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)

I think I have found a somewhat elegant way of explaining why the answer to B is infinity not zero.  I think the best way to describe it is to see how in essence you are trying to chase infinity and will never catch it.

To illustrate it I will use a similar but simpler example where you add the next 2 marbles at each step N and remove marble N.  In this method this is what the jar looks like at each step

step 1
add 1,2 and take 1
{2}

step 2
add 3,4 and take 2
{3,4}

step 3
add 5,6 and take 3
{4,5,6}

as you can see at the end of step N the jar will contain the marbles numbered N+1 to 2N.  Thus will have N Marbles in it.
Thus after an infinite number of steps it will contain an infinite number of marbles.  The paradox is resolved because you have to realize that although after an infinite amount of steps you have removed marbles 1 to infinity (and thus appears all are removed) there is a greater infinity of marbles left in there.

Posted by Daniel on 2006-07-03 20:08:52