyond  Re: Permutation
What about the empty space. Doesn't that make it 15!?

February 26th, 2013, 02:07 PM  #3  
Newbie Joined: Feb 2013 Posts: 2 Thanks: 0  Re: Permutation Quote:
 
February 27th, 2013, 07:15 AM  #4 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Permutation
If you are allowed to move each square independently then there are 15! ways to place the other 15 squares. However, in a typical "15 puzzle", you cannot do that. You can only move into configurations that are even permutations of the original positions (which is, typically, ).

February 27th, 2013, 12:11 PM  #5  
Global Moderator Joined: May 2007 Posts: 6,770 Thanks: 700  Re: Permutation Quote:
 

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