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How long does a sequence of random decimal digits (0, 1, 2, ..., 9) need to be before you can "reasonably" expect the sequence to contain all numbers from 0 through 999 (inclusive).

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It's up to you to define "reasonably".

E.g.: The sequence 1823 contains 1, 2, 3, 8, 18, 23, 82, 182 and 823.

The sequence 1053 contains 0, 1, 3, 5, 10, 53, and 105.

justme
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    This is obviously related to the Coupon Collector's problem but the interdependency among sequences makes it not quite the same thing. (Note that you could just ask for 'all possible three-digit sequences' and have virtually the same problem, but one that might be easier to analyze.) Interesting question! – Steven Stadnicki Oct 08 '15 at 19:13
  • Define what random means for the digits in the sequence. If every natural number is equally likely to be chosen then there's no hope of finding such a length. – Spencer Oct 08 '15 at 19:13
  • @Spencer 'Digits' defines that pretty clearly; I think it's natural to assume a uniform distribution that assigns an independent probability $\frac1{10}$ to each digit in the sequence. – Steven Stadnicki Oct 08 '15 at 19:14
  • @StevenStadnicki, ah I understand now. – Spencer Oct 08 '15 at 19:17

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