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# if there are infinite monkeys typing at infinite typewriters, how long does it take to type every work of Shakespeare's?

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if there are infinite monkeys typing at infinite typewriters, how long does it take to type every work of Shakespeare's?

Guest Apr 7, 2015

#3
+26971
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Never mind the whole works, just consider the phrase "to be or not to be" There are 18 characters (including the spaces).  Suppose the monkeys can type 18 characters a second and they only ever hit the 26 lower case letters of the English alphabet plus the space key.  Then there are 27^18 possibilities, so this many/18 seconds to get through them all (hence to guarantee getting the phrase). This many seconds is:

$${\frac{{{\mathtt{27}}}^{{\mathtt{18}}}}{\left({\mathtt{18}}{\mathtt{\,\times\,}}{\mathtt{3\,600}}{\mathtt{\,\times\,}}{\mathtt{24}}{\mathtt{\,\times\,}}{\mathtt{365}}{\mathtt{\,\times\,}}{\mathtt{1\,000}}\right)}} = {\mathtt{102\,439\,781\,348\,723.257\: \!530\: \!001\: \!284\: \!246\: \!6}}$$

Approximately 102439781348723 millenia.

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Alan  Apr 7, 2015
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We can't say.......but....since every permutation is possible.....it theoretically could be done.....

Unless.....you used some of Nauseated's monkeys........they are well-read with regard to both Shakespearean tragedies and comedies.......they could bang out something in a jiffy for you....!!!!

CPhill  Apr 7, 2015
#2
+10

Alas, tis true!

Guest Apr 7, 2015
#3
+26971
+13

Never mind the whole works, just consider the phrase "to be or not to be" There are 18 characters (including the spaces).  Suppose the monkeys can type 18 characters a second and they only ever hit the 26 lower case letters of the English alphabet plus the space key.  Then there are 27^18 possibilities, so this many/18 seconds to get through them all (hence to guarantee getting the phrase). This many seconds is:

$${\frac{{{\mathtt{27}}}^{{\mathtt{18}}}}{\left({\mathtt{18}}{\mathtt{\,\times\,}}{\mathtt{3\,600}}{\mathtt{\,\times\,}}{\mathtt{24}}{\mathtt{\,\times\,}}{\mathtt{365}}{\mathtt{\,\times\,}}{\mathtt{1\,000}}\right)}} = {\mathtt{102\,439\,781\,348\,723.257\: \!530\: \!001\: \!284\: \!246\: \!6}}$$

Approximately 102439781348723 millenia.

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Alan  Apr 7, 2015
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