Question 79
Let $n$ be an integer greater than or equal to $2$. Consider the ways of lining up $n^2$ numbers consisting of $n$ numbers each of $\{1, 2, \dots, n\}$ from left to right. Is there a way to line them up to satisfy the following condition?
Condition: For any integer $k$ with $1 \le k \le n^2 - 1$, the remainder obtained when the sum of the first $k$ numbers on the left is divided by $n$ is different from the remainder obtained when $k$ is divided by $n$.
Condition: For any integer $k$ with $1 \le k \le n^2 - 1$, the remainder obtained when the sum of the first $k$ numbers on the left is divided by $n$ is different from the remainder obtained when $k$ is divided by $n$.