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 The solution isn't... by Ken Haley)

I disagree.  I'm going to take very much the same position as SilverKnight and Brian Wainscott, whose comments you can read below.

No, we can't add or subtract infinities, because they're not numbers.  Infinities are cardinals (I encourage you to google cardinals and infinite sets), meaning they are the sizes of sets.  The set of marbles we add is infinite (aleph-null) and the set we take away is infinite (aleph-null).  But they are not necessarily the same set, just the same size.  And we are not necessarily subtracting the sets, at least not in the normal sense of subtract, but removing all elements of the latter set from the former set.  The leftover marbles form a new set.  In the first case, this new set is {1,2,3,4,5,6,7,8,9,11,12,13,...} and in the second case, the new set is the null set.

In a way, it doesn't matter how the marbles are labeled.  In a way, though, it does.  Marbles Bonanza II, posted this morning further explores this.

Posted by Tristan on 2005-06-22 01:03:08