The Past Asks You: Citrus Harvest, 1307
Tacuinum Sanitatis
The Past has questions as well as answers. Here’s one that’s been confusing people since the Middle Ages:
I go to a garden, and I come to the foot of an orange tree. I take one fruit. And then I take one-tenth of the remaining fruits. Then another person arrives after me, and takes two fruits, and again one-tenth of the remaining fruits. Then another person arrives and takes three, and again one-tenth of the remainder. Then another person, who takes four, and one-tenth of the remainder. And thus many people arrive. Then the person who comes last, that is, at the end, collects all the rest. And this person doesn’t find either more or less than the others got. And everyone gathers the same amount of fruit. And as many people as there were, that many fruits each person had. I want to know how many people there were, and how many fruits each one collected, and how many fruits there were in total.
Jacopo da Firenze, Tractatus algorismi
Medieval agricultural practices: more complicated than you imagined. Good luck!
Your local high school mathlete would identify this as an algebra problem and should be able to tell you how many tenths of a citrus-picker you need to hire. Back in the 1300s, though, they didn’t have symbolic expressions (“x+1=2”) the way we do and they make this question far more tractable. While the Islamic world and the ancient Greeks contributed substantially to algebra, it wasn’t until Descartes that we had something similar to modern notation.
There’s a lovely book about the Renaissance mathematician, Jerome Cardano, called The Quantum Astrologer’s Handbook. Amongst other things, it describes the public contests that would be held by roving minstrels of math. “I challenge you to tell me that number which when cubed is equal to the sum of one and the thing itself, less its square.” (1 is a solution. -1 is as well, though I’m not sure they’d accept a negative answer...) Math is not required to enjoy- no exercises left to the reader... https://www.goodreads.com/book/show/36277283-the-quantum-astrologer-s-handbook