If the following sheet is folded to form a cube, then find out how many dots…

In a straight strip of four connected squares that folds into a cube, the 1st and 3rd squares become one opposite pair and the 2nd and 4th squares become the other opposite pair, because each fold turns the square 90 degrees further around the cube. Any square attached to the side of one square in that strip becomes one of the two faces left over, and since a cube has only three opposite pairs, two side-flaps like this must be opposite each other.

1. In this net, the one-dot, two-dot, four-dot and six-dot faces form a single connected strip of four squares, running in that order.

2. By the strip rule, the one-dot and four-dot faces (1st and 3rd in the strip) become one opposite pair, and the two-dot and six-dot faces (2nd and 4th) become the other.

3. The three-dot face is attached to the side of the two-dot face, and the five-dot face is attached to the side of the six-dot face — these are the two remaining faces.

4. Since the strip has already used up the other two opposite pairs, the three-dot face and the five-dot face are left as the final pair, so they must be opposite each other.

Cross-check by adjacency: once folded, the five-dot face shares an edge with the one-dot, two-dot, four-dot, and six-dot faces — that is, with every face on the four-square strip — so the three-dot face, which never touches it, is confirmed as the one directly opposite.

So the face opposite the five-dot face carries three dots.