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)

You theorhetical math guys are a bit over my head, so forgive a poor holder of just an engineering degree. If these observations are cliched, please ignore.

As I understand infinity it is used to describe a set size that is infinite. But this problem indicates that you stop processing marbles at the end of a minute. At that time the number of marbles in the jar (and those discarded) ceases to be infinite. You put them in the jar and in 1/10 the cases taken them back out. Once you stop doing so you have limited the set of marbles. therefore it is not infinite.

There is a finite number x which is the number of times you went through the process of putting in and taking out. (don't tell me that you did it an infinite number of times) once you stop, which you did at the end of the minute you have limited the number of interation and it is no longer infinite.

so, the answer to questions A and B are both 9x where x is defined as the number of iteration you performed.

Posted by FatBoy on 2003-09-09 11:05:26