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)
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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
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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 20071219 00:52:15 