How can a 2x4 rectangle be cut (and still remain in one piece) and be able to be folded into a 1x1x1 cube?

How about a 3x3 square?

The previous two solutions do satisfy the problem.

If someone wanted a solution which is more free standing (rather than just a covering of a cube), then here is one solution each which doesn't fold along the grid lines (and doesn't cut at all)

 __ __ __ __
|__|__|__|__|
|  |  |  |  |
|__|__|__|__|
|__|__|__|__|

If one makes right angles with the folds between the 1x1 squares, (to form a tube shape) and then folds the flaps down from left to right (tucking the last one in), it makes a cube. (The flaps form the top and bottom of the cube.)

For the 3x3

    
   /_\
 /_|_|_\
<|_|_|_|>
  \|_|/
   \ /

The following greek cross can be contained in the 3x3 sheet with a little border (about 1/5 inch) The five squares shown form the bottom and sides of the cube, (push each of the side triangles against a side) and the corner flaps can be folded and tucked in a similar manner from the previous folding. (A little bit of the corner on each corner will need to be folded over though before doing this.)

Posted by Gamer on 2007-12-19 00:52:15