# The Concept of the Combinatorial Mean (CMean) Conjecture

## The sQuaricon Pattern in Combinatorics

Introduction

The n-Queens problem is well known and solved on any regular chessboard. When the problem has extended to the toroidal (modular) board it was discussed rarely in the math literature (1) and, consequently, some uncertainty occurred regarding the number of possible solutions ( e.g. oeis.A051906) on such a board. I hope, the previous enthusiastic article (2) gave some new facts regarding the ‘translated solutions’ that are kind of ostensibly solutions (see Chapter 4 in the mentioned article).

In this article, I would like to give a more concise presentation of the sQuaricon pattern matrices and go one step ahead…

# The modular n-Queens-Completion problem solved by a sQuaricon pattern

## (for n=p, n=p-1)

I am a long-time enthusiast in math and would like to keep this status in future. So, all my claims exposed here should be taken with reasonable caution at least until the full experts’ verification. This article is a preprint version in work…

• this is the 3rd Revised version, as of July 21, 2019

I will try to show and prove (with a little bit outdated math knowledge and notification) 4 Claims that make n-Queens Completion Problem transparent and simple to apply:

Claim-1: the n-Queens-Completion problem on modular board is solvable in the polynomial time for any n=p, (proof in…

# n-Queens Completion Problem solved for n=p, n=p-1

very soon here will be published full article of simple but efficient way how to solve n-queens completion problem 