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```
Date: 809045738
Date: Mon, 21 Aug 1995 18:42:32 -0400
From: Anonymous

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

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

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

Hello!

Well, perhaps I was a little bit too excited when I said I had found
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

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