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 Interestingly by Sam)

Actually, the interesting thing in case A is that the number of marbles outside the container is a greater infinity than the number of marbles inside. That is because, while there is exactly one marble outside the jar for every marble inside (1=>10, 2=>20, etc), the converse is not true. Every power of ten is outside the jar, and none of them but ten itself have a corresponding value n/10 inside the jar (100, 1000, 10000, ...).

Posted by DJ on 2003-09-08 22:58:25