**Digits 1-9**.

N is a 10-digit positive integer which contains each of the

*ten*base-10 digits

**0 to 9**exactly once, such that:

(i) The number formed by the

*last two digits*is divisible by 2.

(ii) The number formed by the

*last three digits*is divisible by 3.

(iii) The number formed by the

*last four digits*is divisible by 4.

and so on

*up to ten digits*...

We will now consider the last three digits of each of the values of N that satisfy all the given conditions and regard them as 3- digit numbers. Let us denote the

**greatest common divisor**of all these 3-digit numbers as G.

It will be observed that a certain 3-digit multiple of G (with no leading zero),

*each of whose digits are distinct*, will

*never occur*as the last three digits of any of the possible values of N.

What is that 3-digit multiple of G which fails to occur?

__Note__: Try to derive a non computer assisted method, although computer program/spreadsheet solutions are welcome.