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 I lost my marbles by Eric)

I don't think that the bounds of actual reality are relevent in these puzzles. A huge number of senerios that are extremely intereting to discuss are based on exactly these sorts of premises.

Just wondering, however, how this puzzle fares in theoretical reality:
For any marble, n, that you remove, you must remove marble n + 1.
Suppose the last marble you remove is even (n is even). Then you must also remove the next marble, and so the last marble you remove cannot be even.
Ditto for odd.
So the last marble you remove may be neither even nor odd.
So you can't remove a last marble.
So the puzzle never ends.

I don't think that this is a silly result. In the case of Achillis and the tortoise, both the time and the distance reduced by half each time, so it was possible to show that, by calculus, Achillis does indeed reach, and then pass, the tortoise. In this case, however, the size of your task does not reduce by half each time. Zeno was trying to use as a premise that you cannot perform an infinite number of tasks in a finite amount of time. This was shown not to be true in the case of the race, but still holds true is the tasks are discrete. So my feeling is tha the apparent paradox (same task leads to different results) is not actually a paradox after all but a result of the impossible premises set out in the question.

Any thoughts?

And where can get some of these dilithium crystals Eric mentioned...?

Posted by Sam on 2003-09-09 10:47:18