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I've heard of the analogy that infinite monkeys with typewriters will eventually produce Shakespeare's Romeo and Juliet, but what if, instead of "eventually", I want "one year". How many monkeys do I need to produce Romeo and Juliet within one year?

What is the function for producing Romeo and Juliet in a certain timeframe as a function of number of monkeys?

Assume that the monkey is basically just a random character generator. It only generates any of the characters that are present in Romeo and Juliet: letters, punctuation, numbers (perhaps? I'm not a literary expert).

Monkeys type at 12 wpm.

Romeo and Juliet is 24545 words long.

Also, a good point was made below: let's amend the question to make it a probability. How many monkeys do I need to have a 95 percent chance of producing the work within a year?

  • There is no way to answer a question like this. What are you assuming about the monkeys? – saulspatz Mar 02 '19 at 16:35
  • I think it’s safe to assume that the monkey chooses a character at random each time. – H Huang Mar 02 '19 at 16:37
  • question is tagged as probability but has nothing to do with it. – adhg Mar 02 '19 at 16:37
  • I think you still just need infinitely many monkeys. If that is the case, then with infinitely many monkeys you can produce the script in as much time as it takes to typewrite it. – frabala Mar 02 '19 at 16:56
  • @HHuang How often does "each time" happen in a year? – Hagen von Eitzen Mar 02 '19 at 17:01
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    $\color{red}{42}$ since this is "the Answer to the Ultimate Question of Life, The Universe, and Everything" – Claude Leibovici Mar 02 '19 at 17:08
  • @HHuang that's a reasonable assumption for the question, but in practice that's far from ture. IIRC somebody actually made an experiment to see what happens, but it's also plausible that it's not independent. Effects like pressing the same button repeatedly or slamming the hand somewhere pushing multiple close by buttons should be highly significant. – quid Mar 02 '19 at 18:15
  • Even taking independence as assumption, you'd need to specify how quickly one monkey types, do you care about capitalization, how many keys are there on the keyboard etc. Moreover, you'll always just get a probability if your restrict to a finite scenario. You could ask how many monkey do you need to have a 50 percent chance of having it after one year for example. – quid Mar 02 '19 at 18:20
  • All good points. I have amended the problem. @adhg Why is the question irrelevant to probability? –  Mar 03 '19 at 17:10
  • now that you have adjusted the question it shows relevancy to probability; before the adjustment it was merely about counting. make sense? – adhg Mar 03 '19 at 17:12
  • The edit makes the question more answerable, but if you want a definite answer you should add the typing speed of the monkeys and the length of Romeo and Juliet. – Arnaud D. Mar 03 '19 at 17:39
  • That makes sense @adhg! –  Mar 05 '19 at 02:14
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    All joking aside this is straight forward and solvable, isn't it. If there are, say 62 characters and Romeo and Juliet is, say 147270 characters long so the probability a monkey types R&J in "a book" or 147270 characters is $\frac 1{62^{147270}}$ so if we type $n$ books the prob not typing R&J is $(1- \frac 1{62^{147270}})^n$ so we want $n$ so that $(1- \frac 1{62^{147270}})^n=.05$. So we need $\frac {12n}{147270}\frac 1{36524*60}$ monkeys. – fleablood Mar 05 '19 at 03:25
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    So we need $\frac {12\log_{1-\frac 1{62^{147270}}}(0.05)}{1472703652460}$ ... which is HUGE*... – fleablood Mar 05 '19 at 03:27

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