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Marbles Bonanza (Posted on 2003-09-08) Difficulty: 4 of 5
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)

See The Solution Submitted by levik    
Rating: 3.6154 (13 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): The solution isn't... | Comment 71 of 87 |
(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.








  Posted by Ken Haley on 2005-06-23 03:52:19

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