Associated Topics || Dr. Math Home || Search Dr. Math

```
Date: 10/19/95 at 7:42:10
From: Gut, Thomas

At eleven o'clock I put ten balls numbered 1,2, ...10 in a box and
immediately take out the ball numbered 1.  At eleven thirty I put
balls numbered 11 through 20 into the box and take out the ball
numbered 2.  At eleven forty-five I put balls numbered 21 through
30 into the box and take out the ball numbered 3. This continues
at time intervals that are  half of the preceding one. How many
balls are in the box at twelve o'clock?

Kindest regards,

Thomas Gut
gut@sebank.se
```

```
Date: 11/5/95 at 16:41:45
From: Doctor Josh
Subject: Re: (no subject)

This is Zeno's Paradox.  Zeno is a dead guy who once argued with
discrete.  Zeno argued that it was discrete because of the fact
that to get anywhere, you have to go half that distance first.
Then you have to go half that distance,and half that distance, and
so on.  Accepting this as the case, he argued that you would never
get there. It turns out that the series,

1/2 + 1/4 + 1/8 + 1/16 + ...

converges to 1.

at every half point.  After a while, you would have a lot of
balls, but you would never reach twelve o'clock (a clever ploy
often implemented by the numbered ball industry).  This question
touches on the basic fabric of time - is it discrete or

-Doctor Josh,  The Geometry Forum

```
Associated Topics:
High School Logic
High School Puzzles

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search