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24-tile puzzle

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Here's a somewhat strange example, where the difficulty of a puzzle is such as 
to make brute-force calculations too time-consuming:

http://ioannis.virtualcomposer2000.com/math/magneticpuzzle.html

The easiest solution will be found by Maple in around half an hour.

If on the worksheet one changes the variable "border:=true", there's no solution 
after running the worksheet for 9 hours on an Athlon 1.78GHz.

The solution time in Maple is also a function of the first move. The first move 
chosen for the simplest solution in the worksheet causes Maple to find a 
solution immediately. If you change the first move, expect a solution time of 
around 25-30 minutes @1.75GHz.

If anyone can tweak the worksheet code or change the first move to find (fairly 
quickly) a solution for "problem one" on the first picture, let me know.

It would also be interesting to see an enumeration of possible "problem one" 
solutions, like I have for the general solution, which I am not totally sure is 
correct, but here goes, anyway.

Classic worksheet for Maple 9 downloadable at the end of the page.

Thanks,
--
I. 

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24-tile puzzle "I.N. Galidakis" <morpheus@olympus.mons> - 2011-09-19 22:07 +0300

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