Queens Independence Separation on Rectangular Chessboards

Abstract

The famous eight queens problem with non-attacking queens placement on an 8 x 8 chessboard was first posed in the year 1848. The queens separation problem is the legal placement of the fewest number of pawns with the maximum number of independent queens placed on an N x N board which results in a separated board. Here a legal placement is defined as the separation of attacking queens by pawns. Using this concept, the current study extends the queens separation problem onto the rectangular board M x N, (M<N),  to result in a separated board with the maximum number of independent queens. The research work here first describes the  M+k queens separation with k=1 pawn and continue to find for any k. Then it  focuses on finding the symmetric solutions of the M+k queens separation with k pawns.