2. 50 businessmen - Japanese, Koreans, and Chinese - are sitting at a round table. It is known that between any two nearest Japanese, there are as many Chinese as there are Koreans at the table. How many Chinese can there be at the table?

## Answer: 32.
Solution. Let there be $-x$ Koreans and $y$ Japanese at the table, then there are $-x y$ Chinese. According to the condition: $x+y+x y=50$. By adding 1 to both sides of the equation and factoring both sides, we get: $(x+1)(y+1)=17 \times 3$. Since $x \neq 0$ and $y \neq 0$, one of the factors is 3, and the other is 17.

Thus, $x=2, y=16$ or $x=16, y=2$. In both cases, $x y=32$.

Criteria. If the solution is incorrect - 0 points.

Only the correct answer - 1 point.

If only one case is considered, $x=2, y=16$ or $x=16, y=2-5$ points. If the solution is correct - 7 points.