I'm guessing no one will be able to answer this but maybe Tableplay. He seems to be the best at high-level math. I can't really discuss where this is applicable but figured it might be interesting to discuss?

So there is a bowl with an undisclosed number of tickets. These tickets each have a number assigned (but random - not a series). When a ticket is drawn the number is announced on the ticket and the ticket is placed BACK in the bowl. This process is repeated for 100 times. You have results like - 1 number 3 times, 3 numbers 2 times, and 91 numbers that were drawn exactly once.

So how do I go backwards from these numbers to estimate how many tickets are in the bowl?

If I was to figure this out - I would write a sim to try various amounts of tickets - then average results and find the one closest to the sample I took during the drawing. For a reasonable programmer these little toy games are really simple to write. It is pretty much my go to solution anytime I've tried to figure out something like this.