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From: g5xiaoyu@cdf.toronto.edu (Xiaoyu Gao)
Subject: Re: eight puzzle decission question
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References: <Pine.GSO.3.93.960623221851.16803F-100000@eddie> <4qm02o$dik@yama.mcc.ac.uk> <Pine.GSO.3.93.960624125544.16803J-100000@eddie>
Date: Wed, 26 Jun 1996 19:44:23 GMT
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In article <Pine.GSO.3.93.960624125544.16803J-100000@eddie>,
Ka Lam  <g5kalam@cdf.toronto.edu> wrote:
>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.

I assume you are talking about tiles (not blank).  After all, a move
is a swap of blank and a tile.  And let me add that if blank is at
different positions at the beginning and the end, then the goal is
achievable only if blank swaps with a tile at a position of different
parity.  i.e. from odd to even, and vise versa.


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

exclusive-or two numbers and exclusive-or the result and the next number.

Xiaoyu Gao
g5xiaoyu@cdf.toronto.edu

