Two Crossed Ladders in an Alley: How Wide Is It?
Two ladders of different lengths are propped up across a narrow alley, each leaning from the base of one wall to somewhere up the opposite wall, crossing each other partway up. You're told the two ladders' lengths and the height above the ground where they cross. Nothing else. How wide is the alley?
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It can be solved, but not neatly: setting up the geometry produces a quartic equation with no simple closed-form answer, so real solutions are usually found numerically. Martin Gardner discussed the problem at length in his book Mathematical Circus (1979), tracing references to it back to at least 1895, though its precise origin is unknown.
— Martin Gardner, Mathematical Circus — Mathematical Circus (Knopf, 1979), pp. 62-64
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