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### Balls and Boxes

```
Date: 9/1/96 at 14:22:24
From: Anonymous
Subject: Balls and Boxes

Explain in detail how you can place 21 balls in 4 boxes so
that there is an odd number of balls in each box.

I came across this problem.  No one in the class can find a
solution.  Is there one?  If any two odd numbers make an even
number, how can 4 numbers add up to an odd?
```

```
Date: 11/05/96 at 19:59:13
From: Doctor Lynn
Subject: Re: Balls and Boxes

Your logic is quite right, but there is a (trick) solution.

The answer to this old problem (which Doctor Jodi worked out) is that
you put boxes into other boxes.

For example, put seven balls into each of three boxes, then put these
into the fourth box.  It then contains 21 balls, which is an odd
number! (groan)

Hope that helps. :)

Write back if you have any other questions you'd like us to answer.

-Doctor Lynn,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
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Middle School Puzzles

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