## 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.

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.

## Stephan 1:07 am

onDecember 20, 2009 Permalink |Presumably the answer is 1? Take 1 marble from bag 1, 2 from bag 2, and so on until 12 from bag 12, then weigh them, and the mass difference from 144 grams is the bag number that contains the light marbles?

## verpa 4:48 am

onApril 17, 2010 Permalink |I think this is variant on a google hiring quiz. Assuming the bags are sealed ( otherwise Stephan’s I think would work ) I think the answer is 2.5. If there were 9 bags, the answer would always be 2. With 10, you can get it best case 2 with a bit of luck, otherwise worse case 3. I tend to be crap at these though.

## Bill 5:14 am

onJuly 21, 2010 Permalink |The answer is one.