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
a functional equivalent by Cory Taylor)
I have two other attempts to clarify things:
1 - OK, forget the labels. Restate the parts as follows. In each step you put in 10 marbles (one at a time). Then for part (A), always take out the last marble you put in. But in (B) always take out the marble that has been in the bag the longest. No labels now, but the same answer. The fundamental difference between (A) and (B) is that in (A), "old" marbles are left in the bag forever. In (B) all the marbles you put in will be removed at some later step. No marble currently in the bag will ever remain there. THAT is what makes them different.
2 - OK, don't like that? Here is one I mentioned before. Start with all the marbles in the container. Thinking in terms of integers, the problems then become: in (A) you throw out all the integers that are multiples of 10. In (B) you throw out all the integers that are multiples of 1.
At each step, I agree that there are an infinite number that have not been thrown out. But after the minute is over (an infinite number of steps), (A) leaves you with lots of integers, and (B) with none.
I'm starting to repeat myself, so I guess I'd best leave this thread....
re: a functional equivalent
