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 Integer infinity by Jeff)

Umm, I think you'll find that Q (the rational numbers) are countable (aleph naught in cardinality)...
A '1-1 Correspondence' can be seen if you take a matrix, each element being an ordered pair in NxN. Each element in the matrix represents a different quotient in Q. Follow the matrix from top left, then snakeing your way away from (1,1) towards the bottom right of the infinite matrix you have created a bijection...

Posted by Barrett Hasseldine on 2004-03-21 21:46:06