We develop lower bounds with often-matching exponential algorithms for several variants of the n-queens problem. In particular, we prove that placing n queens onto an \(n \times n\) board with holes requires \(2^{\varTheta (n)}\) time for both decision and counting, assuming the Exponential Time Hypothesis (ETH) and #ETH respectively. The same result extends to more general manifolds. If the \(n \times n\) board has no holes, but some of the queens are already placed, then completing the placement of n queens is known to be NP-complete and #P-complete; we show that both versions require between \(2^{\varOmega (\sqrt{n})}\) and \(2^{O(n)}\) time, again assuming (#)ETH.