You have an empty container, and an infinite number of marbles, each numbered with an integer from 1 to infinity.

At the start of the minute, you put marbles 1 - 10 into the container, then remove one of the marbles and throw it away. You do this again after 30 seconds, then again in 15 seconds, and again in 7.5 seconds. You continuosly repeat this process, each time after half as long an interval as the time before, until the minute is over.

Since this means that you repeated the process an infinite number of times, you have "processed" all your marbles.

How many marbles are in the container at the end of the minute if for every repetition (numbered N)

A. You remove the marble numbered (10 * N)

B. You remove the marble numbered (N)

(In reply to re(2): How about this variation? Any Input FatBoy? by Brian Wainscott)

nah,
It was not the infinite number of marrbles in the bag or jar. What was catching me up was the fact that you stopped processing them.
I'm willling to accept that in this kind of discussion we suspend disbeleif for the sake of discussing the calculations. But I think I can describe a little better what my concerns are, if anyone's interested I'll give it a try, if not then go ahead and ignore this...:
The problems states: "...you have processed all of your marbles." That sounds to me like you have stopped. If you have stopped then just before (some incredibly infinitely small time before) you put a marble in teh container and deiscovered that your infinite supply was gone. That marble was the last marble you put in. If there is a "last" marble then the number of marbles is finite.

Put another way, when you reached into your supply to pick up that last marble it was the only one there, your supply was a set of 1 marble (CLearly finite) since you can not make an infinite set finite simply by taking things out of it that means that the supply was not infinite in the first place.

This is all part and parcel to the suspension of disbelief that is necessary for this kind of thought. Perhaps if the initial problem had said something like how many marbles were where in the last infinitessimally small unit of time before the minute ends I would not have had a problem. In that Schroedingerian blur of probablilities, I can swallow the inifinities involved.

It seems to me that the way the problem is set up, the minute can not end.

At any rate, I didn't respond to your first "how about this variation?' posting because I figured that everyone had had enough of hearing about my concerns and that they were sort of getting in the way of the broader discussion of the concepts involved. Its sort of like a group of Catholic theologians discussing their interpretations of the tripartite nature of God adn being interrupted by an athiest who wants to argue about the feasability of immaculate conception. Its not that the theoogians don't want to discuss immmaculate conception. ITs just that they have already stipulated there positions on it and are working based on that agreed framework.

Posted by FatBoy on 2003-09-12 07:32:41