21. Find the smallest natural number that is a multiple of 36 and in whose representation all 10 digits appear exactly once.
21. Since the desired number is divisible by 36, it must be divisible by 4 and 9. In this number, the last two digits should represent the largest two-digit number divisible by 4. This number is 96. The remaining digits should be written from the digit 9 to the left in descending order, but since the leftmost digit cannot be 0, the leftmost digit is 1. Since the sum of all single-digit numbers is 45, the desired number is divisible by 9. The desired number is 1023457896.