You are given a cube of unit edge length. Find the shortest distance between two opposite vertices (i.e. the end points of a space diagonal) if your path between the two vertices has to be on the surface of the cube.
+310 The shortest distance is the edge of a cube plus a diagonal of the base square. (Draw a diagram, and after a bit of trial and error & intuition, you should see why). So the answer is \(1+\sqrt2\).
