Problem: Each face of a cube is marked with a letter. The cube is shown in 3 different positions.
Determine the letter on the face opposite:
• the face marked X. • the face marked A. • the face marked C.
Solution
Comparing the cube in positions 1 and 3, we see that the letter Y is on the face opposite letter X. Position 1 shows that B is at the top or bottom of X and position 2 shows that A is at the top or bottom of X. Therefore A is on the face opposite B. By elimination, C and Z are on opposite faces. We can also solve this by visualizing rotations about the three axes and picturing the orientations of the letters.
