O desafio das oito rainhas: um estudo sobre as soluções fundamentais do problema

Abstract

A million dollars awaits the solver of the chess challenge: arranging a thousand queens on a 1000x1000 chessboard so that none of them attacks another queen. This prize is offered by the Clay Mathematics Institute and remains unclaimed to this day. But the classic chess problem involves "only" eight queens on an 8x8 board, this study aims to explore solutions to this challenge using a mathematical approach based on the concepts of isometry: rotation and reflection applied to the board, along with combinatorial analysis concepts such as permutation, arrangement, and simple combination applied to piece arrangement. The goal is to find configurations that meet the problem's constraints and analyze whether these configurations are fundamental or derived from existing ones through the geometric properties of the chessboard. To achieve this, the strategy involves reducing the eight queens to the smallest possible number that allows a solution to the problem, beginning with four pieces. The results reveal new perspectives in solving the challenge, identifying symmetrical configurations representing equivalent solutions. It can be concluded that by applying simple mathematical concepts, it was possible to explore an old, classic problem in the field of computing, which involves a more complex algorithmic approach, in a simple and understandable manner for all readers.