Drop a needle onto a floor of parallel lines enough times and it will compute pi
Take a needle exactly as long as the gap between a floor's parallel lines, and drop it randomly over and over, recording how often it lands crossing a line versus landing clear of one. Georges-Louis Leclerc, Comte de Buffon, posed this problem in 1777. What does the ratio of crossings to total drops have to do with the number pi, and how could dropping needles possibly estimate it?
Reveal the answer
The probability of a crossing works out to exactly 2/pi, so flipping the ratio from enough trials gives an estimate of pi itself, purely from physical randomness rather than any geometric construction. It's one of the earliest known problems solved using geometric probability, and it later inspired the broader class of 'Monte Carlo methods,' which estimate hard mathematical answers by running large numbers of random trials rather than calculating directly.
— Georges-Louis Leclerc, Comte de Buffon, Essai d'arithmétique morale — 1777