Here’s a quiz that’s mostly geometrical, but you may need to do a bit of mechanical/engineering research to get to the answers.
The Vex Versaplanetary gearbox offers single stages ranging from 3:1 reduction down to 10:1 reduction. These gearboxes are driven at the sun gear, have a fixed annular gear, and drive output on the planetary carrier. Assuming that there are at least three planet gears of the same size as each other, what are the theoretical highest and lowest possible reductions possible for a single stage gearbox of this type? For purposes of this calculation, you may allow the teeth to be infinitesimally small, so that this becomes a “roller box” rather than a gear box.
As with Ether’s quizzes, I’m not looking for full mathematical rigor, but show enough of your work that I can tell where your numbers are coming from.