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On Average (Posted on 2004-01-26) Difficulty: 4 of 5
What is the expected number of rolls of a fair, normal 6-sided die, one is required to make, so that each of the 6 numbers comes up at least once?

Hint: this is not necessarily an integer answer
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As an aside, it would be interesting to see the computer program simulation of this, but this would not be proof of the solution (merely evidence supporting the proof).

See The Solution Submitted by SilverKnight    
Rating: 3.7500 (4 votes)

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re(2): solution plus simulation-- and another question or two | Comment 4 of 11 |
(In reply to re: solution plus simulation-- and another question or two by SilverKnight)

There is an analytical way of solving the likelihood of having gotten all 11 possible dice totals after n throws. The formula has so many terms that a computer is almost essential. To find the mode and median requires doing this for multiple values of n, and thus could be considered brute force. The mean requires enough to essentially account for "all the possible" values of n (the quotes indicating we stop after essentially having probability 1.000000000000000 of having reached the goal), and so is even more of a brute force method. But it doesn't get as far down as picking each possible sequence of throws, or be a mere simulation.
  Posted by Charlie on 2004-01-26 14:58:49

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