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One to Nine

Math brain teasers require computations to solve.


Puzzle ID:#29716
Fun:*** (2.69)
Difficulty:*** (2.98)
Submitted By:shenqiangAcn****!!




Arrange the digits from 1 to 9 to make a 9-digit number ABCDEFGHI which satisfies the following conditions:

1) AB is divisible by 2;
2) ABC is divisible by 3;
3) ABCD is divisible by 4;
4) ABCDE is divisible by 5;
5) ABCDEF is divisible by 6;
6) ABCDEFG is divisible by 7;
7) ABCDEFGH is divisible by 8;
8) ABCDEFGHI is divisible by 9.

There is only one solution.

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Apr 12, 2006

wow... very good teaser, though I thought this to be more of a Logic brainteaser than a Math brainteaser
Apr 12, 2006

well there is more than one number. I found the following number that also satisfy the conditions: 222.456.564
Apr 12, 2006

I think you are only supposed to use each of the digits 1-9 ONCE.
You can't repeat 2, etc.
I agree with the logical nature, too. I didn't do much math.
Apr 12, 2006

i actually found deciphering the sixth statement as easy, because i can actually mentally determine if a number is divisble by 7, and what remainder it would have after the division (fast)
Apr 12, 2006

I meant that, comparing to others, this is the hardest.
Nov 24, 2006

I tried to make another number - but looks like you were right, the highest I got up to was 1,620,549 without repeating digits.
Jan 02, 2009

Great teaser! My process of solving it was exactly the way you describe it, down to the order of checking for division by 7.
Jan 02, 2009

I do agree that this is more of a logic brain teaser than math...although knowing the rules for divisibility requires some minimal math knowledge.
Mar 08, 2017

Thanks for your puzzle.

I managed to solve it with glpsol (a free linear and mixed integer programming solver, available for most platforms). I uploaded the model file that I used to pastebin for anyone who might be interested to play with it.

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