16. In a table tennis tournament, sixth-graders and seventh-graders participated, with the number of sixth-graders being twice the number of seventh-graders. The tournament was a round-robin. The number of matches won by seventh-graders was $40 \%$ more than the number of matches won by sixth-graders. How many participants were there in the tournament?
82.16. Let $x$ be the number of seventh graders. Then the number of points $N_{7}$, scored by the seventh graders, is no more than $x \cdot 2 x + (x^2 - x) / 2$, and also $N_{6} \geqslant 2 x(2 x-1) / 2$. We get

$$
2 x^{2} + (x^{2} - x) / 2 \geqslant \frac{7}{5} x(2 x-1)
$$

from which it follows that $x \leqslant 3$.

By enumeration (or otherwise), we find that $x=3, N_{7}=21$, $N_{6}=15$. In total, there were nine participants.