Question 135
We have 1000 small cubes of sidelength $1$ cm. All have magnetised faces, with three faces being north poles and the three opposite faces being south poles. We assemble them into a “megacube” of sidelength $10$ cm, using magnetism to connect them: two faces that touch must have opposite polarity. Your task is to determine how many configurations the megacube can have. Two configurations are different if they give different magnetic sensor readings, according to the following rules:
1. We can sense the polarity of faces of small cubes that lie on the outside of the megacube, except that we cannot test the bottom face of the megacube because it is too heavy to lift or even move.
2. If two configurations give different readings, but we could move (e.g. rotate) one to get the other, treat them as distinct, again because the megacube is too heavy to move.
1. We can sense the polarity of faces of small cubes that lie on the outside of the megacube, except that we cannot test the bottom face of the megacube because it is too heavy to lift or even move.
2. If two configurations give different readings, but we could move (e.g. rotate) one to get the other, treat them as distinct, again because the megacube is too heavy to move.