The scribe Ahmes's 'aha' problem
Problem 24 of the Rhind Mathematical Papyrus, copied by the scribe Ahmes around 1650 BCE, poses a riddle about an unknown quantity the Egyptians called 'aha': a quantity, added to a seventh of itself, makes 19. What is the quantity? Ahmes solves it without algebra, using a guessing technique later called the method of false position. Can you find the quantity?
Reveal the answer
16 and 5/8 (written by Ahmes as the unit fractions 16 + 1/2 + 1/8). His method: guess a convenient value divisible by 7, see how far short of 19 the guess falls, then scale the guess by that same ratio to land on the exact answer. At roughly 3,650 years old, it's one of the earliest surviving examples of algebraic reasoning.
— Ahmes (scribe), Rhind Mathematical Papyrus — Problem 24, c. 1650 BCE