> < ^ Date: Tue, 19 Sep 2000 07:48:04 -0400
< ^ From: Bob Harris <nitlion@mindspring.com >
< ^ Subject: Re: GAP commands equivalent to magma's InverseWordMap and sol

Thanks Andrew (Andrew Solomon <andrew@illywhacker.net>) for your
suggestions. I'll try those tonight when I get home from work.

Since you asked about what the puzzle actually is, the fellow who posted it
at rec.puzzles (Kevin Buzzard <buzzard@ic.PUZZLE.ac.ELZZUP.uk>) had found it
on his nokia cell phone. It is called "rotation" at Nokia's web site
I think this variant is level 5.

The puzzle is a 4x4 square of numbers. There are four operations, each of
which involves rotating the numbers in a 3x3 square clockwise. So, in the
diagram below, one move is the cycle (1,2,3,7,11,10,9,5). The numbers
maintain orientation-- they don't rotate; if they did, that would add
another layer of complexity for the solver.

 1  2  3  4
 5  6  7  8
 9 10 11 12
13 14 15 16

Anyone who's interested in an archive of the discussion ofthis puzzle (it's
about a 40K byte text file), let me know. The discussion focuses primarily
on finding minimal move sequences to swap two given tiles.

There's a very well done java applet for a similar puzzle at


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