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Pentagon Puzzle

```Date: 09/18/2002 at 21:43:13
From: Zoee
Subject: Pentagon puzzle

Zoee and her whole family are stumped!

Question: Write the numbers 1 through 10 in the boxes below
(the diagram shows a pentagon in the shape of a house with 5 boxes
from peak to floor on each side of the house, and three along the
bottom) so each side of the pentagon has a sum of 14.

We would appreciate your input - please!

The Davidsons
```

```
Date: 09/18/2002 at 22:51:44
From: Doctor Peterson
Subject: Re: Pentagon puzzle

Hi, Zoee.

I think it looks something like this, with three numbers on a side,
right?
_
_     _
_           _

_         _

_   _   _

The first thing I do with a problem like this is to think about the
total of all the numbers. The sum of 1 through 10 is 55. The sum of
the five sides is 5*14=70. But if I add those five sums, I have added
the five corner numbers twice each, since each is on two sides, so
the sum of the corners is the difference between 55 and 70, or 15.

But what five numbers add up to 15? Their average will be 3, so they
have to be 1,2,3,4,5. Put those in the corners in some order:

1
_     _
5           2

_         _

4   _   3

Now try to fill in the remaining numbers so that each side adds to
14. If you find that is impossible, try rearranging the corners; you
may be able to see why it was impossible, which will give you ideas
for the best way to arrange the corners. I had no trouble finishing.

For further discussion, see the Dr. Math archives:

Magic Pentagon
http://mathforum.org/library/drmath/view/56732.html

If you have any further questions, feel free to write back.

- Doctors Peterson and Sarah, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Number Sense/About Numbers
Elementary Puzzles
Middle School Number Sense/About Numbers
Middle School Puzzles

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