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More 10-Digit Numbers

- Find the smallest 10 digit number that uses all the digits 0-9, and the
first N digits (taken as an N-digit number) are divisible by N.
- Now cycle the division requirement. Find the smallest 10 digit
number that uses all the digits 0-9, and the first N digits are divisible by
(N+k mod 10 + 1) for k = 0 to 8.
(Sorry that expression looks worse than it is.)- For example, for k=0, The first digit is divisible by 2, the first two
digits are divisible by 3, ..., all 10 are divisible by 1.
- For k=7, The first digit is divisible by 9, the first two digits are
divisible by 10, ..., all 10 are divisible by 8.

Source: Original, based on a previous puzzle
from Martin Gardner.

Solution

Mail to Ken