The six faces of a cube are painted in six different colours: red, blue, green, yellow, white and black. The cube is set down three times, each time with the red face on top, and each time the colour facing you and the colour on your right are noted. First: blue in front, green on the right. Second: green in front, yellow on the right. Third: yellow in front, white on the right. Which colour is on the face opposite blue?

Red stays on top every time, so the cube is only being spun about its upright axis and the four side faces keep their order round the cube. Reading front then right each time gives blue → green, green → yellow, yellow → white, so the ring of side faces runs blue, green, yellow, white and back to blue. In a ring of four, the face opposite one of them is the one two steps along, so blue faces yellow (and green faces white). The traps: green is seen right beside blue, so it is a neighbour and can never be the opposite face; black is the bottom face, which is opposite red, not blue.