In this puzzle we ask how many ways six squares can be arranged to form a cube.

A cube has six faces, each a square. Look at this pattern of six squares.

If you print this on paper and cut it out, you will be able to fold and tape it into a cube (download pattern).

Now look at this arrangement of six squares: You can't fold this one into a cube. How many different patterns of six squares are there that can be folded into a cube? How many are there for which it is not possible?