Question 73
Let $a_1, a_2, \dots, a_{123}$ be positive integers such that
* $a_1, a_2, \dots, a_{123}$ is a permutation of $1, 2, \dots, 123$, and
* $|a_1 - a_2|, |a_2 - a_3|, \dots, |a_{122} - a_{123}|$ is a permutation of $1, 2, \dots, 122$.
Prove that $\max(a_1, a_{123}) \ge 32$.
* $a_1, a_2, \dots, a_{123}$ is a permutation of $1, 2, \dots, 123$, and
* $|a_1 - a_2|, |a_2 - a_3|, \dots, |a_{122} - a_{123}|$ is a permutation of $1, 2, \dots, 122$.
Prove that $\max(a_1, a_{123}) \ge 32$.