Problem 8-2. Calculate the sum $1^{2}+2^{2}-3^{2}-4^{2}+5^{2}+6^{2}-7^{2}-8^{2}+9^{2}+10^{2}-\ldots+2017^{2}+2018^{2}$.
Solution. Note that for any $k$ the equality $k^{2}-(k+1)^{2}-(k+$ $2)^{2}+(k+3)^{2}=4$ holds. Therefore, the entire sum is equal to $1+504 \cdot 4+2018^{2}=4074341$.

| Grade | Score | Content criterion |
| :---: | :---: | :--- |
| + | 20 | Complete solution |
| .+ | 18 | Solution is correct, but there are minor flaws that do not affect the solution or the final number is not calculated |
| $+/-$ | 17 | Arithmetic error with correct reasoning |
| $+/ 2$ | 12 | Correct idea with errors |
| $-/+$ | 8 | Description of the counting method without the actual counting or multiple errors |
| - | 0 | Solution is completely incorrect/only the answer |