2 problems

Let $Q(n)$ denote the number of classical $n$-queens configurations, and let $T(n)$ denote the number of toroidal $n$-queens configurations. A classical configuration places $n$ qu…

For $n\ge 3$, consider pairs $(1,a_1),(2,a_2),\ldots,(n,a_n)$ such that $\{a_1,\ldots,a_n\}=\{n+1,n+2,\ldots,2n\}$. Slater's conjecture. Solutions exist for every $n$ other than…