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)

Theoretical mathematics tells us that two sets are the same size iff there exists a one-to-one & onto function between the two. The size of the set of integers is deemed aluph null (spelling?). This is also the same size as the set of even integers (since n -> 2n is a valid one-to-one onto function). However, for example, the number of rational numbers is not aluph null since it takes 2 integers to produce all of the rationals. By this reasoning, every set in the puzzle contains aluph null marbles.

Posted by Jeff on 2003-12-29 20:56:56