8.1. Does there exist a ten-digit number, divisible by 11, in which all digits from 0 to 9 appear?
Answer. Yes, for example, 9576843210.

Solution. Let's consider a possible way to find the required number. Note that a number is divisible by 11 if the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions is divisible by 11. If we write all ten digits in descending order, that is, 9876543210, then this difference will be 5. If we swap 5 and 8, the first sum will increase by 3, and the second sum will decrease by 3, so their difference will become 11. Therefore, the number 9576843210 is divisible by 11.

Comment. Any correct number provided - 7 points.