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5 Books for Quantitative Analyst Beginners

Nine Digit Number - Math Puzzle

Source: Sent to me by Sudeep Kamath via http://puzzletweeter.com/2013/06/21/884/

Problem: 
Find a nine digit number abcdefghi that uses all the digits 1,2,3,...9 exactly once and satisfies:
a is divisible by 1
ab (2 digit number with digits a and b) is divisible by 2
abc (3 digit number with digits a, b and c) is divisible by 3
.......
.......
abcdefghi is divisible by 9.

Update (29/06/2013):
Solution: Posted by JDGM, Anti, Meghana Kolan, Shwetabh Sameer and Unknown in comments! A more detailed solution provided by me in comments!