The lotus in the pond
A lotus stalk rises exactly half a cubit above a still pond. A gust of wind bends it sideways until its blossom touches the water's surface two cubits from where the stem originally stood. Assuming the stem itself doesn't stretch, how deep is the pond?
Reveal the answer
3.75 cubits deep (and the stem is 4.25 cubits long). Treat the bent stem as the hypotenuse of a right triangle: if d is the depth, the stem's full length is d + 0.5, and by the Pythagorean relation (d+0.5)^2 = d^2 + 2^2, which solves to d = 3.75. It's one of the best-known problems from Bhaskara II's Lilavati (1150 CE), still used today to teach the Pythagorean theorem.
— Bhaskara II, Lilavati — Chapter on the Pythagorean theorem, c. 1150 CE