Project Description: When Wordplay Meets Mathematical Logic!
Are you intrigued by the art of puzzle-solving? Have you ever looked for more elegant solutions to a puzzle or mathematical problem? Then this project is for you! Wordle took the world by storm in 2021, with people addicted to trying to figure out the five letter word in as few guesses as possible. Its popularity spawned many other word games, including the Waffle Puzzle, named so for its distinctive shape. In the Waffle Puzzle, six 5-letter words are arranged in a waffle-shaped grid, each one scrambled. Your mission? Unscramble them by strategically swapping letters. Much like Wordle, the puzzle provides valuable feedback, signaling whether a letter is correctly placed or if an entire word has found its home. In this puzzle game, the creator promises that every puzzle can be solved in exactly 10 moves. The goal of this project is to figure out how to reliably find the most efficient solution when we already know the answer.
To tackle this problem, we will use permutations, a topic from abstract algebra. In the first part of the project, we will introduce the concept of permutations, and learn how to multiply permutations, find their parity, find orders of permutations, find their lengths, and other properties. With a solid understanding of these properties, we will then look at popular puzzle games through the lens of permutations, and then finally, we will tackle the Waffle puzzle. Many further questions arise from this viewpoint. The questions that we ask and answer in this project will be determined by the interests and ideas of the students. If so inclined, we may think about other puzzles that may be able to be solved with permutations, or develop simple computer algorithms to create our own Waffle puzzles that can be solved in a specified number of moves.
Takeaways: By the end, you’ll have a profound grasp of permutations, especially as they apply to real-world puzzles. You will get a firsthand understanding of how mathematicians uncover new knowledge by exploring abstract ideas. You will also sharpen your ability to dissect complex problems, identify patterns, and develop innovative solutions.
Prerequisites: A love for puzzles is a must! Completing some level of Discrete Mathematics and/or Linear Algebra is not required, but may be helpful. You do not need to have taken group theory or abstract algebra for this project.