13.403 Three logging brigades are competing. The first and third brigades processed wood twice as much as the second, while the second and third brigades processed wood three times as much as the first. Which brigade won this competition?
Solution. Let $x, y, z$ be the volumes of work of the teams. Then, according to the conditions, $\left\{\begin{array}{l}x+z=2 y, \\ y+z=3 x,\end{array} \Rightarrow 4 x=3 y \Rightarrow y>x\right.$.

But from the first equation $z=(y-x)+y$, hence $z>y$.

## Answer: the third team.