Task 2. What is the smallest natural number that is divisible by 2022 and whose notation starts with 2023?
Answer: 20230110.

Solution. Let the number we are looking for have $n+4$ digits, then it has the form $2023 \cdot 10^{n}+a, a<10^{n}$. Subtract from it $2022 \cdot 10^{n}$, we get that $b=10^{n}+a$ is also divisible by 2022. That is, we need to find a number that starts with 1 and is divisible by 2022. Numbers divisible by 2022 are 0, 2022, $4044,6066,8088,10110, \ldots$. Thus, the number $b$ is at least five digits, so $n \geq 4$. Under this condition, the smallest value of $b$ is 10110, so the number we are looking for is $10110+20220000=20230110$.

Grading criteria: 20 points for a complete solution. 5 points deducted for estimating $b$ without estimating $n-$ 5 points. 0 points for an answer without justification.