Let $N$ be a natural number. We uniformly choose a random number between $1$ and $N$ (both inclusive) and subtract it from $N$. If we repeat this on the new number obtained, what is the expected number of trials needed to reach $0$?
The crux is that the limits of random distribution change depending on the previous number. How can we handle this?
Edit: Random number in range [1, N] i.e. you have N choices for the random number, each one having the same probability of 1/N (uniform distribution).
Then after subtracting, the resultant number obtained becomes new N. So, N is not constant. N is changing according to the previous random number.
A more practical version: you have N chocolates and you eat some random number (as described above) each day. After how many days will the chocolates get over?
As a follow-up to the discrete case, what if the uniform distribution is continuous?