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Bascule's Book (Posted on 2002-07-03) Difficulty: 5 of 5
Bascule is reading a book. What is the probability that the first digit of the page he is on is 1, 2, 3, 4 or 5?

a) obtain an expression
b) approximate a numerical value

See The Solution Submitted by Cheradenine    
Rating: 2.7500 (8 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts re: well.. | Comment 23 of 41 |
(In reply to well.. by Cheradenine)

> since the proportions are
> similar in all 10^x intervals, an expression
> in the form of a sum for these intervals will
> have a limit as x tends to ∞
>
> this reasoning implies that there exists
> a value between 0 and 1 which is the
> single correct answer to the question
> (probably between 0.8 and 0.9)

I'm going to have to disagree with this one as well. I don't think the quantity will ever converge. For each 10^x interval, there will be a fluctuation between 0.55 and 0.95 or somewhere thereabouts (I haven't worked out the actual numbers). Every octave exhibits this behavior. It's a bit like asking for the limit of sin x as x approaches ∞. It's a well-defined expression, but there is nevertheless no convergence.
  Posted by friedlinguini on 2002-07-10 05:11:44

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