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)
How would you have thought differently about the problem if all the marbles had started in the container? Then the problem would look like this:
You have a container holding an infinite number of marbles, numbered 1 to infinity. At the start of the minute, you remove one marble. You do this again after 30 seconds, then again in 15 seconds. You continuously repeat this process, each time after half as long an interval as the time before, until the minute is over.
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)
Do you think this problem is different? If so, why? If not, why not?
How about this variation?
