A room and a spider A room has the shape of a rectangular cuboid. The edges are 3, 4 and 5 metres. There is a spider in one of the corners. The spider now walks to the corner on the other end of the space diagonal using the shortest possible route. How much distance does the spider travel? * * * I think the solution is $ \sqrt {5^2+4^2}+3$ metres, but I am unsure.

If you "unfold the box" (into what I recall being called a net) as rectangles shaped in a cross (see here for what I mean < then you can draw the shortest line with a straight rule, and you can work out its length with Pythagoras's theorem.

It turns out that it is not fastest to cross the floor diagonally and then walk up one of the edges.