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)

assuming at 30 seconds you put in marbles 11-20 and then at 45s you put in 21-30 and so on...

in A and B. your just removing one of the 10 marbles.  either the smallest numbered one left in your container (B), or the last one that you just put in (A).  at the end there are infinite marbles left.

(A) the first round you take out marble (10*1)=10, the second (10*2)=20...

(B) the first round you take out marble N=1, the second N=2... but at the end you are taking out marble number infinite/10 and there are still infinite marbles left in the container.

Posted by jamie on 2005-10-19 00:05:22