You have 100 bags of 100 marbles. All of the marbles in all of the bags are identical 1 gram marbles, except for one of the bags, which contains marbles that weigh 1.001 grams. You have a scale that can to an accuracy of 0.001 grams.
What is the minimum number of weighings required to identify the bag with the slightly heavier marbles?
You only need 1 weighing.
Proof
Number each bag from 1 to 100. Onto the scale put \(i\) marbles from bag #\(i\). That is put 1 marble from bag #1, 2 marbles from bag #2 and so on.
The total number of marbles, \(M\), on the scale is:
\[\begin{align} M & = \sum_{i=1}^{100} i \\ & = \frac{100 (100 + 1)}{2} \\ & = 5050 \end{align}\]The difference between the actual weight and 5050 grams divided by 0.001 will give you the number of the bag with the slightly heavier marbles.