This reminds me of something about flash games in the 2000s. I was in high school at the time and every morning in class I would check onemorelevel, kongregate, etc for new games. There was a pattern in flash games where someone would make a great simple game with an interesting, novel, or long-forgotten mechanic. It would get to the frontpage of all these sites, and a few months later you'd see that mechanic mixed with every other popular flash game mechanic. It was really cool to see a community of creative people embrace an idea and then beat it to death in a short period of time. I think in a lot of other creative genres, this kind of "copying your idea but a twist" is seen as poor form, plagiarism, or derivative. Maybe the flash game community was low enough stakes that it welcomed that kind of community engagement. I wonder what the people actually making the games thought.
Anyway, this is a really cool example of that. It's wordle, but with a twist.
“Immature poets imitate; mature poets steal; bad poets deface what they take, and good poets make it into something better, or at least something different. The good poet welds his theft into a whole of feeling which is unique, utterly different than that from which it is torn.” https://www.benshoemate.com/2012/08/02/what-does-it-mean-goo...
My side-project this week has been searching for an optimal Wordle strategy. I figured it would make a great blog post but I haven't got that far yet.
Step 1 is to find an optimal starting word. My most insightful finding so far has came from trying to define a cost function for comparing potential starting words. It turns out that "% of potential guesses [not] eliminated" is an excellent loss function.
Importantly, the full set of all Acceptable Guesses is knowable. For any given (guess, answer) pair, the game provides feedback about each character (or digit). There are basically three pieces of potential feedback: (N)ot Used, (U)sed Elsewhere, (E)xact Match. For example, a single guess might produce the feedback "NUNNE". Each of these will eliminate some subset of Acceptable Guesses which means you can attribute a fixed value between 0.0 and 1.0 to any piece of feedback, and multiply those together to get the loss score of a given guess. Average that across all Potential Answers to get a cost score.
Not sure what my goal of this post is. Guess I just wanted to share that these games are as much fun to analyze as they are to play (if not more).
I've given some light thought to this: There are several which are considered "good starting words", that mainly contain lots of vowels or most common used letters (such as "audio", Raise, etc). Then, as a second word, you could use another word that complements those letters (audio/rents, raise/mould ).
But there is a better strategy (similar to what is used in those interview puzzles of "From N weights, find 1 that is different in X measurements of a scale): The fact that you input some vowels and see that they are not in there, tells you that the remaining ones MUST be in the word (treating Y as a vowel as well). So it might be possible to come up with a strategy that uses that negative information as well to minimize the search space.
I made a lil clone of wordle and found that the full list of solutions, past and future, is right there in the minified js. Could be useful for your analysis.
Maybe I shouldn't be sharing this, it's a bit sad to break the illusion that the creator is picking a new word for us every day.
I went to the source code of wordle & copied all 12000 words to an excel sheet Column A, starting from row 4.
3rd row for next 18 columns has drop down filter.
You guess any word with at least 2 vowels, if 3 better, no repeat letters. You get some grey, some yellow, some maybe green.
2nd column to 6th column on excel sheet is the Grey Letters, Not Found in Answer. In this, 2nd row, if u find any grey you type it here. The formula from row 4 downwards in this group checks if its top input cell is empty, if yes, true, if not empty, then it check if that letter exists in its row cell of column A. If exists, false (grey means no letter), otherwise true.
Column 7th to 11 are yellow. Same thing, row 2 gets input, 4th row onwards checks if this exists in Column A cell, true, otherwise false. If input cell empty, then True.
Column 12 to 16 gets green letter input. Here input goes by position, if 2nd letter is green, you type it in 2nd column of this group, which is 13th column.
Formula in 4th and next checks if input empty, true, otherwise if input exist in exact position, true, otherwise false.
17th column is empty & narrow, to create a gap.
18th column returns 0 if any false found in while row. Any false means this word is not the answer. Otherwise returns 1.
A separate one cell counts all those 1, tells me how many potential answers are. After every try/word, one can filter this last column on 1.
This website is currently hosting a competition until the end of the month for Wordle strategies if you want to see how it compares: https://botfights.io/game/wordle
Interestingly, I made a coding challenge for this exact problem a few years ago. You can find it on the Code Golf StackExchange website: https://codegolf.stackexchange.com/questions/26858/guess-the....
The challenge is named after the Lingo TV show which used the concept repopularized by Wordle.
Lingo itself took inspiration from a 1955 paper game named Jotto.
Regarding strategies used in the challenge, the best performing solution was an adaptation of a Mastermind solver.
I use WEIRD, my completely untested and I researched intuition being that knowing common consonants are in a word isn’t helpful unless you get the right place, but knowing the vowels is. At least that was my logic when I first played and my brain produced WEIRD.
I’m sure it’s far from optimal, but I continue to use it because I obviously understand how I came to choose it, and it “works” and survivor bias is powerful :)
I recall seeing HN posts from people working out “optimal” starting words and guess patterns, but I just like mine :)
Since you've been looking into it, how are words with multiple of the same letters treated on Wordle. If there are two (or three) 'E' in the solution or the guess?
I've spent some time analyzing Wordle (my starting words are SOARE and then BUILT, unless I've already got strong clues from SOARE).
If the answer has one E and you guess a word with two Es, only one of the Es will be marked correct (green/yellow). If one of the Es is in the correct place, it will be green and the other one grey. Otherwise the first E will be yellow and the second grey. So if the answer has fewer Es than your guess the game tells you.
If the answer has more Es than your guess there is no indication of this.
Today 538 gave the optimal starting word and all the best second words, with a 60% chance of solving it in three words. Completely ruined the game, in my opinion.
log(100000) is 5, so approximately 1 in 5 numbers below 100k is prime. Obviously those in the range 10000-99999 are less dense, but primes are still surprisingly common.
That being said, the pool you're really working from is the numbers with last digit 1, 3, 7, or 9. One out of every 4.6 such numbers under 10^5 is prime. So just guessing until you find a prime is practical.
Also, the following script might help to make the game more accessible (or to help you cheat :P) -
// note: game doesn't seem to automatically clear at the end, so in the dev console use:
// window.localStorage.clear();
// then refresh the page
const prime = n => {
for (let i = 2, s = Math.sqrt(n); i <= s; i++) {
if (n % i === 0) {
return false;
}
}
return n > 1;
}
const generateNums = digits => (
m => [...Array(9 * m).keys()].map(i => i + m)
)(Math.pow(10, digits - 1));
const generate5DigitPrimes = () => generateNums(5).filter(prime);
const all5DigitPrimes = generate5DigitPrimes();
// updated to take an optional array (defaults to all5DigitPrimes)
// this means you can chain the check function to do things that normal regex can't do
// e.g. check(/some_regex/, check(/some_other_regex/))
const check = (r, a = all5DigitPrimes) => a.filter(p => r.test('' + p));
Usage:
paste the above code into the dev console
type 'all5DigitPrimes' and press Enter to see a list of all 5-digit primes
type 'check(/some_regular_expression/)' to see a filtered list of primes that match your regular expression
I thought coming up with primes would be very challenging, but then my first three guesses were all prime (all I did was pick numbers that ended with odd numbers that weren't five). I got it on the fourth after a few attempts at entering the number - the prime constraint here makes it easier.
There are 8,363 five digit primes. If you limit your guesses to numbers ending in 1, 3, 7, and 9, there is a 23% chance of randomly picking a prime.
Amusing to see people starting with odd digits so much. You're going to have to use an odd digit in every guess, so you can more efficiently explore the space by going after all the even digits first with 24683.
apparently 9.3% of all '5 digit' numbers are prime, so random guessing isn't a bad strategy - you'll find one in 10.75 totally randomly chosen numbers to be prime.
Being a little smarter, prime number can only end in a 1, 3, 7 or 9 - (ending in 0, 2, 4, 6, 8 would be even, ending in 5 would be odd), so in fact it's more like 25% of 'likely' guesses.
IIRC, randomly guessing is _always_ a good strategy for "give me a prime in the range [a, b]" , in other words that's what's used for algorithms that need primes anyway. Either guess and check or guess and increase-by-2-until-prime.
Does work _much_ better in this range than at crypto sizes though.
All one- and two-digit numbers that look prime are prime, except 91.
This assumes that you can easily identify
- multiples of 2 and 5 (by their last digit)
- multiples of 3 (the sum of their digits is divisible by 3)
- multiples of 11 (for two-digit ones, they have both digits the same: 11, 22, 33, ..., 99)
- squares
So the first number that looks prime but isn't is the product of the two smallest primes that aren't "easy", which is 7*13 = 91.
I intuited a probably-inaccurate trick with exponentially raising a small prime (e.g 7*7*7etc), doubling the multiple (*2), and subtracting 1 (to get an odd number).
That got me two substantially-different primes and narrowed my numbers a lot, which then became guesswork.
The number you come up with in that way is at least guaranteed to not be divisible by 2 or 7. Obviously that doesn't mean it's prime but it definitely helps your odds.
Then recall that "less" includes a regex-based search on the / key.
This doesn't give you direction as to the best to try, of course, but it's hard to beat it in terms of bang for the buck if you're just going to try a few.
You can guess a prime relatively easily given a few attempts, as besides 2 and 5, all other primes will have a 1, 3, 7, or 9 as its least significant digit. So, for starters, you'd never guess a number with any other least significant digit.
Yeah I would really rather this just let me guess non-primes even though that would make it more challenging. Trying to find a prime by guessing randomly over and over is pretty frustrating.
I thought the same, but it rejects guesses that are not valid prime numbers. So you'll find some with trial and error. With that it took me only three guesses.
Readit News
Anyway, this is a really cool example of that. It's wordle, but with a twist.
Step 1 is to find an optimal starting word. My most insightful finding so far has came from trying to define a cost function for comparing potential starting words. It turns out that "% of potential guesses [not] eliminated" is an excellent loss function.
Importantly, the full set of all Acceptable Guesses is knowable. For any given (guess, answer) pair, the game provides feedback about each character (or digit). There are basically three pieces of potential feedback: (N)ot Used, (U)sed Elsewhere, (E)xact Match. For example, a single guess might produce the feedback "NUNNE". Each of these will eliminate some subset of Acceptable Guesses which means you can attribute a fixed value between 0.0 and 1.0 to any piece of feedback, and multiply those together to get the loss score of a given guess. Average that across all Potential Answers to get a cost score.
Not sure what my goal of this post is. Guess I just wanted to share that these games are as much fun to analyze as they are to play (if not more).
But there is a better strategy (similar to what is used in those interview puzzles of "From N weights, find 1 that is different in X measurements of a scale): The fact that you input some vowels and see that they are not in there, tells you that the remaining ones MUST be in the word (treating Y as a vowel as well). So it might be possible to come up with a strategy that uses that negative information as well to minimize the search space.
Maybe I shouldn't be sharing this, it's a bit sad to break the illusion that the creator is picking a new word for us every day.
3rd row for next 18 columns has drop down filter.
You guess any word with at least 2 vowels, if 3 better, no repeat letters. You get some grey, some yellow, some maybe green.
2nd column to 6th column on excel sheet is the Grey Letters, Not Found in Answer. In this, 2nd row, if u find any grey you type it here. The formula from row 4 downwards in this group checks if its top input cell is empty, if yes, true, if not empty, then it check if that letter exists in its row cell of column A. If exists, false (grey means no letter), otherwise true.
Column 7th to 11 are yellow. Same thing, row 2 gets input, 4th row onwards checks if this exists in Column A cell, true, otherwise false. If input cell empty, then True.
Column 12 to 16 gets green letter input. Here input goes by position, if 2nd letter is green, you type it in 2nd column of this group, which is 13th column.
Formula in 4th and next checks if input empty, true, otherwise if input exist in exact position, true, otherwise false.
17th column is empty & narrow, to create a gap.
18th column returns 0 if any false found in while row. Any false means this word is not the answer. Otherwise returns 1.
A separate one cell counts all those 1, tells me how many potential answers are. After every try/word, one can filter this last column on 1.
I’m sure it’s far from optimal, but I continue to use it because I obviously understand how I came to choose it, and it “works” and survivor bias is powerful :)
I recall seeing HN posts from people working out “optimal” starting words and guess patterns, but I just like mine :)
If the answer has one E and you guess a word with two Es, only one of the Es will be marked correct (green/yellow). If one of the Es is in the correct place, it will be green and the other one grey. Otherwise the first E will be yellow and the second grey. So if the answer has fewer Es than your guess the game tells you.
If the answer has more Es than your guess there is no indication of this.
https://aditya-sengupta.github.io/coding/2022/01/13/wordle.h...
Now come up with a hash that starts with many zeroes.
That being said, the pool you're really working from is the numbers with last digit 1, 3, 7, or 9. One out of every 4.6 such numbers under 10^5 is prime. So just guessing until you find a prime is practical.
Also, the following script might help to make the game more accessible (or to help you cheat :P) -
Usage:paste the above code into the dev console
type 'all5DigitPrimes' and press Enter to see a list of all 5-digit primes
type 'check(/some_regular_expression/)' to see a filtered list of primes that match your regular expression
https://pastebin.com/sQtekXCW
There are 8,363 five digit primes. If you limit your guesses to numbers ending in 1, 3, 7, and 9, there is a 23% chance of randomly picking a prime.
Being a little smarter, prime number can only end in a 1, 3, 7 or 9 - (ending in 0, 2, 4, 6, 8 would be even, ending in 5 would be odd), so in fact it's more like 25% of 'likely' guesses.
Does work _much_ better in this range than at crypto sizes though.
This assumes that you can easily identify - multiples of 2 and 5 (by their last digit) - multiples of 3 (the sum of their digits is divisible by 3) - multiples of 11 (for two-digit ones, they have both digits the same: 11, 22, 33, ..., 99) - squares
So the first number that looks prime but isn't is the product of the two smallest primes that aren't "easy", which is 7*13 = 91.
Unlike Wordle, I assume it's unreasonable to expect a player to know primes so I don't think I'd call this cheating.
That got me two substantially-different primes and narrowed my numbers a lot, which then became guesswork.
My guesses in the end:
by the way am I supposed to take some meaning from the italicized '7' or was that just a typo?
This doesn't give you direction as to the best to try, of course, but it's hard to beat it in terms of bang for the buck if you're just going to try a few.