2. Tine was at a competition where he was supposed to solve 20 problems. For each correctly solved problem, he received 8 points, and for each incorrect solution, 5 points were deducted. For a problem he did not attempt, he received 0 points. He found out that he had scored 13 points. How many problems did he attempt?
I/2. If he correctly solved $p$ problems and incorrectly solved $n$ problems, then $8 p-5 n=13$ and it is clear that $n$ must be an odd number. Since he solved 20 problems, $p+n \leq 20$. The equation $8 p-5 n=13$ can be written in the form $8 p-8=5+5 n$ or $8(p-1)=5(n+1)$. Therefore, the number $n+1$ must be divisible by 8 and can only be $n=7$, since $n \leq 20$ must be an odd number. For $n=7$, we also get $p=6$.

Tine solved 13 problems at the competition, 6 of which were correct and 7 were incorrect.
Writing $8 p-5 n=13$ ..... 2 points
Estimating $p+n \leq 20$ (or e.g., $p+n+s=20$, where $s$ denotes the number of problems he did not solve) ..... 1 point
Determining that $n=7$ and $p=6$ satisfy the derived equation ..... 1 point
Checking or excluding other possibilities ..... 2 points
Answer: 13 problems ..... 1 point