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### Pentagon Puzzle

```
Date: 9/12/96 at 19:56:55
From: Johnny Taylor
Subject: Pentagon Puzzle

Three numbers are placed on each side of a pentagon, the numbers on
the corners being used on two sides.  Using each of the numbers 1-10
only once, each side has to add up to the same number.  We have come
up with one solution, but need three more.  Can you help?

Amanda Taylor
```

```
Date: 10/27/96 at 22:52:11
From: Doctor Lynn
Subject: Re: Pentagon Puzzle

I've put all four solutions in a picture called

http://mathforum.org/dr.math/gifs/pentgons.jpg

In case you can't read it for some reason, here are the values reading
round from a corner:

1, 10, 3, 6, 5, 7, 2, 8, 4, 9
This comes from putting them in every other place and then working
back filling the gaps.

10, 1, 8, 5, 6, 4, 9, 3, 7, 2
This is the same as the first, but you count down from ten, so every
value is subtracted from 11.

1,10, 5, 2, 9, 4, 3, 6, 7, 8
This is done the same way as the first, but first putting in the odd
numbers, then the evens.

10,  1, 6, 9, 2, 7, 8, 5, 4, 3
This is done by subtracting each of the previous values from 11 as
before.

I hope that helps.

-Doctor Lynn,  The Math Forum
Check out our web site!
```
Associated Topics:
Middle School Puzzles

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