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
more by Cory Taylor)
Consider this: Given the problem as posted and consider part (B). If you say there are marbles in the container after the minute has expired, pull one out. What number will be written on it? N you say? But that marble was thrown out in step N of the process......
The point is, there is no marble that you can point to that was not thrown out before the minute was over. You cannot pull a marble from the bag. So the bag is empty.
And there is one major difference between (A) and (B) that you missed. In A, the marble thrown out is always one of the last 10 you put in. So the other 9 will always remain in the bag. In (B), the marble thrown out (after the first step) is always from a previous step. So no marble is ever safe: each of the 10 you just put in will get removed at some specific later step. That is the difference between (A) and (B). It is not just a matter of labels....