If you were eating a soup from a bowl with 500ml of soup taking 25ml spoonfuls, and the rain replaced the volume that you ate at the same rate as you ate it, how many spoon fulls would it take for the soup to be completely replaced with water? Also, when that happens, would it still be the same soup?
Well 14 spoonfuls wouldn’t finish the soup even if it wasn’t raining so that’s definitely wrong.
Ok, Now I’ve got some sort of estimate. Still didn’t do it “the proper way”, because writing a simulation was more fun than reading a few Wikipedia articles about mathematics, which would have taken… probably only a fraction of the time I spent on writing some horrible R code that produces suspicious results.
My simulation is based on keeping track of different kinds of molecules. First, I calculated how many water and soup molecules there are. I assumed that they both have the same molar mass. I also assumed that 500 ml = 500 g, which is close enough IRL. The number of each molecule type doesn’t have to be a whole number, so fractions are allowed. When the soup molecule count drops to 0.5, it means that there’s a 50% chance of 1 soup molecule being present. I’m not entirely satisfied with this implementation, but it felt reasonable at the time. Anyway, I set the threshold of my while loop to 0.5 soup molecules.
Anyway, here are the results!
It took only 1146 spoons to scoop out the final molecule with 50% certainty. If you used a smaller 5 ml spoon, it would take 5848 spoons, which is still way smaller than I expected. I really thought it would be something totally absurd like the the number of atoms in the observable universe. I feel kinda skeptical about my code until I see a proper mathematical proof about this.
Close enough, somebody mathed it out to 1144 in the comments