The net of a cube is drawn as a horizontal strip of four squares, labelled P, Q, R and S from left to right. A fifth square T is joined to the top edge of Q, and a sixth square U is joined to the bottom edge of Q. The net is folded up into a cube. Which of these pairs of faces ends up sharing an edge?

A strip of four squares wraps right round the cube, so its 1st and 3rd squares end up facing each other and so do its 2nd and 4th: P is opposite R, and Q is opposite S. T and U stick out on either side of the same square Q, so they too end up facing each other. That accounts for all three pairs of opposite faces, and on a cube any two faces that are not opposite must share an edge — so P and T meet. The traps are the three opposite pairs themselves: P and R, Q and S, and T and U are exactly the pairs that can never touch.