A MATHEMATICAL AND COMPUTER- BASED ALGORITHMIC METHOD FOR CONSTRUCTING ODD-ORDER EQUAL-SUM MATRIX NUMBER PUZZLES FROM ARITHMETIC SEQUENCES.

Abstract: It is important to say that number puzzles and equal sum matrices have been highly researched because of their strong connections to mathematics, pattern recognition, and problem solving by means of algorithms. However, a lot of methods of design of such matrices involve mathematical formulas and approaches that can be challenging for those who lack necessary mathematical knowledge. The goal of this research is to introduce the technique of design of Matrix Number Puzzles of odd orders based on arithmetic progressions where the sum of all rows, columns, and two diagonals must be the equal. Design Science Research Methodology (DSRM), an algorithm development, and mathematical validation methodology are selected for this research. Construction involves Straight-Line Left-Angle Procedure (SLLAP) and Straight-Line Right-Angle Procedure (SLRAP) processes in generating the embossed matrix pattern. The other values which are not part of the embossed matrix are then organized by using of the Interchanging Values and Placing Them in the Corresponding Locations (IVPTCL) process. The process is demonstrated by the use of odd-order square matrices of (3×3), (5×5), (7×7), (9×9), and (11×11). In the finished matrices, it can be observed that the construction process being discussed is able to generate equal sums of the selected arithmetic sequences in all rows, columns, and main diagonals. Furthermore, the process performances as the foundation for implementing the process in a computer program in which the input parameters are the order of the matrix, first value, and common difference using the programming language of Python.

Keywords: Square matrix of odd order, arithmetic series, Matrix Number Puzzle, SLLAP, SLRAP, IVPTCL, equal-sum matrix, algorithm design, mathematics.