9-2-1. Non-zero numbers $a, b, c, d, e, f$ are such that among the products $a c d, a c e, b d e$, $b d f$ and $b e f$ exactly one is positive. Which one?
Answer. $b d e$.

Solution 1. Notice that $(a c e) \cdot(b d f)=(a c d) \cdot(b e f)$. Therefore, exactly one of these four numbers cannot be positive. This means that the remaining number $b d e$ is positive.

Comment. There are examples where the product $b d e$ is indeed positive, while the others are negative. For example, $a>0, c>0, d>0, e>0$, $f<0$.