
And "e" Appears from Nowhere: Quick Numerical Experiment with Clojure - RBerenguel
http://www.mostlymaths.net/2010/08/and-e-appears-from-nowhere.html

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cjg
This is the most interesting bit: "Select a random number between 0 and 1. Now
select another and add it to the first. Keep doing this, piling on random
numbers. How many random numbers, on average, do you need to make the total
greater than 1? The answer is e."

The proof appears right at the bottom.

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RBerenguel
And the proof is simpler than it would appear from reading the enunciate (at
least that's what I think, of course!)

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pjscott
That proof is amazingly clever.

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technoguyrob
Could be an easy Putnam problem.

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Confusion
I think you are underestimating the complexity of coming up with an analogy
that works. For instance, solving the same problem for 'How many numbers are
needed to exceed 2' is already _much_ harder and I don't think there exists a
similar 'easy' proof.

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etal
For kicks, here it is in R:

    
    
      PlusRandom <- function(initial, steps) {
        if (initial > 1) steps
        else PlusRandom(initial + urand(1), steps + 1)
      }
    
      mean(replicate(100000, PlusRandom(0,0))
    
      [1] 2.71872

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Marticus
I like it, although reading it at 9 AM this morning just hurt until I could
think about it in more detail later.

Pretty awesome really.

