perplexus.info :: Paradoxes : Marbles Bonanza

Marbles Bonanza (Posted on 2003-09-08)

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.)

Most certainly not Zero.

| Comment 77 of 87 |

Let me offer the following, Mark, to demonstrate your error:

Let the set A contain all whole numbers greater than 0.

Let the set B contain all whole numbers greater than 12.

Let the set C contain all elements of A that are not also elements of B.

How many numbers are in A? An infinite number. Or, as you would put it, "Infinity."

How many numbers are in B? An infinite number. Or, again, in your terms, "Infinity."

How many numbers, then, are in C? Is it "infinity minus infinity," and therefore zero, as your infallible TI-89 would claim?

Or is it 12?

Posted by David Bernat on 2006-01-17 17:02:11

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