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Let Us Know About Possible Mistakes.
9/12/2008 6:08:14 PM

Posts: 77
How come you always go up to 6 digits only? Instead of 9 digits?

I think you might be better of inserting copies of the file you developed in the 1960's, when Dell was at Dag Hammarskjold Plaza in New York City.

That chart always covers the possibilities of up to 9 digits.

9/24/2008 2:11:08 PM

Dell Editorial Staff
Dell Editorial Staff
Posts: 156
Thank you for your posting. There is only one 9-digit combination which would be applicable to our puzzles: 123456789. However, we are considering adding 7-and 8 digit combinations to the PDF in the Solver Resources section of our website. Thanks again for your message and happy solving!

4/24/2009 3:45:17 PM

Posts: 77
There already are 7 digit and 8 digit possibilities covered in the file Sums.pdf

If this file is on somewhere yu could simply remove the one 9 digit line and the solving aid and copy that file into Solving Resources.

4/27/2009 3:31:41 PM

Gary Kleppe
Gary Kleppe
Posts: 8
It's not too hard to work out these combinations on the fly. More fun and educational than carrying a cheat sheet around.

1) Write down numbers 1, 2, 3, ... in order until you have as many digits as you're looking for. Write down the combination. (Note: If you're only looking for combinations which add up to a certain total then, obviously, only write it down if the total is what you want.)

2) Increase the last digit one number at a time until you can't increase it any more. Each time, write down the combination. (See note above.)

3) When you can't increase the last digit, increase the next-to-last one, and then set the last one to one higher than what the one you just increased is now at. Write down the combination and do step 2 again.

4) Continue in this manner. When you can't increase either of the last two digits, increase the third from the end, and after increasing a digit always set the following ones to the next higher numbers. If there aren't enough higher numbers to populate the last digits, then you've taken the digit you've been increasing as high as you can and you should move left one digit.

This probably sounds more difficult than it is. As an example, here are seven-digit combinations:

1234569 (can't increase the last digit anymore, so increase the next-to-last)
1234579 (same again here)

Now we can't increase the 8, since if we did there'd be nothing we could put in the last place. So bump up the 5 instead:

1234679 (now we must increase the 7)
1234689 (now the last one we can increase is the 6)
1234789 (now we're all the way back to the 4)

...and so on. The continuation of this is left to the reader.

Alternately, you can start from the top and count down, i.e. 98765432, and then you decrease one digit at a time to get all of the combinations.

4/29/2009 2:07:50 AM

Posts: 59
I usually look at these by observing what possible combination(s) can be excluded, given that all nine digits equal 45. For example, if the seven digit total is 42, it means the 1 and 2 are missing. If the total is 28, the 9 and 8 are missing. As an example in the middle of the range (where the most number of possible combinations are always found), if the total is 35, then the possible missing combo is either 1-9, 2-8, 3-7 or 4-6. Eventually multiple choices, when they exist, can be removed from consideration, and the missing combo can be determined.

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