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(5): Respectfully, I disagree with all (save perhaps eric) by Brian Wainscott)

Look, Bryan and SilverKnight too

You do not have to explain to me the basics of this kind of problem to me. I completed college too included Calc through to differential equations. I was raised in a family that did math for fun. My grandfather factored liscense plate numbers to pass the time on long trips. I also took Philosophy and understand the whole firing an arrow at a hare and all that.

I also get the fact that you all have provided the answer that was expected. I have no doubt that when levik posted this puzzle he was looking for the kind of thought you are showing.

The simple fact is. The way this problem is stated, all of that thought does not apply. Yes, you can continue to devide time into smaller and smaller discrete units and no matter how small the unit of time is there is always one half of that unit. I get it.

The problem with this case is you are not talking about time which as a continuem can be infinitly sliced up. You are talking about a number of items (marbles). At the end of one minute you stop moving marbles around and your have a set of marbles in the jar and a set of marbles that have been in the jar and come back out. Those sets are limited and unchanging. You have stopped, no more are going in and no more are coming out. You have limited the set. It is no longer infinite. It does not matter how many marbles are in the jar or how fast you put them in their. Once you stop putting them in there, there is a limited finite number. It will not change. It had an end. it is measurable, it is finite.

No, you can't count all of the intergers because the set of integers is infinite it doesn't matter how fast you count because there is no end, there is always another one coming along. But the number of marbles in the jar does not change, there is not another marble coming along. If you count it you will come to the end.

Posted by FatBoy on 2003-09-09 14:40:44