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Mail-from: From cube-lovers-request@life.ai.mit.edu Wed May 27 11:37:46 1998
Message-Id: <01BD8995.A6F13540.Johan.Myrberger@ebc.ericsson.se>
From: Johan Myrberger
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To:
Subject: RE: Magic jack
Date: Wed, 27 May 1998 17:34:05 +0200
Organization: Ericsson Business Networks AB
On 27 May 1998 09:36, Philip Knudsen wrote:
> Apart from Magic Jack and Vadasz Cube, there also exists a german
> produced puzzle called "IQUBE". Like the Magic Jack, this is a 3x3x3
> sliding puzzle with 26 smaller cubes. Cubes have colours red, green and
> yellow, and it is possible to arrange them so the entire surface is
> either red or green. Yellow is possible with red or green centres. IQUBE
> comes with a leaflet that suggests a total 12 different solution
> possibilities....
Some years ago (around 1989?) I made a computer search on this kind of
puzzle.
The idea was "is there a way of colouring the 27 cubies (and then remove
one) so that a 3x3x3 cube can be arranged (with sliding block moves) to
show all external sides of either of three colours".
Since a 3x3x3 cube shows 9x6=54 cubie sides at one time, and 27 cubies have
in all 27x6=54x3 cubie sides all "cubie sides" would be used in one
configuration each.
So - I hunted for the answers to:
1) Is such a colouring possible?
2) Which cubie would be nicest to remove?
My search showed that 1) was indeed possible, and that there is one
distinct way for the colouring (not counting reflections etc) and 2) It is
possible to choose a cubie to remove so that the space will be positioned
in one of the space diagonals for each of the three solutions.
If anyone is interested I can dig out the specific colouring.
Regards
/Johan Myrberger
mailto:Johan.Myrberger@ebc.ericsson.se
http://home.bip.net/johan.myrberger