The spider and the fly

Question

A rectangular room is 30 feet long, 12 feet wide and 12 feet high. A spider sits on the middle line of one end wall, 1 foot below the ceiling. A fly sits on the middle line of the opposite end wall, 1 foot above the floor, and does not move. The spider must crawl along the walls, ceiling or floor (no jumping, no webs). What is the length of the shortest route? The straightforward route, up 1 foot to the ceiling, 30 feet along the ceiling, and 11 feet down the far wall, is 42 feet. Beat it.

Accepted Answer

Forty feet, by a route that crosses five faces: the spider's end wall, the ceiling, a side wall, the floor and the fly's end wall. Unfolding. Any crawling route can be straightened by cutting the room along suitable edges and laying the faces flat; the shortest route on the surface is a straight line on some unfolding. The obvious unfolding (end wall, ceiling, end wall in a straight strip) gives 1 + 30 + 11 = 42 feet. The clever unfolding. Lay out the faces so that the route goes: up the spider's end wall to the ceiling, across the ceiling, down a side wall, across the floor, and up the fly's…

The spider and the fly

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