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!