Question 5
For each permutation $x_1, x_2, \dots, x_{10}$ of $1, 2, \dots, 10$, compute
$$
|2x_1 - 3x_2| + |2x_2 - 3x_3| + |2x_3 - 3x_4| + \dots + |2x_{10} - 3x_1|.
$$
Let $S$ be the maximum possible value of this sum. Find the number of permutations attaining $S$.
$$
|2x_1 - 3x_2| + |2x_2 - 3x_3| + |2x_3 - 3x_4| + \dots + |2x_{10} - 3x_1|.
$$
Let $S$ be the maximum possible value of this sum. Find the number of permutations attaining $S$.