Task 1. Find the largest four-digit number in which all digits are different, and moreover, no two of them can be swapped to form a smaller number.
Answer: 7089.

Solution. If the digit 0 is not used, then the digits in each such number must be in ascending order, and the largest of such numbers is 6789. Since a number cannot start with zero, using 0, one can obtain additional suitable numbers where 0 is in the hundreds place, and the other digits are in ascending order. The largest of such numbers is 7089.