Question 172
Two ordered sequences $x_1 \le x_2 \le \dots \le x_n$ and $y_1 \ge y_2 \ge \dots \ge y_n$ of positive integers are written in two rows, one above the other:
$$
x_1 \ x_2 \ \dots \ x_n
$$
$$
y_1 \ y_2 \ \dots \ y_n.
$$
Denote by $M = \max(x_1 + y_1, x_2 + y_2, \dots, x_n + y_n)$ the maximal sum of numbers in columns.
Could it happen that after the numbers in the second row were rearranged, the maximal sum of numbers in columns became less than $M$?
$$
x_1 \ x_2 \ \dots \ x_n
$$
$$
y_1 \ y_2 \ \dots \ y_n.
$$
Denote by $M = \max(x_1 + y_1, x_2 + y_2, \dots, x_n + y_n)$ the maximal sum of numbers in columns.
Could it happen that after the numbers in the second row were rearranged, the maximal sum of numbers in columns became less than $M$?