The Mathematics Behind Sudoku and How to Create Magic Squares

Sudoku puzzles date back to the 1800s in France and were introduced to America in the late 1970s. Since then, the puzzle has become a worldwide phenomenon. This thesis will be of expositional nature including the works of books and mathematical papers such as [2], [14], and [15], among others. The pages ahead will contain answers to some common questions about Sudoku such as, what is the minimum number of starting clues that will produce a unique solution? On the other side of the spectrum, what is the maximum number of starting clues that won’t produce a unique solution? Taking Sudoku one step farther, this paper will talk about Magic Squares and the algorithm used in making them. Even more interesting is that the al- gorithm provides the makings of a multimagic square, where every entry in a magic square is squared, with the rows, columns, and diagonals still adding to the same number [15]. See the Appendix for the computer code in the program MATLAB that creates multimagic squares

Finding magic squares with Douglas—Rachford algorithm

In this expository paper, we show how to use the Douglas—Rachford algorithm as a successful heuristic for finding magic squares. The Douglas—Rachford algorithm is an iterative projection method for solving feasibility problems. Although its convergence is only guaranteed in the convex setting, the algorithm has been successfully applied to a number of similar nonconvex problems, such as solving Sudoku puzzles. We present two formulations of the nonconvex feasibility problem of finding magic squares, which are inspired by those of Sudoku, and test the Douglas—Rachford algorithm on them.The first author was supported by MINECO of Spain and ERDF of EU, as part of the Ramón y Cajal program (RYC-2013-13327) and Grants MTM2014-59179-C2-1-P and PGC2018-097960-B-C22

An Alternative Sudoku Puzzle with Letters While Addressing Math Anxiety

Math anxiety remains a critical issue affecting student performance and confidence across grade levels throughout the world. This paper looks at the impact of math anxiety on students and also how using letters instead of numbers with Sudoku puzzles can perhaps alleviate math anxiety and number anxiety as an alternative to doing Sudoku puzzles and turning students on to the logic of magic squares and Sudoku puzzles. This paper shares data on math anxiety levels by grade level from a study, provides some examples of some Sudoku puzzles with Greek letters and our English alphabet along with much research, and recommendations of best practices for teaching math and addressing such concerns in light of the reality of math anxiety existing in a world where we are preparing young people for a STEM world. The data in this study shows an upward trend in higher math anxiety levels as students increase in grade level. It is evident teachers need to do more starting in the early grades and each grade to use best practices for teaching math and also use math anxiety reduction strategies to work on reducing math anxiety as students advance each grade level. Research, best practices for teaching mathematics, strategies, and a survey are included