1. 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.
2. Find the smallest 10 digit number that uses all the digits 0-9 and is divisible by 1 through 10.
3. Find the smallest 10 digit number that uses all the digits 0-9 and:
   • the first digit is divisible by 1,
   • the first 2 digits (taken as a 2-digit number) are divisible by two,
   • the first 3 digits (taken as a 3-digit 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