Question 146
Let $n \ge 3$. Let a sequence $a_1, a_2, \dots, a_n$ of integers, the following operations are admitted. For any $1 \le k \le n-2$, we can
1) increase $a_k$ and $a_{k+2}$ by 1 each, and decrease $a_{k+1}$ by 1, or
2) decrease $a_k$ and $a_{k+2}$ by 1 each, and increase $a_{k+1}$ by 1.
Starting from the sequence $1, 2, \dots, 2022$, is it possible to arrive at a constant sequence after performing a finite number of operations?
1) increase $a_k$ and $a_{k+2}$ by 1 each, and decrease $a_{k+1}$ by 1, or
2) decrease $a_k$ and $a_{k+2}$ by 1 each, and increase $a_{k+1}$ by 1.
Starting from the sequence $1, 2, \dots, 2022$, is it possible to arrive at a constant sequence after performing a finite number of operations?