Fall 2008 Problem 8: Gift wrapping

You have a perfect cube with a side length of 1 foot. You have a square piece of paper that is 3 feet on a side. You wish to wrap the cube with the paper with no gaps or overlaps with one shape cut out of the paper. Your shape must be one continuous piece of paper and cannot consist of shapes connected only corners (e.g., you cannot have two squares which touch only at a corner).

Solution

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Non-student Chris Evert gave the correct answer. As you can see in the picture above, the shape will cover the cube, but has a height and width equal to two diagonals of a cube face (or 2 times the square root of 2). Thus, this shape will easily fit on our paper.

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