Question 99
Let $n\ge2$ be a natural number. Find, as a function of $n$, the largest natural number $d$ for which there is a permutation $a_1,a_2,\ldots,a_n$ of $1,2,\ldots,n$ satisfying
$$|a_i-a_{i+1}|\ge d\quad\text{for }i=1,2,\ldots,n-1.$$
$$|a_i-a_{i+1}|\ge d\quad\text{for }i=1,2,\ldots,n-1.$$