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)
Either way... you do "process" all the marbles.
Well... let's start with (B):
The set of marbles you put in... is {1, 2, 3, 4, ....} all the way to infinity.
The set of marbles you take out is {1, 2, 3, 4, ....} all the way to infinity.
They are equal, therefore there are no marbles left.
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Now... for (A):
The set of marbles added is {1, 2, 3, 4, ...},
But the set you remove is {10, 20, 30, 40, ....}
While the sets are both EQUAL IN SIZE, many particular marbles have not been removed, so there are still an infinite number of marbles remaining at the end of the minute.
Solution (I think)
