4 problems

For a positive integer $n$, let ${\rm qc}(n)$ be the largest integer such that every partial $n$-queens configuration on an $n\times n$ chessboard with at most ${\rm qc}(n)$ queens…

An $n$-queens configuration is a placement of $n$ mutually non-threatening queens on an $n \times n$ chessboard, and let ${\mathcal{Q}}(n)$ denote the number of such configurations…

Let $N$ be a positive integer. A number $N$ is $Q$-irreducible if none of the $N\times N$ solutions to the N-Queens Problem can be represented as a composition of solutions on smal…

Asymptotic upper-bound conjecture. For every integer $n$ not divisible by $2$ or $3$,