American Billions

Stage: 3 Challenge Level:

Find the ten-digit number which uses each of the digits $0$ to $9$ once and has the following properties:

1. the first digit from the left (the billions digit) is divisible by $1$
2. the number formed by the first $2$ digits from the left is divisible by $2$
3. the number formed by the first $3$ digits from the left is divisible by $3$
4. the number formed by the first $4$ digits from the left is divisible by $4$
5. the number formed by the first $5$ digits from the left is divisible by $5$
6. the number formed by the first $6$ digits from the left is divisible by $6$
7. the number formed by the first $7$ digits from the left is divisible by $7$
8. the number formed by the first $8$ digits from the left is divisible by $8$
9. the number formed by the first $9$ digits from the left is divisible by $9$
10. the number itself is divisible by $10$. What is the number?

As always, please tell us your strategy when sending in your solution.

Published September 2001,January 2009.

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