Sample Problem

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?


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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.