Problem of the Week: Octahedron
Let n be a nonnegative integer. For each point (i, j, k) in three-dimensional space such that i, j, and k are integers satisfying |i| + |j| + |k| ≤ n, place a unit cube centered at (i, j, k) with edges parallel to the coordinate axes. The result will be an arrangement of cubes similar to an octahedron, having n + 1 cubes along each diagonal edge. For example, if n = 5, the result is the shape shown below. (An animated version is also shown, and a larger version is available.) What is the surface area of this shape, in terms of n?
Winner
Last week's winner was Tobias Davis.
Other entries which were correct and had sufficient justication were: Rob Brase, James Carraher, Christopher Haccius, Seth Hoffert, Alan Holdorf, Travis Johnston, Yuchen Ling, Huong Nguyen, and Michael Schaal.
