7.1. Append one digit to the left and one digit to the right of the number 2016 so that the resulting six-digit number is divisible by 72 (provide all solutions).
Answer: 920160 and 120168. Solution. The desired number must be divisible by $72=8 \cdot 9$. For divisibility by 8, the three-digit number formed by the last digits must be divisible by 8. Since 16 is already divisible by 8, we need to append 0 or 8 on the right. For divisibility by 9, the sum of the digits must be divisible by 9. In the first case, we then need to prepend a nine (if we prepend 0, it will become a five-digit number), and in the second case, we prepend a one.