A pig farmer wants to buy 100 pigs with 100 shilling. Now a boar costs ten shillings, a sow costs five shillingsand two piglets can be bought for one shilling.” How many boars, sows, and piglets can the pig farmer buy so that he spends all his money?
The buyer has bought one boar (b), nine sows (s) and 90 piglets (p): from the linear system of equations b + s + 2p = 100; 10b + 5s + p = 100, it follows that 19b + 9s = 100, whose only solution is that b = 1, s = 9.
The oldest collection of mathematical problems in Latin was probably written by Alcuin (735-804 AD). The greatest scholar of his time was not only Charlemagne’s most important political advisor, but also the Headmaster of the Aachen Court School. 53 of his puzzles are compiled in the “Propositiones”.