Closing the gap and settling the problem of queens on an $n\times n$ board, each attacking at most one other

Kristina Ago, Bojan Bašić, Radojka Ciganović

Let $q(n)$ denote the largest number of queens that can be placed on an $n\times n$ chessboard so that no queen attacks more than one other queen. We prove that $q(n)=\lfloor4n/3\r…