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)
A: There are an infinite number of marbles in the container. If there were only a finite number of marbles in the container, then there is some number M for which every marble in the container is numbered less than M. But at the end of the Mth interval, there are 9M marbles lef in the container, and none of these will ever be removed.
B: The container is empty. If it were not empty, then you could pull a marble out. Suppose you did, and the marble was numbered M. But in the Mth interval, you took out the marble numbered M, which is a contradiction. Hence you cannot take out any marbles, and the container is empty.
Solution
