Majka, Vašek, and Zuzka solved problems over the weekend. Majka and Vašek solved a total of 25 problems. Zuzka and Vašek solved a total of 32 problems. Moreover, Zuzka solved twice as many problems as Majka.

How many problems did Vašek solve?

(M. Dillingerová)
Zuzka calculated twice as many problems as Majka. Thus, the total number of problems calculated by Zuzka and Vašek is the same as the total number of problems calculated by Majka and Vašek, increased by the number of problems calculated by Majka.

Zuzka and Vašek calculated a total of 32 problems, Majka and Vašek calculated a total of 25 problems, so Majka calculated 7 problems $(32-25=7)$. From this, we get that Vašek calculated 18 problems $(25-7=18)$.

Evaluation. 3 points for the initial reasoning; 3 points for the calculation and conclusion.

Note. If $m, v$, and $z$ denote the number of problems solved by Majka, Vašek, and Zuzka, respectively, then from the problem statement we have $m+v=25, z+v=32$, and $z=2m$. The previous thoughts can be succinctly written as follows:

$$
32=2m+v=m+m+v=m+25 \text{, }
$$

thus $m=7$ and $v=18$.