Crossing the moat with two short planks

Question

A castle with a square footprint is surrounded by a moat 10 metres wide on all sides, with square outer corners. You have two planks, each 9.8 metres long, and nothing to fasten them together or to the ground. Neither plank alone can span the moat. How do you cross? Check with numbers that your arrangement actually works.

Accepted Answer

Lay the first plank diagonally across an outer corner of the moat, its ends resting on the two outer banks. Lay the second plank from the middle of the first plank to the inner corner of the moat. Both fit, with room to spare. The geometry. Put the outer corner of the moat at the origin, with the two outer banks along the axes. The inner corner of the moat (the castle's corner) is at (10, 10). Rest the first plank with its ends on the two banks at distance d from the origin, at (d, 0) and (0, d). Its length is d times the square root of 2, so with a 9.8 m plank, d = 9.8 / 1.414 = 6.93 m (a li…

Crossing the moat with two short planks

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