Numbers from Numbers

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

Dear Dr. Math,

Could you please help me figure out this math problem? How do you get 
the number 87 only using the number 1994?  

Thank you for your help.

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.

To find out more information about this type of math puzzle, go to 
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/