Two merchants can't turn a profit on pigs together — but split up, they suddenly can
Alcuin's puzzle: two merchants pool 100 coins and buy pigs at five for two coins, 250 pigs total. Selling them all together at the same rate they paid, they can't make a single coin of profit. But when they split the pigs between them and each sells his share at a different rate, they walk away ahead. How?
Reveal the answer
They divide the 250 pigs into two batches of 125, one of better pigs and one of worse. One merchant sells 120 of his at two pigs per coin (60 coins); the other sells 120 of his at three pigs per coin (40 coins), together recovering exactly the 100 coins they started with, while 10 pigs (5 from each merchant) are left over completely free, as pure profit. Selling jointly at the original blended rate could never produce this gain; splitting the batch and pricing each portion differently does. It's one of about 53 problems in Alcuin's Propositiones ad Acuendos Juvenes, written around 800 CE for Charlemagne's court.
— Alcuin of York, Propositiones ad Acuendos Juvenes — c. 800 CE