10.1 A weirdo didn't mind and recorded 2022 numbers in a circle, and it turned out that each number coincides with the absolute difference of its two neighbors. Determine which numbers were recorded if their sum is 2022.
Solution 1: Note that all the written numbers are non-negative. Let the largest of them be $N$. The difference between two numbers from 0 to $N$ can only be $N$ when these numbers are 0 and $N$, so on one side of the number $N$ stands 0, and on the other side - also $N$. If on one side of zero stands the number $N$, then on the other side stands $N$ as well. Therefore, the numbers on the circle go in the following order: $N, N, 0, N, N, 0, \ldots, N, N, 0$. Their sum is $1348 N = 2022$, so $N = 3 / 2$.

Solution 2: Note that all the written numbers are non-negative. If the number 0 is written or if there are two identical numbers among the adjacent ones, then the numbers go in the order $N, N, 0, N, N, 0, \ldots$ and $N = 3 / 2$. Otherwise, adjacent numbers cannot be equal, and let $a < b$ be two adjacent numbers, where $0 < a$. The second neighbor of $b$ can be either $a + b$ or $a - b$. Since $a - b$ is negative, on the other side stands $a + b$. Similarly, after $a + b$ comes $a + 2b$, then $a + 3b$, and so on. We get that each subsequent number in the circle is greater than the previous one, which is impossible.

## Criteria:

- Only the answer with an example -1 point;
- The problem is solved in the case when among the numbers there are $0-3$ points.