1. In a small village live 4 good friends Goran, Zoran, Jovan, and Stojan. Each of them has an older brother who is named after one of his friends. The name of each of their fathers is the name of one of his friends. Each father, along with his two sons, have different names.

The father of Stojan and the brother of Jovan bear the name of the child whose brother is called Jovan. The brother of the child who bears the name of Zoran's brother is called as the child whose father is Goran.

Whose father is called Stojan?
Solution. Let's denote the children with the initial letters of their names, i.e., with $\Gamma, 3, J, C$. If $X$ is one of the children, then we denote by $B(X)$ the name of his brother, and by $T(X)$ the name of his father. Then, the conditions of the problem, through these notations, can be formulated as follows:

(1) $X \neq B(X) \neq T(X) \neq X$, for every $X \in\{\Gamma, 3, J, C\}$

(2) $B(X)=J \Leftrightarrow T(C)=B(J)=X$

(3) $X=B(3) \Leftrightarrow T(B(X))=\Gamma$

Since $T(C) \neq C$ and $T(J) \neq J$, the following two cases are possible:

$1^{0} T(C)=B(J)=\Gamma$

Then, according to (2), $B(\Gamma)=J$, from which $B(3)=C$. However, according to (3), it follows that $T(B(C))=T(3)=\Gamma$, which is not possible, since $T(C)=\Gamma$.

$2^{0} T(C)=B(J)=3$

Then, from (2) we have that $B(3)=J$, and from (3) that $T(B(J))=\Gamma$, i.e., $T(3)=\Gamma$. So, we have that $B(J)=3$ and from $B(3)=J$ and $T(3)=\Gamma$, it follows that $B(\Gamma)=C, B(C)=\Gamma$ and $T(C)=3$. Thus, $T(J)=C$, from which $T(\Gamma)=J$.

Therefore, the father of Jovan is called Stojan.