The main element of the 3D puzzle Random Generator’s design is a cube with an octahedron inside it that in its turn contains a metal ball to provide weight. This construction is powered by a rack-and-gear drive initiated manually and providing energy through a driven gear that rotates a three-axle gear. This is how the cube with all its contents begins to move, which is important for summoning the magic of randomness. Of course, we can only call it magic until we know the science of it. And to learn it, let us take a closer look at the main structure.
The vertices of the octahedron coincide with the sides of the cube. In this way as the energy of the system expires and it stops moving, gravity suspends the metal ball in the lowest part of the octahedron and due to the inclination of the walls it rolls within, it ends up in one of the octahedron’s vertices pulling in down. Whichever of the vertices turns up in the bottom, the side of the cube it is attached to will be right under it and parallel to the floor. In this way, the side of the cube with the answer will be the one facing up on the opposite side.
The probability to get any of the vertices facing down is virtually the same due to symmetry of the octahedron that rotates freely around the axis of its mass. This leads us to a simple conclusion that the probability to receive one of six answers is 1/6 or 0.167.
Every side of the cube positioned by the vertex of the octahedron, has a message: one says “YES”, the other “TRY AGAIN”, etc.
* An octahedron is a regular polyhedron with eight faces (equilateral triangles) and six vertices.