Problem of the Week
Welcome to the Centenary Math Problem of the Week contest! You can always find the most recent problem of the week below. You can also look at the current scores or read the rules.
Congratulations to Brent Krise (1st place and longest streak) and Matthew Chumley (2nd place) in the Fall 2008 POTW contest! The contest will return next semester.
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
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.