Rigid cube..! problem

You want to construct a rigid wire skeleton of a one-inch cube by using 12 one-inch wire segments for the cube's 12 edges. These you intend to solder together at the cube's eight corners.

"Why not cut down the number of soldering points," a friend suggests, "by using one or more longer wires that you can bend at sharp right angles at various corners?"

Adopting your friend's suggestion, what is the smallest number of corners where soldering will be necessary to make the cube's skeleton rigid?


click on the title for solution......


SOLUTION: 

Eight, since, no matter how you bend the wire, it's still necessary to solder another piece of wire to each corner. This is because three edges meet at each vertex, and the bent wire can only produce two of these at most without soldering. This makes it necessary to solder the third edge at each vertex in order to make the cube rigid.