A round city, 8,000 feet around — how many houses fit inside?
In one of Alcuin of York's medieval puzzle problems, a circular city has a circumference of 8,000 feet. Every house built inside it must measure exactly 30 feet by 20 feet. How many such houses can the city hold?
Reveal the answer
Alcuin's own answer was 6,400 — he replaced the circle with an equivalent rectangle and divided that up evenly, a crude shortcut. It badly undersells the real number: modern computer packing methods fit over 8,300 houses (8,349 in one published arrangement) into the same circle, nearly 30% more than Alcuin thought possible. Historians of mathematics consider this the earliest recorded circle-packing problem. Problem 29, "De Civitate Rotunda" ("On the Round City"), Propositiones ad Acuendos Juvenes, c. 800 AD.