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## One to Nine

Math brain teasers require computations to solve.

 Puzzle ID: #29716 Fun: (2.7) Difficulty: (2.98) Category: Math Submitted By: shenqiang

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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 mercenary007 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 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. calmsavior 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) shenqiang Apr 12, 2006 I meant that, comparing to others, this is the hardest. grungy49 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 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 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.