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I don't know if there is some equation for this problem, but I wrote an algorithm to solve it instead.
You throw a die and write down the numbers until you have rolled every number at least once. On average, how many rolls until you have marked down every number?
I think the answer is 14.7.
I don't know how to write it as a formula but the basic idea is: Sum 6/6..6/1
If that's right, can you get an average of how many numbers you have marked down by your nth roll?
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