# [S] Superman.

Rolf Turner (rolf@math.unb.ca)
Thu, 7 May 1998 09:53:56 -0300 (ADT)

This question has ***nothing*** to do with S/Splus;
I just figured there are so many clever and knowlegable
people in this list ....

I apologise to those who are annoyed by my taking up
bandwidth with non-S/Splus material.

so as not to waste any more S/Splus bandwidth on frivolity.

probability problem. (Sorry 'bout that alliteration.)

I found this problem in a book (I ***think***) some time ago, and now
I can't remember where, and it's driving me nuts. I thought it was
in one of Sheldon Ross's books, but I can't locate it in any of those
that are on my shelves.

The problem goes like this:

At one minute to midnight, Superman places ping-pong balls
labelled 1, 2, ... 10 in an urn (with infinite capacity!).

At 1/2 minute to midnight he returns, and places balls labelled
11, 12, ..., 20 in the urn, and REMOVES ball 10.

At 1/4 minute to midnight he returns, and places balls labelled
21, 22, ..., 30 in the urn, and REMOVES ball 20.

At 1/8 minute to midnight he returns, and places balls labelled
31, 32, ..., 40 in the urn, and REMOVES ball 30.

....

How many balls are in the urn at midnight?

Now suppose that instead of removing balls 10, 20, 30, ... at
successive steps, he removes balls 1, 2, 3, ...
NOW how many balls are in the urn at midnight?

Finally, suppose that at each step (after the first) he removes
one of the k balls in the urn at random (with probability 1/k).
How many balls are in the urn at midnight?

Let me emphasize that I'm not asking for help in solving the
problem. (I can do THAT; sheesh!!!) I'm asking ``Where did I
***see*** the damned problem in the first place?'' Anyone recognize
it? (I think it's a cutie --- nice and counter-intuitive.)

cheers,

Rolf Turner
rolf@math.unb.ca
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