A puzzle comprises a cube (11) having translucent faces and a plurality of light sources (46, 55) one behind each face to cause illumination as the cube is turned about axes normal to the faces. Gravity-sensitive or orientation-sensitive switches (47,48) such as mercury switches, are connected to an electronic circuit (57, 58, 59, 60) acting to compare the switching states and switching movements of the switches with a pre-programmed sequence to determine whether and which of the lamps (46, 55) to illuminate. In use of the puzzle the faces will light up when a predetermined sequence of rotations about three orthogonal axes is performed correctly to match the switching sequences with the stored sequence.