Puzzle of Tangential Relevance to Organic Chemistry

One of my Honours students, Victor, set me a logic problem yesterday. He’s noticed that I’m always busy, rarely around, and have a month-old baby, so I guess he thought I needed something to do. He said “Imagine you have 12 bags of marbles, and each bag has 100 marbles in it. All the marbles look identical. The marbles in 11 of the bags each weigh 10 g, but one of the bag contains all 9 g marbles.”

I was thinking “what’s this got to do with the extremely interesting experiments you need to be doing right now to complete your Honours thesis?” and he enlightened me: “You have an electronic balance,” (that’s the Chemistry relevance right there) “so how many weight measurements do you need to make to identify the bag with the light marbles?” I said “the obvious answer is four” and he said “No, way too many” and left my office.

How many measurements to detect the light bag?

How many measurements to detect the light bag?

I worked on setting a tute quiz, then something in the back of my brain squeezed out the answer. Would be nice to do a supramolecular host/guest version of this with mass spec somehow.