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Searching for a 3x3 magic square of Squares

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…

Counting Quoridor Fence Arrangements

I learned about the game of Quoridor when my sister begged me to play the game with her husband. “Somebody’s got to beat him at it!” she said. I beat him once, and then he upped his game and I haven’t beat him since. But the game gave me something to think about: How many ways can you place fences on the board? Fence Placement Rules Here’s what the Quoridor board looks like: You can find the rules…

Modeling the Rubik's Cube in a Spreadsheet

This little project came from two things: The fact that you can start with a solved cube and repeatedly apply a pattern of moves until...

The Rubik's Cube Perfect Scramble

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...

Welcome to Solutions Looking for Problems

I am a programmer with an almost unhealthy obsession with math. Occasionally, my job provides some intriguing challenges where I can...