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From: Ka Lam <g5kalam@cdf.toronto.edu>
Subject: Re: eight puzzle decission question
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Message-ID: <Pine.GSO.3.93.960624125544.16803J-100000@eddie>
To: Simon Read <s.read@cranfield.ac.uk>
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Date: Mon, 24 Jun 1996 16:57:00 GMT
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On 24 Jun 1996, Simon Read wrote:

> By extension, this says that you can get from one position to another
> if the change can be constructed out of an EVEN numbe of swaps of pairs
> of tiles. You can't get from one position to another if it needs an
> ODD number of swaps.
> 
> There is an even simpler result for this, which I can't recall exactly.
> It's something like the exclusive-or of all positions, or the sum of
> (tile number) x (position number). If it's even, it stays even for all
> time; if it's odd, likewise. You can't get from an "odd" position to
> and "even" position.


when you say (tile number) x (position number), what is B count as?
and how is the position numbered? like this?
	
		1 2 3
		4 5 6
		7 8 9

And I don't understand how to do exclusive-or on a bunch of numbers.

Thanks for your help.

--
University of Toronto                  g5kalam@cdf.utoronto.ca
Art & Science                          ae197@freenet.toronto.on.ca
Ka Lam                      Home Page: http://cdf.utoronto.ca/~g5kalam
   Administrator of Methodist (H.K.) Primary & College Mailing-List
    Vice President of UoT Computer Science Student Union, 1996/97

