Received: from MCC.COM (TCP 1200600076) by AI.AI.MIT.EDU 1 Mar 89 05:01:57 EST Date: Wed 1 Mar 89 04:00:05-CST From: Clive Dawson Subject: Force Field To: cube-lovers@ai.ai.mit.edu Message-ID: <12474493626.38.AI.CLIVE@MCC.COM> 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 -------