One hundred people, one hundred bushels of grain, three different rations
A wealthy 8th-century head of household orders 100 bushels of corn handed out to exactly 100 people under his roof, men, women and children among them. Every man is to receive 3 bushels, every woman 2, and every child just half a bushel, with nothing left over. How many men, women and children are there?
Reveal the answer
The equation (5 x men + 3 x women = 100) has six valid whole-number answers: 2 men/30 women/68 children, 5/25/70, 8/20/72, 11/15/74, 14/10/76, and 17/5/78. It's one of the world's oldest surviving 'distribution' arithmetic puzzles, from Propositiones ad Acuendos Juvenes ('Problems to Sharpen the Young'), a set of riddles attributed to Alcuin of York (c. 735-804), tutor to Charlemagne.
— Alcuin of York, Propositiones ad Acuendos Juvenes — c. 800 AD