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: Respectfully, I disagree with all (save perhaps eric) by SilverKnight)

as you pick up each marble and put it into the jar, and (in 1/10 of the cases) take it back out. you define it as being part of a group (those you put in the jar).
you cuold have (if you had chosen to) counted them as you did so. (yes this would be taxing but if you can move marbles in an infinitessimally short time then you certainly can incrimite a number in your head). At the end of a minute you stop. You have coutned all the marbles you put in the jar, therfore they are no longer infinite. You have defined it (made it finite).
Even if you do not choose to count them in your head the action of moving them into and out of the jar defines the number of them and the action of ceasing to move them limites the number.

As for you circle analogy, it is not apt. drawing a circle in no way defines the number of digits to the right of the ratio of its circumfernece to its diameter.

The number of digits is equivilant to the initial infinite set of marbles at teh beginning of the puzzle.
A more apt analogy is if you were to calculate that ratio infinitly quickly, writing down the result as you go. at the end of a minute you have a number of digits on the (presumably huge) page. the number of digits is unimaginable huge but it is not infinite. the moment you stopped writing numbers you defined the number of those digits and made it finite.
just as when you stop putting marbles into (and taking them out of the) the jar you have defined the number of marbles in the set.

Posted by FatBoy on 2003-09-09 11:52:42