If you are given many closed sacks filled with different amounts of identical marbles, how could you determine the weight of a single marble without opening the sacks? (Assume the weight of the sack material can be ignored.)

The only thing I could think of was to weigh the bag but its says to ignore the weight.

To determine the weight of a single marble without opening the sacks, you can use a two-step process involving weighing and some mathematical calculations. Here's how you can do it:

Step 1: Weighing Process
1. Take any sack and remove a certain number of marbles from it.
2. Weigh the remaining marbles in the sack using a precise scale and record the weight.
3. Divide the total weight of the remaining marbles by the number of marbles you removed. This will give you the average weight of each individual marble inside the sack.

Step 2: Calculating the Weight of a Single Marble
4. Now, choose another sack that hasn't been opened yet.
5. Take the extracted marbles from the first weighed sack (with known average weight) and place them one by one onto the scale, noting the total weight of those marbles.
6. Divide the total weight of the marbles in the second sack by the known average weight obtained from step 3.
7. The result will give you an estimate of the number of marbles in the sack.
8. Finally, divide the total weight of the marbles in the sack (obtained from step 5) by the estimated number of marbles (obtained from step 7). This will give you the weight of a single marble.

It is crucial to note that this method assumes that the marbles in each sack have a consistent weight and there are no other factors (such as variations in marble size or differing materials) that may affect the weight.