The Spider and the Fly Problem

Henry Ernest Dudeney (1857-1930) is generally regarded as England's greatest creator of mathematical puzzles. The following puzzle is reproduced verbatim from his book "The Puzzles".

"Inside a rectangluar room, measuring 30 feet in length and 12 feet in width and height, a spider is at a point on the middle of one of the end walls, 1 foot from the ceiling, as at A; and a fly is on the opposite wall, 1 foot from the floor in the centre, as shown at B [see diagram below]. What is the shortest distance that the spider must crawl in order to reach the fly, which remains stationary? Of course, the spider never drops or uses its web, but crawls fairly."

HINT: The answer is not as obvious as it might first appear.

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