AIME I #15 2008

[stupidityismygam]

A square piece of paper has sides of length [unparseable or potentially dangerous latex formula] From each corner a wedge is cut in the following manner: at each corner, the two cuts for the wedge each start at distance [unparseable or potentially dangerous latex formula] from the corner, and they meet on the diagonal at an angle of [unparseable or potentially dangerous latex formula] (see figure below). The paper is then folded up along the lines joining the vertices of adjacent cuts. When the two edges of a cut meet, they are taped together. The result is a paper tray whose sides are not at right angles to the base. The height of the tray, that is, the perpendicular distance between the plane of the base and the plane formed by the upper edges, can be written in the form [unparseable or potentially dangerous latex formula] where [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] are positive integers, [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] is not divisible by the [unparseable or potentially dangerous latex formula]th power of any prime. Find [unparseable or potentially dangerous latex formula]

http://www.artofproblemsolving.com/Foru ... c&id=13175

[88bobcat]