I acquired a cube puzzle called Force Field a few weeks
ago which I don't recall having seen discussed on this
list. It's called Force Field (by Mattel), and it consists
of 8 cubies, each measuring about 1" on a side, and each
solid black. The idea is to arrange these 8 cubies into
a 2x2x2 cube. This sounds and looks trivial, until you
learn that there are magnets attached to some (but not all)
of the inner surfaces of the cubies. This means that
the sides of two cubies may:

a) repel each other
b) attract each other but jog off-center (since
the magnets are not necessarily at the center of the side)
c) neither attract nor repel each other (if magnets
don't exist on both of the sides involved)
d) attract each other and stay perfectly aligned

The final 2x2x2 cube has to hold together perfectly, without one
or more of the cubies popping out. Furthermore, it is not enough
to juxtapose the sides with no magnets, since the final cube has
to be placed in a special stand which balances it on one of
its corners. This is the acid test-- the cube might look ok when
resting on the table, but in order to survive in the stand, all
internal sides must actively attract each other with perfect
alignment.

I finally had to resort to temporary labels on the cubies in order
to systematically search for a solution. One of the first things
you learn is that each cubie has 3 magnets, precisely the number
required. This cuts down the search space tremendously: since the
3 sides with magnets must be internal, this constrains a particular
corner of each cubie be at the center of the large cube. But it
still involves over 33 million possible positions (3^8)*(7!).

I'd be interested to hear if any of you folks have played with this,
and if anybody has developed a procedure for putting the cube together
which does not involve labeling, which is what I'm working on now.

Happy cubing,

Clive
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