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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: My ideas? | Comment 24 of 83 |
(In reply to My ideas? by Gamer)

Well... to be specific, I think you said that you can't multiply or divide infinity (not dividing BY infinity).

I'm not sure what dividing by infinity means, unless you're implying dividing by a variable as the variable grows towards infinity. In which case, you are talking about the "normal" limit described by calculus.

You said in your first post "so it's infinity times 9 divided by 10... Wait, we can't divide or multiply infinity".
I don't see why not. But an infinity multiplied by, divided by, added to, or lessened by a constant is the same infinity.

Again, I would refer you to studies about what infinities mean and that they are normally dealt with as sets of elements and operations (often mappings) ON those sets.

--- SK
  Posted by SilverKnight on 2003-09-09 21:13:01

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