#### Find the 9 digit number iq

##### Puzzle on numbers - Find the 9 digit number

This is a math puzzle on numbers.

Question
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.

From condition 4, we know that E equals 5.

From conditions 1, 3, 5 and 7, we know that B, D, F, H are even numbers, therefore A, C, G, I are 1, 3, 7, 9 in some order.

Furthermore, from conditions 3 and 7 we know that CD is divisible by 4 and GH is divisible by 8 (because FGH is divisible by 8 and F is even). Because C and G are odd, D and H must be 2 and 6 in some order.

From conditions 2 and 5, we know that A+B+C, D+E+F, G+H+I are all divisible by 3.

If D=2, then F=8, H=6, B=4. A+4+C is divisible by 3, therefore A and C must be 1 and 7 in some order, G and I must be 3 and 9 in some order. G6 is divisible by 8, therefore G=9. But neither 1472589 nor 7412589 is divisible by 7.

Therefore D=6, and F=4, H=2, B=8. G2 is divisible by 8, therefore G=3 or 7. A+8+C is divisible by 3, therefore one of A and C is chosen from 1 and 7, the other is chosen from 3 and 9.

If G=3, then one of A and C is 9, the other is chosen from 1 and 7. But none of 1896543, 7896543, 9816543 and 9876543 is divisible by 7.

Therefore G=7, one of A and C is 1, the other is chosen from 3 and 9. From 1836547, 1896547, 3816547 and 9816547, only 3816547 is divisible by 7 (the quotient is 545221).

Therefore, the number we are looking for is 381654729

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