1 2 3 4 5 6 7 8 9 0 = 100

Date: 01/24/2002 at 05:52:15
From: Connie
Subject: Numbers Adding Together

Dear Dr. Math,

1 2 3 4 5 6 7 8 9 0 = 100

Leave the numerals in this order. Place only addition and subtraction 
signs to make it a true statement. 

I have figured out that you can leave some of the numbers, for example 
you don't have to put signs in every one of them. You can say: 

123 - 4 + 5 + 6 + 7890 = 100 

or something like that.  

Please write back.
Connie Chen

Date: 01/27/2002 at 10:59:17
From: Doctor Steve
Subject: Re: Numbers Adding Together

Dear Connie Chen,

I like what you have figured out. My first thought is that there must 
be lots of ways to do this and I think the key is to pick some 
combination as a starting point and then see if I can make the other 
numbers work out. 

In this case I tried starting with a simple combination that I know 
would make 100, and see if I can make the rest of the numbers cancel 
each other out. 

If I use 90, then I just need 10 more to make 100. I could add 8 and 2 
to make 10. 

So far I have:

 + 2                + 8 + 90 = 100

Then all I need to do is figure out how 1,3,4,5,6,and 7 can be 
combined to cancel each other out. So I'll use my method again and 
pick a combination and see if I can make it work. 

6 + 7 is 13. Can I make the other numbers equal to 13? Hey, 
1 + 3 + 4 + 5 is 13. So, I just need to subtract those.

- 1 - 3 - 4 - 5 + 6 + 7

Perfect. Now I could just combine those numbers  with my original 
choices and I'll have 100. Do you see how?

Try another combination and see if you can make it work.

- Doctor Steve, The Math Forum
  http://mathforum.org/dr.math/