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This question already has an answer here:

If pi goes on forever and is completely random, if ascii would be mapped onto pi would you eventually find the Declaration of Independence in it? If so, by what digit of pi can we reasonably expect this to happen?

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marked as duplicate by Asaf Karagila, Thomas Andrews, Namaste, saz, Najib Idrissi Nov 16 '14 at 16:26

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There are 1137 words in the Declaration of Independence, assume five letters per word gives 5685 letters.
Three digits are enough per Ascii character, so 17055 digits.
You can expect any digit to appear once in ten; any pair of digits to appear once in 100, and so you might expect the Declaration of Independence to appear once every $10^{17055}$ digits.
It is not known whether $\pi$ is 'normal', so the Declaration of Independence might never appear at all.

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  • $\begingroup$ Ok cool whats the difference between a normal number and a non normal number? $\endgroup$ – user2640586 Nov 16 '14 at 14:11
  • $\begingroup$ Exactly what we are talking about - that every sequence appears the expected proportion of the time. en.wikipedia.org/wiki/Normal_number $\endgroup$ – Empy2 Nov 16 '14 at 14:20
  • $\begingroup$ by the way I know it's been a long time since I asked this question but I just had this thought: letters which are predominantly in the declaration of independence only make up 52/256 ASCII values. does this sway the odds? Or would we have to do something like 3 digit number mod 52? $\endgroup$ – user2640586 Jan 4 '15 at 0:22

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