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
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