14.1.9 * Does there exist a ten-digit number, in which each digit appears exactly once, and which is divisible by 11.
Parse a ten-digit number where each digit appears exactly once, the sum of the digits is $0+1+2+\cdots+9=45$. If the sum of the digits in the odd positions and the sum of the digits in the even positions differ by 11, then this ten-digit number is divisible by 11. That is, as long as the sum of the digits in the odd positions (or even positions) is $(45+11) \div 2=28$, then this ten-digit number is divisible by 11.
Therefore, 1294357680 meets the requirement.