Your package from Orinoco has finally arrived!
It's the Master Chef's Environmentally-Friendly Measuring Cup Set. It comes with 64 measuring cups having a volume of 1 cup, 1/2 cup, 1/3 cup, 1/4 cup, ..., all the way down to 1/64 cup.
Because these are master chef's cups, they have master features:
- when in the presence of sufficient ingredient to fill themselves completely, they instantly fill to capacity with the ingredient at the command "riempire!"
- when not in the presence of sufficient ingredient to fill themselves completely, the command "riempire!" does nothing
- when full, they instantly and completely empty themselves at the command "vuotare!"
Because these are also environmentally-friendly cups, each cup instantly dissolves into fresh mountain air after one use (that is, upon being emptied). No waste, no pollution.
You have a giant 25 US gallon tub of nutmeg and an empty 1 gallon soup pot. As a master chef, you know that the best soups must have some nutmeg in them, but ideally as little as possible, making for perfectly nuanced flavour.
Using only your set of 64 single-use cups to transfer nutmeg between your nutmeg tub and soup bowl, both to and from, what is the smallest nonzero amount of nutmeg you can leave in your soup bowl?
For example, you could transfer 1/2 cup, then 1/3 cup, then 1/4 cup of nutmeg to the soup bowl, then 1 cup back to the tub to be left with 1/12 cup in the soup bowl.
There is, of course, an optimal solution to the puzzle, but it's extremely hard to intuit (in my opinion), hence everyone's best attempts are welcome. The lower, the better!
(Disclaimer: This problem is, at its core, mathematical. It isn't a lateral thinking puzzle, there are no tricks, and you can disregard any realistic physical limitations such as errors in measurement or being left with an unreasonably tiny quantity of nutmeg.)