Millions of people tackle Wordle every day, trying to uncover a hidden five-letter word in the New York Times’ wildly popular puzzle game. Now, researchers at Binghamton University, State University of New York, say they have developed a mathematical approach that can solve Wordle with a remarkable 99% success rate.
The goal of Wordle is simple. Players have six chances to identify a secret five-letter word. Each game begins with five empty squares and no clues.
When a player enters a guess, such as “BRAVE,” the game responds with colored squares that provide hints about the hidden word:
- Grey means the letter does not appear in the secret word.
- Yellow means the letter is in the word but is in the wrong position.
- Green means the letter is both correct and in the correct position.
Using these clues, players continue making guesses until they either find the answer and turn all five squares green or run out of attempts.
Using Information Theory to Solve Wordle
The research team, led by Assistant Professor Congyu “Peter” Wu, turned to Shannon entropy, a mathematical concept used to measure uncertainty. Instead of focusing on words that seem most likely to be the answer, the method identifies guesses that reveal the greatest amount of information and eliminate the largest number of possibilities.
“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.
According to the researchers, the key insight is that the best guess is not always the one most likely to be correct. Sometimes a more informative guess can dramatically narrow the field of possible answers.
“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.”
The strategy can appear somewhat random because it prioritizes gathering information over directly pursuing the answer. To use it while playing Wordle, a player would run a separate script/program and enter the color-coded feedback after each guess. The program would then recommend the next word that is expected to provide the most useful information.
A 99% Success Rate
To evaluate the approach, the researchers compared it with a more traditional Wordle strategy that emphasizes frequently used letters (e.g., “A,” “E,” “R”).
In computer simulations, the information theory-based method successfully solved 99% of Wordle puzzles. The conventional approach solved about 90%.
From Classroom Assignment to Published Research
The project began not as a formal research initiative, but as a class assignment. Wu challenged students to demonstrate how information theory could be applied to a real-world problem.
That classroom exercise eventually evolved into a published scientific paper.
Co-author Talal Aladaileh said the journey from coursework to publication reflects the strength of Binghamton’s School of Systems Science and Industrial Engineering.
“The courses here don’t just teach concepts; they push you to apply them in ways that have real, lasting impact,” Aladaileh said.
Wu noted that the project serves as an excellent example of how information theory can be used to improve performance in practical tasks.
“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 study, “Solving Wordle Using Information Theory,” was published in the Northeast Journal of Complex Systems.