Two palm trees, two birds, one fish — where do the birds meet?
Two palm trees stand twenty and twenty-five cubits tall, sixty cubits apart. A bird perches at the top of each. Both spot a fish on the ground between the trees and swoop down to it in straight lines, flying at exactly the same speed, arriving at the very same moment. How far from the base of each tree does the fish appear?
Reveal the answer
The fish sits where the two straight-line flight paths are equal in length — since both birds fly at the same speed and land together, you need the point between the trees' bases equidistant from both treetops, found with the Pythagorean theorem. The puzzle appears in 'Miftah al-Hisab' ('Key to Arithmetic', 1427) by the Persian mathematician Jamshid al-Kashi, better known for his work on decimal fractions and a refined value of pi.
— Jamshid al-Kashi, Miftah al-Hisab (Key to Arithmetic) — Samarkand, 1427