Musings Too many interests, too little time

The Anti-N-Queens Problem

The N-Queens problem is a well-known problem and it consists of placing N non-attacking queens on an NxN chessboard. It is solvable for any n > 3.

In February 2021, I explored a related similar problem, tentatively named Anti-N-Queens. A simple formulatin of the problem is the following:

What is the maximum number of “safe” squares when N queens are placed on a board?

A square on the board is considered safe when it is not threatened by any queen on the board. There is no restriction that the queens are not attacking each other, nor (obviously) that any rule of chess must be followed.

The complete results for two variations of the problem can be found on this document. The same paper has been published online and has a DOI of 10.5281/zenodo.4672187

Update

My results for the maximum number of safe squares when placing N queens on a standard 8x8 chessboard were accepted and published in the Online Encyclopedia of Integer Sequences (OEIS) as sequence A342151.

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