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### Numbers from Numbers

```
Date: 04/26/97 at 01:13:05
From: Greg Livingston
Subject: Math puzzle

Dear Dr. Math,

the number 87 only using the number 1994?

Sincerely,
Greg
```

```
Date: 07/15/97 at 19:08:49
From: Doctor Terrel
Subject: Re: Math puzzle

Hi Greg,

My, you certainly have a tough question there, don't you?  I like this
sort of problem.

I can provide a nice solution by using an idea that may be new to you.
It's called "summation". If we need or want to add up all the whole
numbers from 1 to 9, for example, we would write "sum 9" or "sigma 9".
That is:

sum 9 = 1+2+3+4+5+6+7+8+9 or sigma 9 = 1+2+3+4+5+6+7+8+9

Sigma is the best way to express this idea in advanced math, but sum
is not a not a bad way to do it either. By the way, "sigma" is the
name of a Greek letter. It looks something like a capital M lying on
its left side. (Can you imagine that? I can't draw a real sigma here
in the computer. Sorry.) Since sigma is the Greek version for "s", and
"sum" begins with an "s", it all fits together.

Can you tell me what these expressions would equal: sigma 5, sigma 8,
sigma 4?

[If you answered 15, 36, and 10, then you're right!]

So, now here is how I can make 87 using the digits 1, 9, 9, and 4:

87 = 1 + sigma 9 + sigma 9 - 4
= 1 +    45   +    45   - 4
= 91 - 4
= 87

Notice that I was able to keep the digits in their regular 1-9-9-4
order. However, doing it that way is not required; you can arrange
them in a different order. Maybe you or someone else can find a
different expression for 87; in this type of activity often there is
more than one way to do a number.

this Math Forum page:

http://mathforum.org/ruth/four4s.puzzle.html

This one shows you how to use four 4s to make numbers. Then there are
two more pages nearby: for 1996 and 1997, which are more like your
idea. Just change "four 4s" with "1996" or "1997" and you see lots of
information.

I hope this helps you out.

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