## Task B-1.3.

Each of the 28 students visited at least one of the three countries. The number of students who visited only Italy and Spain is equal to the number of students who visited only Italy. No student visited only Spain or only Greece. Six students visited Greece and Italy, but not Spain. The number of students who visited only Greece and Spain is five times the number of students who visited all three countries. If the number of students who visited all three countries is even and different from zero, how many students visited only Italy?
## Solution.

We solve the problem using Venn diagrams. Let $x$ be the number of students who visited only Italy, and $y$ be the number of students who visited all three countries.

![](https://cdn.mathpix.com/cropped/2024_05_30_a25c851e6461b5bf7f1cg-03.jpg?height=429&width=465&top_left_y=405&top_left_x=727)

In set $I$ are all who visited Italy, in set $\check{S}$ all who visited Spain, and in set $G$ all who visited Greece. According to the conditions in the problem, we fill in the diagram. We have

$$
\begin{aligned}
& x+x+6+y+5 y=28 \\
& 2 x+6 y=22 \\
& x+3 y=11 \\
& x=11-3 y
\end{aligned}
$$

Since $y$ is even and different from 0, and $x \geqslant 0$, the only possibility is $y=2$.

Then $x=11-6=5$. Therefore, 5 students visited only Italy.