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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): more | Comment 40 of 83 |
(In reply to re: more by SilverKnight)

You're implicating here that the "value" of infinity is static. This couldn't be more untrue. If infinity minus infinity were zero and infinity divided by infinity was one, then we wouldn't even have calculus in the first place, and this question would be gibberish.

The set of all odd, positive integers is indeed of infinite size, as is the set of all positive integers. However, they are not the "same" size. In one case, the value of infinity is twice that for the other case. This is precisely what were boiling down to here in the marbles problem. Sure I'll concede that for evey value n, the nth marble has been removed, however, there is another, completely independant infinity of marbles (which happens to be 9 times as large as the first infinity) which never gets counted. The only alternative to this is that infinitely adding 9 to a number will produce a result of zero. Forget the math and realize the situation. I am good at math, but certainly no expert - I'm not going to debate with you the intricacies of the equations or the definitions of limits. Just look at what the results are incrementally, and the expand these infinitely - this must produce the same results as a valid mathematical model. In this case, the two are very much at odds, and unless you can convince me that there is a flaw in the basic reasoning (not the math) ive produced, theres really no argument. An infinite number of nines summed cannot equal 0.

  Posted by Cory Taylor on 2003-09-15 14:49:05

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