3 problems

Let $q(n)$ be the maximum number of queens that can be placed on an $n\times n$ chessboard such that every queen attacks at most one other queen. Determine $q(n)$ for every positiv…

Let $\beta\geq 2$ be a base. A pair $(a,b)$ is a reversed sum-product pair in base $\beta$ when the sum of $a$ and $b$, written in base $\beta$, is the reversal of the base-$\beta$…

Haddley and Worsley's conjecture. Every monohedral tiling is a subtiling of a radially generated tiling.