10Digit Numbers
 Find a 10 digit number such that:

the first digit tells how many zeros are in the number,

the second digit tells how many ones are in the number,

the third digit tells how many twos are in the number, etc.

Find the smallest 10 digit number that uses all the digits 09 and
is divisible by 1 through 10.

Find the smallest 10 digit number that uses all the digits 09 and:

the first digit is divisible by 1,

the first 2 digits (taken as a 2digit number) are divisible by two,

the first 3 digits (taken as a 3digit number) are divisible by three, etc.
Source: 1,3. Martin Gardner. 2. Pi Mu Epsilon Math Journal.
Taken from "Ken's Puzzle of the Day", May 5, 1994
Solution
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