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 reply to
solution by Charlie)
For part 2, I got the same solution as Charlie, but for part 1 I got a different solution. Following his system for describing the paper and the folds:
+++++
 F r Bk
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 LBtR T 
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Either remove the unlabeled square or cut it separate from either L or F.
Cut between the F and the Bt, and between the r and the R.
Bt stays on the Bottom. Fold up L and R to form the Left and Right.
Then Fold T over to make the Top. Then Bk, r and F will be pointed toward the back (and off to the right) from the top; fold it back, downward, to make the Back.
Now r and F are pointing to the right when viewed from the front. Fold it forward so that so the r overlaps the R, and then bring F across in front to complete the cube. If the unlabeled square was left attached to F, fold it to cover the Left, or fold it to cover the back if it was attached to the Left.

Posted by nikki
on 20071218 15:56:53 