Question 24
(IND 1) An odd integer $n\ge3$ is said to be “nice” if there is at least one permutation $a_1,a_2,\ldots,a_n$ of $1,2,\ldots,n$ such that the $n$ sums $a_1-a_2+a_3-\cdots-a_{n-1}+a_n$, $a_2-a_3+a_4-\cdots-a_n+a_1$, $a_3-a_4+a_5-\cdots-a_1+a_2$, $\ldots$, $a_n-a_1+a_2-\cdots-a_{n-2}+a_{n-1}$ are all positive. Determine the set of all “nice” integers.