A cube is marked 1, 2, 3, 4, 5, and 6 on its 6^{ }sides.
The pictures are of three different orientations of the cube. What number is
opposite 3?

We note that the only face not adjacent to one face is the face opposite it. We can see that 1 is adjacent to 4, 6, 2, and 3, so that 5 is opposite 1. Then, 4 is adjacent to 6 and 3, which leaves 2. This leaves 6 and 3 opposite one another.

In these problems, the key is to note that the only face not adjacent to a given face is the one opposite to it. Also, note that only one face may be opposite to a given face, so that once you’ve paired a face, it may be eliminated from future considerations.