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).

(1/6)*6 is the minimum number of rolls that can be made if you get a different roll each time. If you don't get all six numbers on the inital six rolls you keep rolling up till infinity because there is no guarantee that you will get all six numbers on a fair 6-sided die. The equation for larger rolls will be (1/6)*(6+i) i being a varible that will be incremented by one each roll after the sixth roll.

Posted by Vincent on 2004-03-09 14:15:17