One die carries the numbers 1 to 6, one on each face, but not in the usual arrangement. It is set down twice. The first time: 1 is on top, 3 faces you and 2 is on your right. The second time: 2 is on top, 3 still faces you and 5 is on your right. Which number lies on the face opposite the 1?

The 3 stays at the front both times, so the die has simply been spun about the front-to-back line, and the four faces round that line — top, right, bottom, left — keep their cycle. The 2 has moved from the right to the top, so every face in that ring has stepped one place the same way: right goes to top, bottom goes to right, left goes to bottom, top goes to left. The second view's right face is therefore the first view's bottom face, which makes the bottom face 5. The face under the 1 is the face opposite it, so 1 is opposite 5. The traps: 6 assumes this die obeys the familiar 'opposite faces add to 7', which the question never promises; 2 and 3 are both seen sitting beside the 1 in the first view, and a face you can see at the same time as another can never be its opposite.