Question 76
Let $n \geqslant 2$ and let $a_{1}, \ldots, a_{n} \in [0,1]$ be real numbers. Determine the maximum value that the smallest of the numbers
$$
a_{1}-a_{1} a_{2},\ a_{2}-a_{2} a_{3},\ \ldots,\ a_{n}-a_{n} a_{1}
$$
can take.
$$
a_{1}-a_{1} a_{2},\ a_{2}-a_{2} a_{3},\ \ldots,\ a_{n}-a_{n} a_{1}
$$
can take.