Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

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

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


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 


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


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
Associated Topics:
Middle School Puzzles

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994-2015 The Math Forum