Question 91
What is the minimum value of the product
$$
\prod_{i=1}^{6} \frac{a_{i}-a_{i+1}}{a_{i+2}-a_{i+3}}
$$
given that $\left(a_{1}, a_{2}, a_{3}, a_{4}, a_{5}, a_{6}\right)$ is a permutation of $(1,2,3,4,5,6)$? (note $a_{7}=a_{1}, a_{8}=a_{2}$, etc.)
$$
\prod_{i=1}^{6} \frac{a_{i}-a_{i+1}}{a_{i+2}-a_{i+3}}
$$
given that $\left(a_{1}, a_{2}, a_{3}, a_{4}, a_{5}, a_{6}\right)$ is a permutation of $(1,2,3,4,5,6)$? (note $a_{7}=a_{1}, a_{8}=a_{2}$, etc.)