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**+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.

Don't hold your breath!

.

Alan
Apr 7, 2015

#1**+13 **

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

#3**+13 **

Best Answer

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.

Don't hold your breath!

.

Alan
Apr 7, 2015