Question 58
Let $n\in\mathbb N$, $n\geq2$, and let $a_1,a_2,\ldots,a_n\in[0,1]$ be real numbers. Find the maximum possible value of the smallest of the numbers
$$
a_1-a_1a_2,\quad a_2-a_2a_3,\quad\ldots,\quad a_n-a_na_1.
$$
$$
a_1-a_1a_2,\quad a_2-a_2a_3,\quad\ldots,\quad a_n-a_na_1.
$$