Question 28
For each permutation $(x_1, x_2, \dots, x_{99})$ of $\{1, 2, \dots, 99\}$, let
$$
L = |x_1 - x_2\sqrt{3}| + |x_2 - x_3\sqrt{3}| + \dots + |x_{98} - x_{99}\sqrt{3}| + |x_{99} - x_1\sqrt{3}|.
$$
Determine the maximum value of $L$, and for how many permutations of $\{1, 2, \dots, 99\}$ this value is reached.
$$
L = |x_1 - x_2\sqrt{3}| + |x_2 - x_3\sqrt{3}| + \dots + |x_{98} - x_{99}\sqrt{3}| + |x_{99} - x_1\sqrt{3}|.
$$
Determine the maximum value of $L$, and for how many permutations of $\{1, 2, \dots, 99\}$ this value is reached.