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
re: The solution isn't... by Tristan)
Tristan, I'm very familiar with the ideas of cardinality, infinite sets, etc.
See my response to the Marbles Bonanza II puzzle, which you pointed out
to me (thanks for that!). I think that puzzle underscores the
point I was trying to make. Here's what I think is
meaningless: Start with an empty set, add an infinite number
(aleph-null in this case) of objects to it, remove an infinite number
of objects from it (again, aleph-null). Now, how many objects are
in the set? It's a meaningless question, because depending on how
you look at it, the answer can be any natural number or aleph-null,
itself. This is what I meant when I said, you can't subtract
infinities in any way that makes sense.
re(2): The solution isn't...
