# 8-QUEEN CHESS PUZZLE’S SOLUTION IMPLEMENTING BACKTRACKING ALGORITHM

IMPLEMENTING BACKTRACKING

ALGORITHM

I. INTRODUCTION

Did you ever think that you can play chess with an eight queen in it? A simple board game, that turned into a tricky game. The Queen is the most powerful piece in the game of chess, but just how many queens can you fit on a chessboard before they start attacking each other? The answer is eight (8), but positioning so many of these influential ladies on a single board is a tricky challenge. Put them in the wrong place relative to each other and they’ll start to think that the board game isn’t big enough for them all, and that it will be it. All out war and tiaras at dawn. Chess is one of the board game everyone is familiar with. One of the reasons why Chess had become one of the oldest and most popular board games mankind had ever played is because of the complexity of the game and simplicity of its objective. The game is played by two players competing for the game’s objective. Each player has a set of Chess pieces consisting of 8 pawns, 2 rookies, 2 knights, 2 bishops, a king and a queen with each piece moves in a unique pattern. To checkmate an opponent’s King, one must have a strategy on how to move each piece on a set. The uniqueness of each set is determined by its hierarchical position – pawn being the lowest and King as the most precious piece in a set. But the most powerful piece in the set is the Queen. Chang (2003) stated that the eight queen problem refers to a configuration which cannot occur in an actual game, but which is based on properties of the queen. The problem is: place eight (8) queens on the board in such a way that no queen is attacking any other.

II. BACKGROUND OF THE PROJECT

The 8-Queen Chess puzzle which was originally proposed in 1848 by the chess player Max Bezzel is a problem of placing eight (8) chess Queens on an 8x8 chessboard so that no two queens attack each other. The problem that is defined by Kumar (2008) stated that the game has 8 queens and an 8x8 chessboard having alternate black and white squares. The queens are placed on the chessboard. Any queen can attack any another queen placed on same way row, or column or diagonal. The problem is to find the proper placement of queens on the chessboard in such a way that no queen attacks other queen. One solution for the puzzle is to determine all possible outcomes that the 8 queens will be placed in the board time complying with the condition that no two queens attack each other. This process is so exhaustive and time consuming for a human to do. A program simulating the problem will require an initial input to the user. This will represent the first queen in the board. After initializing the first queen, the program will now search for the next 7 queens that will satisfy the condition of the problem.

III. OBJECTIVES

The objectives of the project is to find a solution for the 8-Queen Chess Puzzle Problem using an algorithm defined and tested to be applied in a real world problem. The study aims to identify the application of an algorithm based on the problem proposed. Researchers must simulate the Algorithm using a program. It must solve the proposed problem and try to deliver output effectively and accurately. The following are the objectives of the study:

1. To find an algorithm that can produce a deliverable where the conditions for the problem are all satisfied. 2. To identify the relationship between the algorithm and the problem background. 3. To create a program that can simulate the algorithm.

4. To show the effectiveness of the proposed solution.

IV. SCOPE AND LIMITATIONS

The study will focus on the 8-Queen Chess Puzzle problem. This game is to position 8 queens on an 8x8 chess board, simulation a real chess game. Algorithms that will be used in the study will be based on the related literatures presented in this research. Such algorithms presented are evaluated by its effectiveness and the application for the problem...

Bibliography: Chang, S.K., Data Structures and Algorithm. World Scientific Publishing Co.Pte. Ltd. (2003)

Eiben A

Kumar, E. Artificial Intelligence. International Publishing House Pvt. Ltd., New Delhi, India (2008).

Muniswamy V.V. Design and Analysis of Algorithms. I.K. International Pvt. Ltd (2009)

Nilsson N.J

Skiena S. S. The Algorithm Design Manual. Springer – Verlag, London (2008)

Wilkinson, S

Wilson, F. 101 Questions on How to Play Chess. Dover Publications, Inc. Don Mills, Toronto, Ontario, Canada. (1994).

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