7.1. A natural number $n$ was multiplied by the sum of the digits of the number $3 n$, and the resulting number was then multiplied by 2. As a result, 2022 was obtained. Find $n$.
Answer: 337. Solution. Let $s(N)$ denote the sum of the digits of the number $N$. Then the condition of the problem can be written as $2 n \cdot s(3 n)=2 \cdot 3 \cdot 337$, i.e., $n \cdot s(3 n)=3 \cdot 337=1011$. Therefore, $n \leq 1011$, so $3 n$ is at most a four-digit number, and $s(3 n)<4 \cdot 9=36$. Thus, $s(3 n)$ cannot equal 337, but must equal either 3 or 1. However, it is clear that the equality $s(3 n)=1$ leads to a contradiction (in this case, $3 n$ would be a power of ten). Therefore, $s(3 n)=3, n=337$. Verification confirms this solution, since $3 n=1011$.