In a flash of red, green, yellow, orange, blue and white, the cube torqued rapidly between the diligent fingers of eighth-grader Anna Halsdorf. Just 14 seconds later, the puzzle was solved. But ...

If you suspend a Rubik’s Cube near the corner of a room and shine lights at its exposed faces, it will cast square shadows on two walls and the floor. A real-world Rubik’s Cube has a gadget at its ...