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?

  • palordrolap@fedia.io
    5·
    1 day ago

    I get 1132 spoonfuls as a lower bound.

    Big assumptions:

    1. Soup is considered identical to water for the sake of molecule count and density.
    2. Soup and water are evenly mixed before each spoonful.
    3. Each spoonful is guaranteed to contain the correct fraction of soup to water from the mix.

    There are ~1.666×10^25 molecules of water in 500 ml (source: WolframAlpha). We seek what power of (500-25)/500 [= 19/20] is small enough to counter this number in order to get to the level of single molecules. This is about 1132.

    But like you point out, it’s going to be tasting watery a long, long time before that happens. It’s 50% rainwater after about 14 spoonfuls (Sanity check: That would be 10 if the container was big enough and no spoonfuls were being removed.). ~90% at 45 spoons and ~99% at 90 spoons.

    • NeatNit@discuss.tchncs.de
      5·
      1 day ago

      I got 1022 as the expected value, see my top level comment.

      Edit: oops, made a big mistake. Will fix it!

      Edit: after correcting I got 1144, much closer to your result 1132.