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?
In both cases below, the unlabeled squares are not needed, but to fulfill the request that the paper remain in one piece, they may be left attached to one of the labeled squares.
| |Bk|F |t |
| L|Bt|R |T |
Either remove the unlabeled square or cut it separate from either L or Bk.
Cut between the F and the Bk, and between the F and the R.
Bt stays on the Bottom. Fold up L, R and Bk to form the Left, Right and Back. If the unlabeled square was left attached to L, fold it to cover the Back, or vice versa if attached to the Back.
Then Fold T over to make the Top. Then t and F will be pointed toward the back from the top; fold it forward so the t overlaps the T, and then bring F down in front to complete the cube.
| L|Bt| R|
| |F | r|
| |T |Bk|
Remove the unlabeled squares or fold them redundantly as in the first part after leaving each one attached to only one other square.
Cut between the T and the Bk and between the F and the r. Leave the Bt on the Bottom. Fold L up to be the Left side. Then fold F up to form the Front, and T further to form the back. Fold R up to form the right side, making r and Bk point toward you. Fold r back over R, so Bk can be further folded to form the Back.
Posted by Charlie
on 2007-12-18 13:17:00