7.3. Append two digits to the number 2020 so that the resulting six-digit number is divisible by 36. Find all possible solutions.
Answer: 32 or 68. Solution: Note that $36=9 \cdot 4$. Since the sum of the first four digits is 4, by the divisibility rule for 9, the sum of the last two digits of the obtained number can be either 5 or 14. In the first case, the two digits we are looking for must form the number 32 (other options with a sum of 5 are $05,14,23,41$ and 50, and none of them work due to the divisibility rule for 4). In the second case, we get only the variant 68, since the options $59,77,86$ and 95 also do not work due to the divisibility rule for 4. Another way to solve this is as follows: divide 202000 by 36 with a remainder, the quotient will be 5611, and the remainder will be 4; then add to the number 201996 (equal to 202000-4) multiples of 36, and we get $201996+36=202032$ and $201996+72=202068$ (adding the next multiple of 36, i.e., 108, will give a number with the first digits 2021).