Suppose $a,b,c,x,y,z$ are pairwisely different real numbers. How many terms in the following can be $1$ at most: 
$$\begin{aligned}
&ax+by+cz,&&&&ax+bz+cy,&&&&ay+bx+cz,\\
&ay+bz+cx,&&&&az+bx+cy,&&&&az+by+cx?
\end{aligned}$$