Researchers used math to crack Wordle

hhhs 3 days ago 26 commentsRead Article on binghamton.edu

ZH version is available. Content is displayed in original English for accuracy.

⚡ Community Insights

Discussion Sentiment

67% Positive

Analyzed from 1133 words in the discussion.

Discussion (26 Comments)Read Original on HackerNews

trollbridge•11 minutes ago

Hacker News commenter uses grep -i ^.u...$ /usr/share/dict/words | grep -i c | grep -i -v '^..c..$' | grep -i -v '^...c.$' to crack today's Wordle

boothby•19 minutes ago

I crushed wordle within a few days of its popularity entering my sphere. It was pretty easy to brute-force a decision tree minimizing the average number of guesses using a lowly python script and a few days of qpu time.

Don't Wordle[1] is significantly more interesting; I've got a solver but the maximum score takes my lowly python script upwards of a day (per day) to solve using brute force. For now, I solve it with a heuristic that terminates in about 20 minutes. My old wordle solver was useful to find a good but suboptimal tree for identifying the answer in 5 undos or less.

Today:

  Don't Wordle 1491 - SURVIVED
  Hooray! I didn't Wordle today!
  ..... 8089
  ..... 4647
  ..... 2492
  ..... 1026
  .Y... 231
  ..G.. 100
  Undos used: 3

    100 words remaining
  x 10 unused letters
  = 1000 total score

My puzzle ethics are: you can and should download the dictionaries of valid answers and valid guesses, you're allowed to keep them separate, but you must not keep the list of answers in its original order.

[1] https://dontwordle.com/

cvoss•3 minutes ago

Another great variant is Unfair Wordle [1]. The opponent does not fix the answer upfront but instead evades the player's guesses as long as possible, providing you with the least information it legally can give (according to the usual rules) while still preserving a valid game completion path. The result is that your guesses end up looking extremely unlucky in retrospect.

[1] https://tweakimp.github.io/unfairwordle/

jezzamon•about 2 hours ago

I thought this was old news? I remember people making videos about using information theory to solve Wordle back when it was particularly hyped. (After writing this I checked, there's even a 3 blue 1 brown video on this)

My favourite along those lines was solving wordle in 1 guess using the distribution of coloured squares on social media https://www.kaggle.com/code/benhamner/wordle-1-6

GL26•about 2 hours ago

Yes 3blue1brown made a series of videos which explains it : https://www.youtube.com/watch?v=v68zYyaEmEA ; https://www.youtube.com/watch?v=fRed0Xmc2Wg .

gkoberger•about 2 hours ago

This isn't groundbreaking science, sure, but it is a great way to get people interested in a topic. After all, it wouldn't be on Hacker News if the word Wordle wasn't in it. I'm a huge fan of using things like this to teach science, math and engineering.

We started using "Solve 100 Wordles programmatically" as our technical interview, and people _love_ it. They get really into it and have fun. It's pretty easy to do inefficiently, and it's great to watch people build on it and try to improve their scores.

It has two benefits: 1/ everyone clearly understands the problem 2/ people see it as fun rather than a drag.

tialaramex•about 1 hour ago

Another small benefit: Everybody understands this isn't what the job is. Nobody is hiring you to beat Wordle, and you solving this is clearly not somehow on the path to their actual task, they are asking you if you can write software which solves a problem and you're demonstrating that you can do that, which makes sense.

I think "Solve 100 Wordles programmatically" sounds like a lot of work, so that'd probably be a "No" from me unless it was last hurdle for a job I was enthusiastic about but unlike "Write a program to solve this class of graph problem" I at least wouldn't be worried that you're trying to get me to do work for free.

Actually Wordle solver as Code Review task sounds like maybe a more interesting live interview than the one we do today. "Here's this mediocre Wordle solver, what is your feedback in review?" has the advantage that they've probably seen a Wordle puzzle before but it's not an example problem they've seen in fifty textbooks.

gkoberger•about 1 hour ago

Well, the 100 Wordles is just "Solve one Wordle" in a for-loop. If you're an even somewhat decent engineer, it takes under 10 minutes to get it working (inefficiently).

Then we encourage people to do whatever they want next: improve their average score, build a frontend UI for it, solve on Hard Mode, etc.

In the past, we never did technical interview questions like this. We always asked people to bring their own project, and work the way they want to. However, with the addition of AI, we hit a wall: we want people to feel they can use AI in a way that mimics how they'd actually work day-to-day, BUT we also need a simple check to make sure they understood engineering basics.

dredmorbius•about 1 hour ago

I'd quickly realised that a set of words which covered most of the alphabet (20 words, leaving b, g, j, q, v, and z excluded) allowed solving virtually all Wordle puzzles. The game quickly lost any challenge.

  wimpy
  crowd
  thank
  fuels

Altering order might give faster results. The order presented leaves the most common letters (e, t) for last. Z is quite uncommon, q is virtually always followed by u, similarly common pairs such as ch, sh, and th, as well as three- and four-letter combinations ing and tion, though those won't show frequently in five-letter words of default Wordle.

It would be possible to vary word choice based on revealed matches and hits, but if your goal is simply to solve (rather than minimise attempts), the above list works quite well.

magneticnorth•about 1 hour ago

> The game quickly lost any challenge.

I only play on hard mode for this reason. My next guess must always be a possible answer based on my current information, and that varies the puzzle enough from day to day that I still find it enjoyable to play occasionally.

dieselgate•34 minutes ago

I haven't played wordle much since it was purchased but NYTimes ran a story in the last couple days saying how "Hard mode" is actually easier based on their research. Just throwing it out there as food for thought not in a "gotcha" sort of way.

https://www.nytimes.com/2026/06/18/upshot/wordle-hard-mode.h...

empath75•6 minutes ago

It's not "easier", it just forces a more guess-efficient strategy.

drivers99•about 1 hour ago

Does that not lead you to situations where you have to guess the last letter on each round? Or do you choose words to avoid getting trapped in that situation in the first place?

copypasterepeat•about 1 hour ago

I try to avoid the common traps, but it can be tricky.

I also impose this additional constraint on myself, which the game doesn't enforce, that I can't reuse letters that have been marked gray. Sometimes you just can't think of the next word, or might be tempted to use a gray letter because that way you could get more information from other letters, but I avoid using them.

magneticnorth•38 minutes ago

Yes, that does happen occasionally, and it's part of the game for me to try and avoid getting trapped like that.

mcphage•28 minutes ago

> I'd quickly realised that a set of words which covered most of the alphabet (20 words, leaving b, g, j, q, v, and z excluded) allowed solving virtually all Wordle puzzles. The game quickly lost any challenge.

You can even go further—there's a set of 5 words which uses 25 out of 26 possible letters, leaving you one more word to enter the right answer.

But here's the thing: while that means you'll almost always win, your # of guesses will always be high.

> but if your goal is simply to solve (rather than minimise attempts)

Pretty much nobody's goal is to simply solve. Once they've played it for a few days, everybody's goal is to minimize guesses. That's the flaw in having a long word list—you always do badly.

topaz0•8 minutes ago

The only virtuous goal is to type some fun words imo.

Brendinooo•35 minutes ago

gotta see how your strategy holds up in sexaginta-quattuordle

lkbm•25 minutes ago

This is how I played Quordle and Octordle, but with just three words (doubt, glyph, raise). Might not scale for all combinations.

starky•about 1 hour ago

>In simulations, their approach solved 99% of Wordle puzzles, while the traditional method solved just 90%.

This seems wrong to me, getting a 98%+ solve rate for Wordle is pretty common.

kps•about 2 hours ago

To paraphrase von Neumann, isn't that how everyone does it?

kens•about 1 hour ago

What I'm interested in is the best starting word. Using Shannon entropy, the paper finds that it is "tares".

bee_rider•32 minutes ago

I think it depends on whether you use a conventional dictionary as the population of possible words, the valid guess list, or the (known, at the time, for the originally version of the game at least) possible solution list. I guess you could also use the possible solution list minus the words that had already been guessed in previous iterations.

I mean, you had to give yourself an artificial constraint because IIRC the next solution was actually built into the page anyway, not obfuscated in any way.

ano-ther•3 days ago

Paper: https://orb.binghamton.edu/nejcs/vol8/iss1/6/

plants•about 1 hour ago

plug to my blog post where I did something similar a few years back! https://willbeckman.com/wordle.html :). Not sure if this is an identical solution, but it was a fun little project.