The n queens problem with forbidden squares

Abstract

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.