Can you find: five five-letter words with twenty-five unique letters? 

Yeah, I was fine with EXPWY. It was HDQRS I had a problem wit.

Someone was writing to a file way back when we were limited to 8 characters. That's how you get HDQRS.doc. I assume that it then became a thing.

@@dodaexploda (thats 9 characters)

@@-_-.-.._. the extension and dot didn't matter except for the extension itself being limited to 3 characters. But it was 8 characters allowed left of the dot.

Fire comment

I don't know if you did that on purpose, but you wrote "didn't want to hear about it" twice. Your comment isn't optimized, either, and I love it.

Yo 🔥ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-rdJ9bsN7JAw.html..

I’m sure that in Matt’s head he was more or less expecting codes that improve the time from 32 days to maybe a week or two. Not a code that solves the problem in 15 minutes…. And with the follow up code being 3072 times faster (i checked), i guess he just added it on because the extra 15 minutes of verification doesn’t really add much to the total time used to make the final video

@@irgyn this appeared to the author as optimizeable

There is also a difference between, "you should have optimized it using this optimization" and "here is a complete optimized implementation that uses somewhat advanced maths".

I really wish he would've said "the Parker algorithm" instead of "Parker's algorithm"

Agreed. Absolutely legendary💀💀

I got it down to 13.7 seconds while still using Python, lol. Definitely optimisable.

I had to give a good laugh at that.

Fr this is exactly what I started thinking when I saw the comments

Should you then post after you ran your own? That still takes a month... 😉

@@landsgevaer you're right, he should have estimated the time his algorithm will take, posted a video 29 days ago, gotten the reply within two days and had the answer way quicker!

Ok Blixor’s Law: If you shake a palm tree hard enough, the train that holds all the turkey slot machine pterodactyl.

@@BizVlogs that's a good one, I'll have to remember it

@@BizVlogs the difference between a duck is that one of its legs is both the same

You should play Wordle on Hard Mode

@@saar144 beside the point lol

Oh, that brings back memories. Had Jotto as a PBM game, wrote my own program (looked flashy, could be optimized probably to certainly) in Turbo Pascal. Only downside was there was no list of words to download at the time so a friend and I spent quite a lot of time on creating a word list. Only to realize it was too much for the array I defined, so we had to weed out "unused" words. Which would have probably killed this exercise. (Different language though)

How do you code a literature search?

@@shoo7130 Mechanical Turk

exactly! and thats ok! hes a mathematician. code is just a tool for him. hes not trained in it this is a huuuuge difference i keep telling people about. i did a computer science degree. i am a software engineer now. I stand by the fact that programming != computer science and we see the difference here. programming gets the job done (matts solution (also this is no diss on matt. hes super smart; software just isnt his expertise and thats ok)). Computer science gets the job done well and efficiently (the graph solution). I dont claim I could have gotten to the same solution, but figuring those types of stuff out is the fun bit for me lol

I was shocked that mentioned the vowels are being key but never used their importance as part of the algorithm. If had put words into buckets that included each vowel and a bucket for y and another without vowels he could have greatly reduced comparison. For example, if the first word included "a" there is no point testing words from the a bucket, if the second word included "e" you don't check the a and e buckets for the next word etc etc. Such an obvious improvement.

@@v.sandrone4268 Even better, if he could verify that all the words need at least one vowel (y included) he could just discard any iteration that has at lease two words using multiple vowels (and technically cut out any individual words that use three) to skip a _ton_ of the processing

He's a *lot* faster than I could ever be!

@@v.sandrone4268 If he uses aggressive pruning, I suspect the gain is moderate, since repeated vowels are found immediately anyways. You do gain a bit because you don't need to check all words, but the time complexity is in the size of the expanded tree, and that doesn't improve. Orange nostril's trick *does* prune the search tree, however.

Can you explain? I don't get it

@@robertr7923 set one for letters that appear in the word, zero for letters that don't. Each word is a 26-bit number up to 64 million or so. So ABOUT would be 00000000000110000100000000000011 or 1,589,251. The nice thing about doing it this way instead of an array of characters or something, is that comparing bits on a computer is very fast. So you AND the two words together and see if the number of bits set to one is 0.

@@letsmakeit110 if you would AND two words with distinct letters in this representation the result would actually be 0, you wouldn't even need to count the bits, very efficient indeed

And fun thing. Someone went and did this and a few other optimizations and solved the entire problem in less than a second.

I used this as an excuse to make the jump from python to C. I created my own implementation of this using your bit trick and it worked wonders (1.5s). Thanks!

No pens or pencils were available so he instead hammered the letters in with a metal stamping kit, I presume

Pen didn't have ink, had to go entirely off pressure, I think

@@coryman125 with a muntz stamp, you mean?

@@feedbackzaloop We've gone full circle!

He didn't have anything sturdy to lean on, so instead used a sheet of playdough

Assuming you know some basic graph theory: If you imagine a graph, where each node is a different 5-letter word, we can connect two words with an edge if they do not share a letter (e.g. "fjord" and "gucks" are connected). The problem we want to solve is finding 5 words that all don't share letters pairwise or in the context of the graph, find 5 nodes that are all connected to each other. Such a collection of nodes is called a clique, and finding cliques of certain sizes is a well-studied problem. Now it is just a matter of going out an implementing some algorithm that solves this problem (Here's the first one I found, don't know if it is what was used: en.wikipedia.org/wiki/Bron-Kerbosch_algorithm)

Benjamin describes it in the GitHub readme - he generated a graph by giving each word a vertex and connecting them with an edge if they didn't share any letters. The groups of words we look for then correspond to vertex sets where each two vertices are connected by an edge. That structure is called a clique, and looking for maximally sized cliques is a well known problem. It's NP-complete in the general case, but this instance is small enough that the algorithms developed for the problem can deal with it just fine.

In this particular case, it isn't so much so that the graph solution is way more efficient. It's just so that Matt's brute force implementation was terribly inefficient 😉. My initial brute force did it in 67 seconds, and using some clever lookup techniques I've got it down to 7. I doubt that can be beaten by using a generic maximum clique algorithm from graph theory.

@@qaysed453 Technically we should already know the exact shape of the clique we're trying to find, so a regular subgraph isomorphism algorithm should suffice

@@kalecgos1 well, a clique is a complete graph, so we always know its shape, aside from the cardinality, so the max clique problem can always be solved by log n applications of a subgraph isomorphism algorithm (this is actually the common proof for subgraph isomorphism being NP complete). I don't know the actual algorithms well enough to tell whether a general isomorphic subgraph search or a clique search would be faster, but the latter is more specific, so presumably it at least wouldn't be slower.

Parker is an interesting combo of a stand up artist and a mathematician. His shows are not for everyone, but they are interesting for those curious in math.

Depending on exactly what you want to time, this could give an inaccurate number since it times the entire process including spinning up the python interpreter, not just the algorithm. That said, yes, time is a wonderfully handy command

@@liorramati265 It includes spinning up the Python interpreter which, upon repeated uses, itself is inconsistent. As the first run might be from disk whereas subsequent runs are from cached memory. This is why when tech sites use time $command as a benchmark they reboot the system between runs.

If you're using Python, it's even better to just use the timeit module

@K.D.P. Ross optimized version is sub 1 second

Unfortunately, NYT have completely removed some definitely valid English words from the list, so the original is still better. All 4 lists are uploaded to the same github account, iirc

@@user-rv9vk8by5i profanity?

@@rngwrldngnr and offensive words

@@user-rv9vk8by5i To be clear, they removed them as ever being possible answers, but they are still accepted as guesses.

@@user-rv9vk8by5i NYT has only removed ['agora', 'pupal', 'lynch', 'fibre', 'slave', 'wench'] without adding any, so the list is functionally the same.

That sounds so odd to me. In my language (Portuguese), it's so simple to know what a vowel is. If it's A, E, I, O or U, then it's a vowel, otherwise it's not. 😆

@@sergio_henrique ye in english 'Y' acting as a vowel is pretty uncommon, so quite a few people dont even know it does lmao

@@aaronl19 prett*y* common, actuall*y*

Y: the alphabet equivalent of gender fluid

@@sergio_henrique that's what happens when a language is mostly loan words like English is lmao

Damn we Dutch are everywhere

What if you allow y for ij as in Old Dutch?

@@thibautsnoeijs but probably mostly in the Netherlands 🇳🇱

Op Nederland?

Yo 🔥ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-rdJ9bsN7JAw.html..

Running code on 3000 computers doesn’t make it 3000x faster.

@@gonzalo_b762 It depends on algorithm. For "embarrassingly parallel" problems you can get totally linear scaling. For example, if you're brute forcing 64 bit encryption, you could just split the whole range to 3000 parts and use 1...2^64/3000-1 for the first computer, 2^64/3000..2*2^64/3000-1 for the second computer etc. If I understood the algorithm correctly, Matt was brute forcing the whole range so it would have been trivial to split into parts.

@@MikkoRantalainen Good point. I’m trying to figure out how you could separate it into equal parts given how the output is dependent on all the input though.

@@gonzalo_b762 For example, when you know that you have to evaluate a list of words, you only test words where the index of the word mod N is J, where N is the total number of machines running in parallel and J is the index for the machine running the algorithm. Some other machine will test all the skipped words. (Of course, any decent optimizing compiler should be able to avoid division and just add N for every loop.)

Someone got it down to a tenth of a second running on a 10yo laptop a couple days ago!

Galaxy brain move right here!

15 minutes is 1/96th.

So does that mean for every 1 second of Ben's code, Matt's code ran for 15 min?

@@DIMOHA25 Ah, so 15 minutes = 1/30th of a day is a new Parker approximation!

@@DIMOHA25 For anyone who's curious (but not curious enough to do the calculations themselves...), 1/30 of a day is exactly 48 minutes, assuming a typical 24-hour day with no daylight saving time change or leap second.

More like a solution squared than a problem squared!

This sounds like a great topic for a follow up video!

I'd love to see a video on that - right now I don't understand it!

I would *love* to see a video about graph theory by Matt Parker. I will bet he has at least one pal who specializes in it.

Thanks for taking one for the team: I was reading the comments while watching the video to see if someone else mentioned this before posting it myself. (At least we can feel vindicated that the theory worked out, all without having to actually code it up!)

Yo 🔥ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-rdJ9bsN7JAw.html..

What about the ten other sets that he overlooked?

He did include the Countdown theme, which I thought was pretty clever. I'm guessing Suzie was a tad beyond the budget.

In Matt's defence, the video did include (multiple photographs of) someone who has in fact sat in Dictionary Corner next to Susie Dent.

@@gregmark1688 It just wouldn't be optimizable.

I'm thinking the same thing. I could swear I saw some movement other than the up and down.

You may be on to something here.

There are so many times in Matt Parker videos where I am just like, "did that really just happen?"

That's the gag

@@michael1 Ahh the obligatory comment of the person not getting the sarcasm and explaining to the sarcastic jokers they did not understand the joke, thereby ironically not understanding theirs. Classic

Could you share the code? It would be awesome to learn from it :) thanks!

@@emorell96 Sorry, I have been caught up for weeks installing a new kitchen. I hope I can get some rather ugly code out there at some point. Meanwhile I should mention that while I'm now slightly below two seconds, I've seen somewhere that some other guy has managed to get significantly below 1 second.

@@NickAskew That's pretty cool, did you ever manage to improve eve further?Still in C# right?

@@jeremyzz Hi. Yes, I've managed to get it to around 2.3 seconds by using various techniques such as Parallel.For(...) and profiling the code to find the bottlenecks. I should mention that others have managed to exceed this by a factor of about 25 times and I am impressed BUT I do not want to see how they did it because I'm looking to see if I can implement my own idea before seeing how they did it, so if you find out no spoiler 🙂 I'm looking at indexing as an option as my current code is a little brute force. I guess rewriting in assembler would help but that's a step too far, I'll stick with C# and framework net7.0.

that s insane

That must have been scary! If I may, though, that's not necessarily a great approach in Wordle - since you can change your strategy based on the feedback from each submitted word, and positive responses almost always contain more information about the solution than negative ones, you want to front load the odds of getting any kind of positive result in the first word to narrow the search space as early as possible ^^ Frequent letters are good, and packing in vowels is great because it's a much smaller search space which in practice will always contain at least one positive result. That's min-maxin to get the answer in as few hits as possible, though, which of course isn't the only way to play it or to have fun ^^

What the heck is a glent brick jumpy vozhd waqfs?

Dubious. If first guess GIVER gives no hits, who would then have an R in the next guess DWARF?

​@@MartinInBC people aren't machines. sometimes u wanna live a little lmao

Those were videos, though, not images.

@ "it's almost as if the photo wasn't a photo at all" 😉

yeah i cringed when he did that

Or just type "time" before the command.

I thought the same thing 🤣

start = … finish = … print(finish - start) is more usual. But hey, any excuse to use Microsoft’s bloatware, hey Matt?

see this is a huuuuge difference i keep telling people about. i did a computer science degree. i am a software engineer now. I stand by the fact that programming != computer science and we see the difference here. programming gets the job done (matts solution (also this is no diss on matt. hes super smart; software just isnt his expertise and thats ok)). Computer science gets the job done well and efficiently (the graph solution). I dont claim I could have gotten to the same solution, but figuring those types of stuff out is the fun bit for me lol

"Calibrating matrices"? You can’t just add an engineering word to an algebra word and hope it means something. Oh wait, looks like something’s wrong with the manifold tesselator.

manifold tesselator sounds good for packing suitcases

I can hear the build music now

@@KyleJMitchell yes you can

Aren't we all?

I concur. I most often play sedecordle. I usually start with three words that share no letters and cover all the vowels. The results from that usually give me an enjoyable challenge that is doable but not too easy.

You also want to prioritise the most common letters. Cracking the Cryptic loves to use SONIC TRADE LUMPY. SIREN OCTAL DUMPY is the same set of letters if you prefer base 8.

@@DeGuerre Indeed. I follow that same principle but rather make up my starters each day. My most recent set was PRUDE MINTY GOALS, which differs only by C/G. I’m sure and C is marginally better, but it’s not a bad set for something made up in the moment.

That's what I do. Usually using WEIRD-FANCY-GHOST-PLUMB

CAMPY WOULD BIGHT FERNS

It's not exactly fair to say "Wordle words" when waqfs and vozhd definitly would not be legal words in Wordle. ... wait, would they?

@@tomdekler9280 As a matter of fact, both "waqfs" and "vozhd" are valid guesses, even now that the NYT took it over. I just tested them to make sure they work.

You did that in visual basic? Bro who hurt you 😆

Unfortunately (as you may have seen by now) some "valid" English words don't have any vowels

@@Henrix1998 technically y is a vowel in those cases

@@thepardigon178 phonetically, yes. Orthographically, no.

Maybe filter instead by lack of vowels and semivowels (w and y in English). Basically every valid word without a vowel has a semivowel.

@@Henrix1998 yes, but I suspect that all ‘real’ words that don’t have a vowel have a y… hence being able to eliminate those with three (not just two) vowels.

The exception to this rule is lots of scientific or mathematical problems, especially simulations, but can also be combinatorial problems of the type in this video (of course in this case it was optimizable but to be honest if you have other stuff going on sometimes it really is easier to just set the code running and come back to it when it’s done rather than spend Time making better code.)

@@interlooper83 but you almost always need to re-run it, or some one else will need to verify it. If you are a 'good' programmer then you won't need to spend time writing code that never finishes. You can think up a better approach while drinking your coffee. Especially with Python, which is used extensively in scientific problems now. My expectation is that simple functions should finish quickly. I try to set similar expectations in the minds of my students. It's not hard to replace the shell sort with quicksort if you are competent you will know that quicksort exists. Even with simulations that may take hours (surely not days!) you can provide a progress log to monitor the state. Perhaps partition so that the time is divided by n times. It is easy to add in timers to see where the time is being taken. It is easy in python to import modules that are compiled code instead of reinventing the wheel using python. It is easy to isolate a function and optimise it with cython to get 100 times speed improvement. Maybe the approach to a simulation is using the wrong variables that are not converging. Maybe you didn't realise that your system does not scale well. So you start with a sample and then release it on a large dataset. Well then, that is when the Cup of Coffee Rule kicks in: interrupt and think about what might have gone wrong or how you can shorten the time. Time is money and also your own valuable attention. Leaving a problem for a week seems to be a waste of both to me. If you are using the cloud a week's processing will cost a fortune. I am still not impressed with any workflow that takes days to complete. It just makes you look amateur.

@@kimollivier He is amateur, he stated that multiple times -_-

@@interlooper83 when I'm on such a problem, I'll always try to spend some time producing a sample set. Need to calculate all the roundabouts in the world? Start with all roundabouts in Iceland. Must find how many days were warmer than average since jura? Start with last two months. Even if making the sample costs days, you'll eliminate the chance of having to rerun a computation that takes days.

@@kimollivier I think this philosophy might be fine to teach in any introductory programming class, but it is naïve in the real world. Many fields in computational science are limited by computing power, and the reason is because some things just take time. Do you think it simply never occurred to the people whose algorithms take hours or days to run (even on the most advanced supercomputing clusters) that they should try to optimize their code?

that's a chunk of my job too - but without a diagram usually :)

I don't think seconds but maybe minute or two

once again, rust is inevitable

Or just do it with constexpr and consteval in C++ (assuming we don't time the compilation time, of course).

@@xarcaz bruh that's not IOI

🦀

I wonder if, using that method and written in C, it could be done in under one second given a powerful enough computer. I'd say probably.

I did this, and I get results really quickly

Yes, that's a great hashing algorithm for this purpose. You're just looking for 5 hashes with no bits in common.

I basically wrote a version of that back when wordle blew up. Depending on the word list, the whole search took anywhere between a few seconds and minutes. Getting a decent wordlist that isn't full of straight up junk words was the hard part, and in the end I could only come up with sensible combinations that had 24 unique letters.

@@nicholasvinen Average C user when python is mentioned. /s

yeah... caught me off guard lol

10:56

And in true French fashion they use 3 times more letters than they need, considering how they pronounce it.

@@matthewwhiteside4619 The 'g' is pronounced. It's very subtle, but it's there. The 't' might also be pronounced, too, if you happened to have multiple "twenties", as in "les vingts". ;^)

@@gregmark1688 The 'g' is definitely not pronounced at all lmao, the 't' indeed might or might not be (depending on context and accent)

It’s Parker about wordle

Wordle inspired which is pretty close.

Thanks for making this mid-week silliness possible!

gvbes

There are ten more, though.

'vozhd' and 'gymps' are in the wordle list, but not in the original wordlist, which leads to some extra worldle solutions

@@whyando What are those extra solutions?

@@stefanpochmann5205 I ran a search a few months ago and remember finding ~9 including waqfs. I only remember this one off the top of my head, but you could just run the script with the improved list and find the rest: waqfs, vozhd, jumpy, glent, brick

I assume whatever word search he used those two had to be excluded (they are missing in some online dictionaries)

In England, Y is not considered a vowel for some reason, despite the fact that it is literally a vowel in that usage lmao.

Using the Linux time command would also report how long it took to spin up the python interpreter, not just how long it took his code to run. Timing it from inside the python code is going to give a way more accurate result in this case (even if doing print(time.time()) twice and then subtracting the results in excel isn't the optimal way to do that 😅)

@@liorramati265 Spinning up python, importing the libraries used and shutting it down takes between 0.05 seconds on my old laptop. It's not going to change the measurement outcome significantly of anything that takes over a few seconds.

But he would have to wait another month for it :D

That would be a more efficient way but it would still produce the same only solution

@@robertr7923 Nope: there's also: jumby clipt waqfs kreng vozhd in the original wordle list!

Yeah it would be best if the wordle list was put into the beginning steps of the process again. Perhaps even you or I could do it and find a few more solutions.

Just imagine the looking at each other like 😳😳

I'm not sure if you can call this an "exact cover problem", because english has 26 letters, not 25.

@@BenjaminGoldberg1 It is not exact cover problem, but you can use that algorithm anyway

"provided you have a quantum computer" is a bit of the problem there then, isn't it

That's a very interesting topic for me, could you please provide any link to an quantum algorithm which does that? What exactly do you mean by "check by the quantum computer" and why you think this problem can be managed that way in a quantum computer? My understanding - at least based on the description - a regular graph algorithm isn't a good fit for a quantum computer?

@@TaranovskiAlex en.wikipedia.org/wiki/Grover%27s_algorithm Basically, you can do unstructured brute force search in O(sqrt(N)*check) time, where N is the number of possible solutions, and 'check' is the time required to verify a potential solution.

-but wouldn't you also need on the order of (5977 choose 5) amount of time to compile the oracle since its so irregular?- Actually, I guess you could incorporate the knowlege of the graph edges of valid pairs of words in just an order of (5977 choose 2) time, then maybe the instructions for confirming a K5 graph is very regular? And that sounds like you would get the speedup as it's much smaller. -And wouldn't you need a quantum computer with a register of (5977 choose 5) many quantum bits?- oopsie

@@JNCressey Incorporate a preprocessed word table as part of the problem, so only q-bits for the word number are needed.

My single-thread Python program takes about 60 seconds as well.

My quordle guesses are WATER BLINK POUCH, or MILKS or MILKY or VOUCH depending on how I'm feeling

Pluck forty badge whims. Octordle is my jam.

Splat mired gonch is optimal

I'm more of a wrong jumpy child steak guy

Frail young chest

Maybe put it on stackoverflow?

If he didn't already know that, and deliberately mispronounced it as brutally as possible, I will eat my own legs.

And "vain"

Rhythm was the first word that popped into my head as a good starting place, but then was immediately struck down due to using two 'h's.

@@japhyriddle and the fact that is has 6 letters and not 5?

crwth

You're right, all that has already been mentioned.

22 minutes is now down to 10 seconds.