Fun Addition

Date: 809045738
Date: Mon, 21 Aug 1995 18:42:32 -0400
From: Anonymous
Subject: 1-9 three-digit addition

Given the numbers 1 through 9, using each number only once, how 
many problems can be formed when adding two three-digit numbers?
Is the sum of the digits in the sum always 18?

Example:  783
         +162
          ---
          945

Date: 809105881
From: Doctor Ken
Subject: Re: 1-9 three-digit addition

Hello!

Well, I don't know the complete answer to your question, but I can 
give you a few more examples pretty cheaply. Once we find one 
solution that works, we can switch the digits in the two summands 
to get new solutions, like these:

  783   782   763   762
 +162  +163  +182  +183
 ----  ----  ----  ----
  945   945   945   945

And whenever we find one solution, we've found a family of four 
solutions, all with the same sum.  That is, unless you consider 
adding the two summands in reverse order to be two differend solutions 
(783+162 vs 162+783).

I've also found another family of solutions, the four generated by 

  729
 +135
 ----
  864

As before, the sum of the digits in the sum is 18, so you may be 
right about that.

I'll keep working on it, and let you know if I or someone else 
comes up with anything else. If you find something yourself, let 
us know!

-Doctor Ken,  The Geometry Forum

Date: 809117699
From: Doctor Ken
Subject: Re: 1-9 three-digit addition

Hello!

Well, perhaps I was a little bit too excited when I said I had found 
another family of answers to your problem. In the meantime, I've 
written a program that searches for all answers to the question, and 
as it turns out there are a whole lot of them: 168, to be exact.  
168 as in 168 + 327 = 495.

-Doctor Ken,  The Geometry Forum