Every day, millions of people play Wordle to find the five-letter words hidden in the New York Times’ most popular puzzle game. Now, researchers at Binghamton University, State University of New York, have announced that they have developed a mathematical approach that can solve Wordle with an astonishing 99% success rate.
Wordle’s goal is simple. Players have six chances to identify the secret five-letter word. Each game starts with five empty squares and no clues.
When the player enters a guess, such as “BRAVE,” the game responds with a colored square that provides a hint about the hidden word.
- Gray means the character is not in the secret word.
- Yellow means the character is in the word but in the wrong position.
- Green means the text is correct and in the correct position.
Using these clues, players keep guessing until they find the answer and all five squares are green or they run out of attempts.
Solve Wordle using information theory
The research team, led by Assistant Professor Congyu “Peter” Wu, focused on Shannon’s entropy, a mathematical concept used to measure uncertainty. Rather than focusing on the words that seem most likely to be the answer, this method identifies guesses that reveal the greatest amount of information and eliminate the greatest number of possibilities.
“Let’s say you come to a guess. Your previous guess eliminates a large number of choices, and guessing a few words based on the remaining choices can put you on a trajectory where information acquisition becomes faster,” said Wu, a faculty member in the Thomas J. Watson College of Engineering and Applied Sciences’ Department of Systems Science and Industrial Engineering.
The key insight, the researchers say, is that the best guess is not necessarily the most likely to be correct. In some cases, a more informative guess can significantly narrow the range of possible answers.
“A subtle but important insight from this paper is that a guess doesn’t have to be the most likely answer, it just needs to be informative,” said Donald Stevens, a doctoral student at Binghamton University. “By applying Shannon entropy, the objective changes to maximizing the expected uncertainty reduction rather than the probability of being correct. In practice, this approach can lead to solving puzzles with fewer guesses.”
This strategy can seem somewhat random, as it prioritizes information gathering over directly pursuing answers. To use this while playing Wordle, the player runs a separate script/program and provides color-coded feedback for each guess. The program then recommends the next word that it expects to provide the most useful information.
99% success rate
To evaluate this approach, the researchers compared it to the more traditional Wordle strategy, which emphasizes frequently used letters (such as “A,” “E,” and “R”).
In computer simulations, we were able to solve 99% of Wordle puzzles using information theory-based methods. About 90% were resolved using traditional approaches.
From classroom assignments to published research
This project began as a class assignment rather than a formal research activity. Wu asked students to demonstrate how information theory can be applied to real-world problems.
This classroom exercise eventually evolved into a published scientific paper.
Co-author Talal Aladaire said the path from coursework to publication reflects the strengths of Binghamton’s School of Systems Science and Industrial Engineering.
“The courses here don’t just teach you a concept, they challenge you to apply it in a way that actually has a lasting impact,” Alladaire said.
Wu said the project is an excellent example of how information theory can be used to improve performance on real-world tasks.
“A particularly creative and valuable intellectual contribution of the team was converting a static measurement in the scientific field (Shannon entropy) into a dynamic solution that helps us better accomplish a popular task. This demonstrates the team’s deep understanding of the lesson content and their talent as engineers,” Wu said.
This study “Solving Wordle using information theory” Northeast Journal of Complex Systems.
