Question 115
Let the sequence $a_1, a_2, \dots, a_{20}$ be a permutation of the integers $1, 2, \dots, 20$. Find the maximum possible value of
$$
\min\{|a_2 - a_1|, |a_3 - a_2|, \dots, |a_{20} - a_{19}|, |a_1 - a_{20}|\}.
$$
$$
\min\{|a_2 - a_1|, |a_3 - a_2|, \dots, |a_{20} - a_{19}|, |a_1 - a_{20}|\}.
$$