Find the number

Question: A number of 9 digits has the following properties:
* The number comprising the leftmost two digits is divisible by 2, that comprising the leftmost three digits is divisible by 3, the leftmost four by 4, the leftmost five by 5, and so on for the nine digits of the number i.e. the number formed from the first n digits is divisible by n, 2<=n<=9.
* Each digit in the number is different i.e. no digits are repeated.
* The digit 0 does not occur in the number i.e. it is comprised only of the digits 1-9 in some order.
Find the number.


The answer is 381654729
One way to solve it is Trial-&-Error. You can make it bit easier as odd positions will always occupy ODD numbers and even positions will always occupy EVEN numbers. Further 5th position will contain 5 as 0 does not occur.
The other way to solve this problem is by writing a computer program that systematically tries all possibilities.

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