The n queens problem with forbidden squares - Chatham, Doug (Utilitas Mathematica, 2019)
Given an n x n chessboard and n > k > 0, we define the (n, k) queens forbidding number for Q n > k) as the minimum number of squares that we can 'for bid so that at most k queens can be put in permitted squares with no two queens in the same row, column, or diagonal. For infinitely many cases, forQ(n, k) = n 2-n k. We also consider some cases where the (n, k) queens forbidding number is less than n2-nk. © 2019 Utilitas Mathematica Publishing Inc.. All rights reserved.