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Math brain teasers require computations to solve.

 

Puzzle ID:#29716
Fun:*** (2.69)
Difficulty:*** (2.98)
Category:Math
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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Comments

mercenary007*jm*
Apr 12, 2006

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

well there is more than one number. I found the following number that also satisfy the conditions: 222.456.564
signmeup74*pl*
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.
calmsaviorAus*
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)
shenqiangAcn*
Apr 12, 2006

I meant that, comparing to others, this is the hardest.
grungy49Aau*
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.
javaguru*us*
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.
javaguru*us*
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.
saska
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.
http://pastebin.com/iyJxDuTA

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