Researchers used math to crack Wordle

# S-M-A-R-T! These researchers used math to crack Wordle - Binghamton News Source: [https://www.binghamton.edu/news/story/6327/s-m-a-r-t-these-researchers-used-math-to-crack-wordle](https://www.binghamton.edu/news/story/6327/s-m-a-r-t-these-researchers-used-math-to-crack-wordle) Every day, millions of people play Wordle, the popular*New York Times*game that challenges users to guess a secret five\-letter word\. Using information theory, a team of researchers at Binghamton University, State University of New York, has developed a method to solve the game with a 99% success rate\. In Wordle, players attempt to solve a five\-letter word within six guesses\. At the start, players are presented with five blank spaces to play any letter of their choosing, with zero hints offered\. When a player guesses a word – say “BRAVE” – the game provides feedback in the form of color highlights\. - Grey indicates that a guessed letter is not part of the secret word - Yellow indicates that a guessed letter is part of the secret word but is not in the correct order - Green indicates the guessed letter is part of the secret word and in the correct order The player keeps guessing and is presented with clues until they guess the correct word and all five squares turn green – or they run out of guesses and lose the game\. ## Cracking the code The research team, led by Assistant Professor[Congyu “Peter” Wu](https://www.binghamton.edu/ssie/people/profile.html?id=congyu.wu), applied Shannon entropy – a mathematical measure of uncertainty – to determine which guesses provide the most information\. Rather than focusing solely on guessing the most likely answer from the get\-go, their method prioritizes guessing words that provide as much*information*as possible to reduce the pool of possible words\. “Let's say you're at a certain guess\. The previous guesses will eliminate a whole bunch of options, and based on the remaining options, guessing some words will send you into a trajectory where information gain is speedier,” said Wu, a faculty member at the Thomas J\. Watson College of Engineering and Applied Science’s School of Systems Science and Industrial Engineering\. “A subtle but important insight from the paper is that a guess doesn’t have to be the most likely*answer*; it simply has to be informative,” said Donald Stephens, a doctoral student at Binghamton University\. “By applying Shannon entropy, the objective shifts to maximizing the expected reduction in uncertainty rather than the probability of being right\. In practice, this approach can lead to solving the puzzle in fewer guesses\.” Their method might seem more “random,” but it is more likely to lead to a successful guess by the end of the game\. To use the method in real time, a player would need to run a script/program on the side\. The player would enter the color\-coded feedback that the game provides, and the program would spit out the next best guess to attempt to provide more information\. The team tested their strategy against a more traditional approach based on guessing common letters \(e\.g\., “A”, “E”, “R”\)\. In simulations, their approach solved 99% of Wordle puzzles, while the traditional method solved just 90%\. ## From class project to publication This research paper didn’t stem from a research study but rather a class project where Wu tasked students to demonstrate information theory to solve a problem\. Co\-author Talal Aladaileh said that the paper’s growth from a course project into a published paper speaks volumes about the rigor, depth, and quality of the[School of Systems Science and Industrial Engineering program at Binghamton\.](https://www.binghamton.edu/ssie/) “The courses here don't just teach concepts; they push you to apply them in ways that have real, lasting impact,” Aladaileh said\. Wu said that the project is a great use of information theory because it actively supports incorporating it to better perform a task\. “What is especially creative and valuable about the team's intellectual contribution,” Wu said, “is that it transformed a static measurement \(Shannon entropy\) in a scientific domain into a dynamic solution that helps accomplish a popular task better, which showcases the team's deep understanding of class material and their talent as engineers\.” The paper,[“Solving Wordle Using Information Theory,”](https://orb.binghamton.edu/nejcs/vol8/iss1/6/)was published in the*Northeast Journal of Complex Systems*\.