1. Find all representations of the number 2022 as the sum of several consecutive natural numbers.
Solution. Let $a$ be the first number of the desired sequence, then

$a+(a+1)+\cdots+(a+p-1)=2022 \quad$ and $\quad p a+\frac{p(p-1)}{2}=\frac{p(2 a+p-1)}{2}=2022$.

Notice that $2022=2 \cdot 3 \cdot 337$, therefore $p(2 a-1+p)=2^{2} \cdot 3 \cdot 337$. Since $p+2 a-1>p$ for natural $a$, then $p<337$ and $p=2,3,4,6$ or 12. Next, we will try the possible values of $p$ and find the corresponding values of $a:$

if $p=2$, then $2 a-1+2=2 \cdot 3 \cdot 337$ and there are no solutions;

if $p=3$, then $2 a-1+3=2^{2} \cdot 337$ and $a=673$;

if $p=4$, then $2 a-1+4=3 \cdot 337$ and $a=504$;

if $p=6$, then $2 a-1+6=2 \cdot 337$ and there are no solutions;

if $p=12$, then $2 a-1+12=337$ and $a=163$.

Answer. There are 3 possible representations: $673+674+675 ; \quad 504+505+506+507$; $163+164+\ldots+174$.

Recommendations for evaluating solutions. If the equations are written in the form of an arithmetic progression and the problem is reduced to solving an equation of the form $p(2 a-1+p)=2022-2$ points.

If the problem is correctly reduced to solving $p(2 a-1+p)=2^{2} \cdot 3 \cdot 337$ and it is shown that $p=2,3,4,6$ or 12 - no less than 4 points.