A leaking wine cask with three cracks, and 7,200 pints to account for
A cask holds 7,200 pints of wine and springs three cracks at once. Through the first crack, a third plus a sixth of the wine leaks out. Through the second, exactly a third leaks out. Through the third, only a sixth leaks out. How many pints ran out through each individual crack?
Reveal the answer
3,600 pints through the first crack (a third-plus-a-sixth equals one half of 7,200), 2,400 through the second (one third), and 1,200 through the third (one sixth) — the three fractions add up to exactly 1, so the whole cask drains dry. It's a problem from the Propositiones ad Acuendos Juvenes ('Problems to Sharpen the Young'), a collection of over 50 puzzles traditionally attributed to Alcuin of York, the English scholar who ran Charlemagne's palace school around 800 CE.
— Alcuin of York (attrib.), Propositiones ad Acuendos Juvenes — c. 800 CE