The minimum number of marbles is:

>!$49$. Put a single marble in $49$ of the bags, and then put all the bags one inside each other, and then put the empty bag inside them all. In other words, going from outside to in, we will have bag-marble-bag-marble-...-bag-marble-bag, and the sequence of the number of marbles in each bag going from inside to out will be $0,1,2,3,...,49$.

We can prove this is the minimum number because:

>! For there to be a different integer number in each bag, the sequence that gives the smallest possible number in the bag with the most marbles is $0,1,2,...,49$, so at least one bag must have $49$ marbles in it.

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With tongue firmly planted in [cheek](https://xkcd.com/169/), the minimal number can be drastically reduced to:

>! $1$ with a simple repeated application of the [Banach-Tarski theorem](https://xkcd.com/804/).