Date: Dec 28, 2012 4:29 PM
Author: quasi
Subject: Re: Probability Pill

quasi wrote:
>William Elliot wrote:
>

>>Each day I take 1/2 an aspirin tablet. I bought a bottle of
>>100 tablets; each day I take out one, if it's whole I break
>>it half and eat a half and put the other half back: if I pull
>>out a half tablet I eat it. I was wondering after I break the
>>last whole one what the expected number of halves are in the
>>bottle? I assume that any piece I pull out has uniform
>>probability.

>
>I suspect that the above question is not actually yours.
>
>If that's the case, what is the actual source?
>
>Is it from a poster in another forum? If so, why do you omit
>mention of the poster and the forum?
>
>Is it from a book or math contest?


Based on the results of a web search, it's almost certain that
William Elliot got the problem from an outside source. There's
nothing wrong with that, but I think he should then at least
attribute the problem to his source.

William's question is a special case of problem E3429 in the
April 1991 issue of the American Mathematical Monthly. It was
proposed by Donald Knuth and John McCarthy and was solved in a
later issue. The AMM editors indicate that the some of the
solvers were already familiar with the problem. I quote the
AMM editors:

Robert High saw a version of it in the MIT Technology
Review of April, 1990. Helmut Prodinger reports that he
proposed it in the Canary Islands in 1982. Daniel Moran
attributes the problem to Charles MacCluer of Michigan
State University, where it has been known for some time.

A detailed discussion of the problem can be found in one of
David Pollard's course handout on expectation:


<http://www.stat.yale.edu/~pollard/Courses/241.fall2011/YaleOnly/notes2011/Expectation.pdf>

See example 7 starting on page 17 and continuing through page 22.

But here's my guess as to how William got the problem ...

A student, unaware of the origin of the problem, received
the problem as a HW problem (possibly a challenge problem
for extra credit) and posted the problem in some forum,
asking for a solution. William then posted the question
to sci.math, with no attribution as to his source.

If solutions had appeared in sci.math, William would
presumably have posted a solution back to the forum where
he first saw the question. But in doing so, would William
have mentioned the source of his solution, giving credit
to the solver? I wonder.

But the above is just a guess.

So William, tell us -- what's the real story?

quasi