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(3): How about this variation? Any Input FatBoy? by FatBoy)

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

Now we are getting to the crux of the problem. The processing, indeed, can not end. However, since the person processing the marbles takes increasingly shorter times to process each succeeding step, that person, although he approches the end of the minute as a limit, never actually reaches the end of the minute.

The question is then passed on to a second participant in the experiment who is in a more "normal" frame of reference. Since the first participant never finished processing, the numbers involved are infinite, but since the second participant is in a reference frame that is past the end of the minute that represents the limit of the time-frame for the first participant's processing, to him the processing is complete, but the numbers are still infinite.

Posted by TomM on 2003-09-12 11:37:09