Through this article and the next several articles, I’m going to share with you something called Chromatic Polynomials. It’s a form of math that is quite powerful in its most basic form, but I’ll show you how to make it even more so. I’ll show you how to apply chromatic polynomials to sudoku, logic puzzles, video poker, slot games, B-Sat problems, and more. I first learned about chromatic polynomials from the paper “Counting complex disordered states by efficient pattern matc

Introduction The question of whether it is possible to create a 3x3 magic square of squares is an unsolved problem in mathematics. There have been many attempts at finding a solution, resulting in many “near misses” - solutions that meet some of the requirements but not all of them. There is an excellent summary of research and attempts at solutions at http://www.multimagie.com/English/SquaresOfSquaresSearch.htm. Here, I will present a purely algebraic approach to a 3x3 magic

The Challenge I was playing with my son’s Rubik’s Cubes and tried to scramble a cube randomly so that no two squares with the same color were side by side. Here’s one way to do it: But I wanted a scramble that looked like a random scramble. No matter how many different moves I made, I couldn’t do it. Every time I separated two squares with the same color, two other squares of the same color would touch somewhere else. Looking for an easy answer, I went to puzzling.stackexcha