Recently I discussed an experiment with a friend. Assume we start a random experiment. At first there is an array with size 100 000, all set to 0. We calculate at each round a random number modulo 2 and select one random position in that array. If the number in the array is 1, nothing is changed and otherwise the pre-computed value is set. The question is: how many distinct hash values would we have added in 1%, 5%, 50%, 95%, 99% of all cases?

Example: 4 rounds with array of size 10:

```
Array Position random number
[0,...,0] 5 0
[0,...,0] 7 1
[0,...0,1,0,0,0] 6 1
[0,..0,.1,1,0,0,0] 6 0
[0,..0,.1,1,0,0,0] 2 0
```

First we considered this a somehow simple problem. But after thinking about for some hours, searching the web and asking some math students we couldn't find a solution.So do you know a probability distribution for this problem?