Solution
How Many Standard Dice?
Show the problem again
A standard die is a cube with faces numbered 1 to 6 such that opposite faces sum to 7. Two dice are the same if one can be rotated to look exactly like the other. How many different standard dice are there? Give an integer.
Worked solution
The answer is 2. Rotate the die so that 1 is on the bottom; then 6 is on top. The faces 2 and 5 are opposite, as are 3 and 4. Turn the die about the vertical axis so that 2 faces you; then 5 is at the back. The only freedom left is whether 3 lies on the left or the right (with 4 opposite). No rotation fixing the 1, 6 and 2 positions can swap left and right, so these two dice are genuinely different: they are mirror images of each other. Real dice come in both "handednesses", though most Western dice use one convention.
Source: Classic exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.