13 ms·
The Miracle Sudoku [video]
- acangiano 6y ago25 minutes you'll be okay with never getting back.
- jurmous 6y agoYou can also if you want turn the playback rate up of the video and have the same satisfaction in half the time :)
- the_duke 6y agoI recently started increasing playback speed on many videos I watch. It's really hard at first, but I quickly got used to it, to the point where I now use an addon to increase playback speed to 3-6x where appropriate. When there's something complicated, or something I want to enjoy and savior, I jump back and slow down. This is an incredible time saver. I got inspired to do this by observing a blind programmer use a screen reader with insane speeds.
- marcus_holmes 6y agoI only recently discovered this, too. I was complaining about how I preferred reading than watching videos, partly because I can read a lot faster than someone can narrate, and because I can "skim-read" text. They suggested playing the video back at a higher speed, and it works fine. Still haven't quite solved the "skim-read" thing - guessing where the narrator stops the "welcome to my channel, smash subscribe and like, etc" bit is tricky.
- bmn__ 6y ago> guessing where the narrator stops the "welcome to my channel, smash subscribe and like, etc" bit is tricky. https://duckduckgo.com/?q=wadsworth+constant+video https://duckduckgo.com/?q=wadsworth+constant+video
- marcus_holmes 6y agohahaha that's awesome, thanks!
- JackDrury 6y agowhich addon are you using for speedup?
- Hitton 6y agoEnhancer for YouTube can do that, but you can also do it with simple userscript. The userscript I found somewhere few years ago: // ==UserScript== // @name Mediabord // @version 01.1 // @description tryd to take over the world! // @author j // @match *://*/* // @grant metadata // ==/UserScript== document.addEventListener('keydown', function(event) { var vidz = document.querySelectorAll('video'); function is_text_box(element){ var tagName = element.tagName.toLowerCase(); return tagName === "textarea" || tagName === "input";} if(is_text_box(event.target)) return false; vidz.forEach(vidz => { switch (event.keyCode) { case 221: // (]) vidz.playbackRate+=0.25; break; case 219: // ([) vidz.playbackRate-=0.25; break; case 220: // (\) vidz.playbackRate = 1; break; case 83: vidz.currentTime+=3; break; case 65: vidz.currentTime-= 3; break; } }); });
- unkulunkulu 6y agoWait, what? Youtube has builtin control for that for years, behind the cog wheel at the bottom right of the video.
- hummusandsushi 6y agoThey're using the addon to be able to get 3x and 6x speedups, which are not available by default.
- deleted 6y ago[deleted]
- imjasonmiller 6y agoThis is great. The max being only two bothered me and I completely forgot that one could do that as well. I'm going to expand on the small script I wrote that sets the playback rate to twice the speed by default [1]. Thank you! :-) 1. https://webapps.stackexchange.com/a/136744/233601 https://webapps.stackexchange.com/a/136744/233601
- metalliqaz 6y agoi don't know how you can go 3-6x. I listen to podcasts at 1.5x and if I go to 2x I don't absorb any information. I think to actually do 2x, I'd have to stop whatever I'm doing (driving, chores, gaming, etc) and focus specifically on the podcast. That feels like I'm wasting time again.
- yesenadam 6y agoReally, you can follow his explanations at 2x?! Less than 1x the satisfaction, I suspect.
- singlow 6y agoBeen addicted to this channel since the lockdown started. Many more than 25 minutes I'm happy to be rid of.
- CamperBob2 6y agoOnce you see that each row appears to be a shifted copy of the same sequence, you'll spend at least part of that time yelling at the screen, hoping he hears you.
- deleted 6y ago[deleted]
- matsemann 6y agoIn fact, all rows are just permutations of the numbers 1-9! Edit: ;)
- quietbritishjim 6y agoThat's always true of all Sudokus. It follows from the rule "no number can appear twice in the same row (or column)" and the fact that there are exactly as many columns as numbers to put in them. What the parent was saying, that all rows are a shift of the same sequence, is much more unusual. In case there's confusion over terminology: starting for example with 123456, then 345612 is a shift (and a permutation) while 345621 is a permutation but not a shift.
- glenvdb 6y agoMy favourite part is his own disbelief as he ... spoiler ... continues to solve it. A few minutes later... when the first three on the board causes a cascade of solvable cells after a build up of deduction. Amazing.
- accidentalrebel 6y agoHe also said he was closed to ending the recording because he thought he was being trolled by the creator. It was fun seeing him slowly realize that it was not a joke at all.
- msoucy 6y agoI once spent an hour trying to solve a sudoku puzzle on a whiteboard in college. It turned out that the person who left it there made a mistake when they started to solve it, so given the state it was in when I started (no way to tell what was original and what was their deduction) it was impossible to solve. I'm not bitter, of course not.
- this_is_not_you 6y agoNow I want a making-of video by the creator of the Sudoku.
- redcodenl 6y agoI wonder how much of that is programmed/automated and how much work is still being done manually... Backtracking and eliminating numbers can be easily automated.
- Fiahil 6y agoI made a sudoku solver back when I was in school. It's quite simple and almost a textbook case for backtracking. Even brute-force algorithms are instantaneous on the hardest puzzles.
- ben-schaaf 6y agoI'm still mesmerized by the 15-line prolog sudoku solver: http://programmablelife.blogspot.com/2012/07/adventures-in-declarative-programming.html http://programmablelife.blogspot.com/2012/07/adventures-in-d...
- conistonwater 6y agoIt's just using a library, you can get the same effect in any language with a constraint satisfaction library.
- redcodenl 6y agoCompletely agree here, the entire 'solver' is a library there. However, it does show how cool and versatile SAT solvers are for people who haven't used or seen them yet.
- bmn__ 6y agohttps://old.reddit.com/r/programming/comments/1awnv/solving_sudoku_with_regular_expressions/ https://old.reddit.com/r/programming/comments/1awnv/solving_...
- SubiculumCode 6y agoAs a college project in C, we were to write a soduku solver. Smart people solved it by programming in fancy heuristics. Not being smart, I just brute forced it...though I tried to be fancy by representing the data at the bit level. I doubt it made it any faster lol. That said, when the hardest Soduku problems in the world succumbed to a brute force search to my lame program in less than a few something something ms, I kind of shrugged at the fancy methods. But I suppose that is why I'm still just a mediocre programmer :) The brute force method was basically move forward until you hit a dead end, backtrack, go forward again until you hit another dead end, etc. Edit: I'm not being dismissive of people who implemented better solutions. Honestly, at the time I was amazed at their skill. But I still chuckle just because the problem is trivially sized for brute force methods, and would have to be scaled much larger to actually make more sophisticated methods worth the effort in any situation other than personal satisfaction and education. In a business situation in which you do not expect the problem to scale, spending more time for a sophisticated solver may not be worth the effort. But yes, Soduku is for entertainment and R&R
- shultays 6y agoI was discussing this with a friend. I too made a brute force sudoku solver. It was somewhat smart since it was keeping track of what options are available for each cell and updates those options as it puts/removes digits. The friend told me he was working on a sudoku solver and was trying to explain his non-brute force algorithm. I told him I did a solver back in collage and it was basically instant even though it is brute force.
- SubiculumCode 6y agoAmazing. I got down voted for my story. HackerNews does not like Mediocre Programmers I guess lol. I bet I could write a better algorithm today if I was motivated. Back then I was not as experienced in programming, and I struggled with even figuring out how to represent the data and the state. Its all about learning from where you were at the time.
- Marazan 6y ago
- jmiskovic 6y agoThe lightning speed of his observing standard rules across the board is impressive but expected after months of practice. The agility with which he picks up new rules and starts working with them is sign of a beautiful mind. This was a pleasure to watch.
- dan-robertson 6y agoI though that too at first but actually they seem well practiced too. Eg other sudoku-style puzzles also have knight move rules. The main trick I missed is the forking one (if I put a 3 here then it reaches here and here by knight’s move therefore it can’t go here). That said It is still impressive and I think practice is not sufficient to explain how fast he is at it.
- ghusbands 6y ago> (if I put a 3 here then it reaches here and here by knight’s move therefore it can’t go here) A possibly-simpler way to look at it is the inverse. Putting a 3 here or here (where it must go) both block this other place, so we know this other place is blocked either way.
- dan-robertson 6y agoYes, that’s something I tried thinking about but computing the intersection of two or more quite large regions turns out to be harder than using the symmetry to only look at one region. There are also tricks one can learn for eg dominos.
- ace32229 6y agoDecades of practice in fact
- shultays 6y agoYeah, the guy is a genius at solving sudokus and makes it look easy. It is amazing how he fast can develop new "algorithms" and the explanation for the for new rules he encounters. And the way he develops/explains those algorithms
- 2easy 6y agoperverts.
- js2 6y ago"Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth." Impressive work from a board that initially appears too open-ended to solve but turns out to have sufficient constraints. Well worth watching. (Aside: the solver reminded me oddly of Professor Falcon.)
- andretti1977 6y agoOh my gosh Professor Falcon!!! You reminded me of those times when as a kid i wad so excited and inspired by that movie!
- aidos 6y agoI almost didn’t watch that’s because who cares about someone solving a sudoku puzzle, but that was brilliant. That’s one happy solver; it was worth it just for the absolute joy he gets from it. Amazingly quick solving too. Good to watch him develop extra strategies during the process.
- deleted 6y ago[deleted]
- matsemann 6y agoYeah, I liked how he realized two possibilities for a number that were next to each other, also meant the box around it could be cleared. I really enjoy finding patterns like these in constraint games. After confirming the pattern for myself a number of times, the brain later just does it on autopilot. If people have tips for similar games I would be happy to try them. Edit, my tips: Simon Tatham's Puzzle Collection [0] has lots of them. Apps exists for mobile devices as well. Everett Caser [1] also have lots of logic games where one can learn patterns. I've played Sherlock and Honeycomb, and my favorite is Willa's Walk. They look a bit funky, but the apps work fine on Android. [0]: https://www.chiark.greenend.org.uk/~sgtatham/puzzles/ https://www.chiark.greenend.org.uk/~sgtatham/puzzles/ [1]: http://www.kaser.com/ww.html http://www.kaser.com/ww.html
- ZeroGravitas 6y agoThere's a book called "Puzzle Ninja: Pit Your Wits Against The Japanese Puzzle Masters" that covers these strategies for a bunch of similar games, as well as background info on the creators and examples of the puzzle try. However, I've found that discovering these strategies myself is actually the bit I like most, so although I've bought the book, I try not to read about the strategies I haven't figured out by myself.
- panzerklein 6y agoPicross 3D is amazing. Should run without any problems on emulator.
- chris_st 6y ago
- zwegner 6y agoIn case anybody sees this comment before the video: I'd highly recommend trying to solve the puzzle yourself. After you see the rules stated in the video, click the link in the info. It took me a bit longer than this guy, but it was a very fun puzzle.
- prawn 6y agoAbsolutely agree. When he was about to start the threes, I stopped watching and saved it to solve with my 7yo that night. My son was the one that got most of the three placements ruled out and enjoyed lording that over me. After completing it, we went back to watch the host solve it. Fun puzzle and just as entertaining watching the host gradually put it together himself.
- vesinisa 6y agoSo to reiterate, this is not solvable by normal sudoku rules alone. Further rules and constraints are provided on the placement of the digits that happen to render it solvable.
- thom 6y agoI'd never done sudoku before and was a little disappointed to find it was so mechanistic. I'd sort of expected there to be some degree of exploration and backtracking, or perhaps having to solve multiple digits simultaneously while attempting to keep it all in your head. Is this puzzle representative of normal sudoku puzzles or do the additional constraints change it?
- graywh 6y agoextensive "exploration and backtracking" (what the community calls bifurcation) is generally avoided when setting puzzles there are more advanced patterns and techniques that can be used with sudoku, but this puzzle doesn't feature all of them
- rtpg 6y agoBasically the challenge is in finding the thought process that leads you to an answer. The kinds of puzzles done on this channel tend to be pretty tough. the designers of the puzzle usually make it so that there's really one good path for solving (and brute forcing _really doesn't work_ relative to thinking hard about the problem). There's a lot of stuff going on in this puzzle that's not at all present in normal sudoku, and things like "OK let's try and look for where _all the 3s could be at once_" is easier said than done.
- louisch 6y agoEver since seeing this video I've been wondering if there's some deeper mathematical basis for this puzzle, because of the extremely regular pattern that it happens to produce. For example, the way consecutive digits are actually in order, but separated by a single square (and looping around the edge of the board)
- macintux 6y agoSee this thread (disclaimer: I have zero clue to its accuracy). https://twitter.com/NikhilBukowski/status/1262622853339336704?s=20 https://twitter.com/NikhilBukowski/status/126262285333933670...
- jianshen 6y agoThere is something irreplaceable about the first time you solve a difficult puzzle, especially one that you anticipate to be daunting. As a Sudoku enthusiast (though not at Simon's level) this was surprisingly vicarious to watch for what's usually a silent solitaire experience. Well done!
- mywacaday 6y agoand we have rotational symmetry! brilliant!
- deepaksurti 6y agoUsing my CL based sudoku solver [1], I got the following solution. The solution is valid but different from what is shown in the video. IIRC, a sudoku board can have multiple solutions but anyone out here can explain why so? I am no sudoku expert or enjoying solving sudokus anyways! [1] https://github.com/dmsurti/sudoku https://github.com/dmsurti/sudoku ``` (setf board #(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0)) ``` ``` * (sudoku:print-board (sudoku:solve board)) 1 2 5 | 6 4 7 | 8 9 3 8 3 4 | 5 9 1 | 6 7 2 9 7 6 | 3 2 8 | 4 5 1 - - - - - - - - - - - 5 8 9 | 2 3 4 | 1 6 7 2 6 1 | 7 8 9 | 3 4 5 3 4 7 | 1 5 6 | 2 8 9 - - - - - - - - - - - 4 9 2 | 8 1 5 | 7 3 6 6 1 8 | 9 7 3 | 5 2 4 7 5 3 | 4 6 2 | 9 1 8 ``` edit: formatting
- hummusandsushi 6y agoYour solution doesn't respect the knight's move and king's move constraints, which cause the original puzzle to have exactly one solution.
- Marazan 6y agoYou have consecutive numbers appearing next to each other. One of the constraints is that no consecutive numbers can appear orthogonally. This isn't a standard sudoku, there are extra rules. There would be a huge number of valid solutions to the board under regular sudoku rules. EDIT: and you've missed the King's move constraint as well and I presume the Knight's move as well.
- prawn 6y agoThe first line of your result fails the orthogonal adjacent rule of this puzzle eight times!
- boomlinde 6y agoYour sudoku solver is solving a different puzzle altogether from the one posed in the video. Sudoku puzzles also don't normally have multiple solutions. The smallest known Sudoku satisfying that constraint have 17 clues. Offering only two clues is possible here because of the additional placement constraints.
- tudorizer 6y agoNot a big sudoku fan, but wow! I might have under-estimated how exciting it can be.
- Jestar342 6y agoThis guys is my "ASMR" bedtime watching. I just love his overall demeanor and child-like thrill from puzzle solving. I can be wired when I start his video and by the end I'll be blissfully calm and head-clear. I think he has a tremendous talent of focus. As other posters have said, he can spot constraints so quickly. I still get a small kick out of spotting something before he does, though. Doesn't happen often, mind.
- pilsetnieks 6y agoI actually had to double check if Sean Lock (https://en.wikipedia.org/wiki/Sean_Lock https://en.wikipedia.org/wiki/Sean_Lock) hadn't taken up a new hobby of solving sudokus on youtube, he both looks and sounds incredibly similar.
- fredley 6y agoHow on earth do you create a puzzle like that? Coming up with the rules it's presumably simple to generate solutions with a computer program, but how do you then work out the cells which need to be filled in order to not only minimally describe a single correct solution, but also leave a reasonable deductive pathway to that solution? I think that's what boggles me most about this, the deductive pathway that's been created by the puzzle creator is a complete joy in its unfolding.
- antfarm 6y agoThere is a pattern in the solution: Consecutive numbers are separated by one field and enumerated horizontally from the left to the right, wrapping around the edges, i.e. ..._4_3_2_1. Every line of the solution has the same sequence of numbers, shifted by 4 places to the left relative to the line above it. This makes me believe the construction is based on a clever observation and repetition of a pattern.
- lonelappde 6y agoAlternatively, count up by 4 left to right (aka your -1 every two squares), and count up by 3 top to bottom within a box.
- macintux 6y agoI don’t have the math background to assess the accuracy of these replies, but they might explain it. https://twitter.com/NikhilBukowski/status/1262622853339336704?s=20 https://twitter.com/NikhilBukowski/status/126262285333933670...
- chongli 6y agoSudoku at its heart is a graph colouring problem. When you add the new constraints, it changes the connectivity of the graph. This sudoku, with all of its extra constraints, becomes a highly connected graph which greatly reduces the number of possible valid puzzles. Throw in the fact that the grid is already symmetric about both axes of reflection and rotationally symmetric about the centre and that further constrains the set of valid puzzles. I'm sure you could write a program to take all these constraints and generate a ton of puzzles and then scroll through them to find ones that look great. It also wouldn't be too difficult to sort them in ascending order of givens.
- swah 6y agoHow do know if a certain puzzle is impossible (ie malformed)?
- matsemann 6y agoThat is a "decision problem": Does this puzzle have a solution? For Sudoku, that's easy to verify. That makes it an NP-problem. But for Sudoku, finding a solution is very difficult, so difficult that we say it's NP-Complete. So the only way to verify that a Sudoku can be solved, is really to try a bruteforce (potensially sped up with guesses/backtracking) and then find out if you cannot continue because of a broken constraint somewhere.
- matsemann 6y ago> For Sudoku, that's easy to verify. I meant: For Sudoku, it's s easy to verify that a given solution is correct. (cannot edit) Of course, being given the solution first in order to even try, can be a bit boring. For that, there exists "zero-knowledge proof" where one can reveal one knows an answer, without actually divulging it. Here is a writeup about someone doing that for Sudoku: https://manishearth.github.io/blog/2016/08/10/interactive-sudoku-zero-knowledge-proof/ https://manishearth.github.io/blog/2016/08/10/interactive-su...
- billfruit 6y agoAny other puzzles with deep deductive reasoning where one can get better at through playing. One comes to mind: hexcells, any others?
- matsemann 6y agoI also asked this question in another thread here, got some responses and included my tips: https://news.ycombinator.com/item?id=23245258 https://news.ycombinator.com/item?id=23245258
- yesenadam 6y agoThere's a whole world of chess composition/problems. You can even be a grandmaster chess composer or solver. Some composers are legendary in the chess world, e.g. Troitzky, Sam Loyd, Kubbel. Chess problems come in various kinds, and are a bit like cryptic crosswords - they seem impossible at first but there are customs, tricks, conventions which make them easier with experience. "The role of aesthetic evaluation in the appreciation of chess problems is very significant, and indeed most composers and solvers consider such compositions to be an art form." https://en.wikipedia.org/wiki/Chess_problem https://en.wikipedia.org/wiki/Chess_problem
- DonCopal 6y agohttps://www.chiark.greenend.org.uk/~sgtatham/puzzles/ https://www.chiark.greenend.org.uk/~sgtatham/puzzles/
- nickysielicki 6y agoHere's a solver in python with z3: https://gist.github.com/sielicki/fd86d68733133f654128519b3c4e12c2 https://gist.github.com/sielicki/fd86d68733133f654128519b3c4... (note, most of the code coming from here, I just slopped together the additional constraints, https://ericpony.github.io/z3py-tutorial/guide-examples.htm https://ericpony.github.io/z3py-tutorial/guide-examples.htm ) $ time python3 game.py [[4, 8, 3, 7, 2, 6, 1, 5, 9], [7, 2, 6, 1, 5, 9, 4, 8, 3], [1, 5, 9, 4, 8, 3, 7, 2, 6], [8, 3, 7, 2, 6, 1, 5, 9, 4], [2, 6, 1, 5, 9, 4, 8, 3, 7], [5, 9, 4, 8, 3, 7, 2, 6, 1], [3, 7, 2, 6, 1, 5, 9, 4, 8], [6, 1, 5, 9, 4, 8, 3, 7, 2], [9, 4, 8, 3, 7, 2, 6, 1, 5]] python3 game.py 7.47s user 0.15s system 97% cpu 7.801 total
- gabrielsroka 6y agoEach row is a cycle [?] of 483 726 159. And even the cycles have a pattern: 665 665 66. That is, you can rotate the first row by 6 to get the second row, then rotate again by 6, then by 5, etc. The columns are almost as consistent, but not quite.
- dreamer_soul 6y agoI love how z3 code looks like magic! Seems like a good library to start getting the hang of
- carapace 6y agoFWIW, "Boring Sudoku" a solver in Prolog w/ CLP(FD): https://swish.swi-prolog.org/p/Boring%20Sudoku.swinb https://swish.swi-prolog.org/p/Boring%20Sudoku.swinb - - - - I don't mean this in a critical way, just an observation. To me the video was boring because watching a human do machine work is frustrating (to me). (As fast and as clever as that fellow is, he's still so slow compared to a computer.) However, designing elegant constraint rules to encode the special constraints of this puzzle is also a puzzle, and that puzzle seems interesting to me. (Although not very because it's not that challenging.) I have the same problem with most video games: after playing just a little while I get bored and want to reprogram the game itself instead of just playing it. Do y'all feel me, or am I just a freak?
- glandium 6y agoFor some reason this video ended up in my Youtube recommendations last week, and I clicked on it because the thumbnail caught my attention. Didn't regret it, and I've watched a few others. Another that was pretty interesting in the development of techniques to approach it: https://youtu.be/Zk4qNEDXFSw https://youtu.be/Zk4qNEDXFSw Edit: Ah no, the first I saw was actually https://youtu.be/hAyZ9K2EBF0 https://youtu.be/hAyZ9K2EBF0 which has a diagonal rule, and a magic square in the middle.
- swyx 6y agoI was just thinking the other day how I've never seen a YouTube video at the top of HN. along comes this video to prove me wrong.
- dathinab 6y agoIt did the follow up sodoku (a new miracle sodoku), which I think probably is a bit easier as it starts with 3,4 in a slightly more useful constellation. I have to say while I'm not the biggest fan of normal sudokus the ones with extra rules are quite interesting. And the cracking the cryptic channel has quite a bunch of such sudokus.
- carlob 6y agoAt the beginning I was wondering whether 9 and 1 were to be considered consecutive. It's not stated anywhere, but it seems that the solution has this property.
- billme 6y agoHere’s link to the puzzle: https://cracking-the-cryptic.web.app/sudoku/tjN9LtrrTL https://cracking-the-cryptic.web.app/sudoku/tjN9LtrrTL About the guide to controlling the interface for the game: https://cracking-the-cryptic.web.app/how-to-play https://cracking-the-cryptic.web.app/how-to-play (Links are little odd, if you want to find them yourself, just click the YouTube, view the video description, it’s the top link.)
- residualmind 6y agohttps://www.google.com/search?q=483726159 https://www.google.com/search?q=483726159
- busterarm 6y agoI immediately saw what the full pattern was when he had half the 2s filled in and was wondering if he saw it and kept going through the solution for the purposes of the video, or didn't see it at all until the end. That never ended up becoming clear and now I'm just left wondering.
- SamBam 6y agoUnsure what you mean by "the full pattern." Do you mean you could work out what the entire grid was, from just half the twos alone?
- busterarm 6y agoThe twos and the existing ones. I made a reasonable guess that proved to be correct. All the twos had symmetry and can be plotted on the grid like a tile pattern...and every increasing number in a row is two positions to the left of the lower number. It was blatant at that point in the vid. Right at around 12:14 and then confirmed by the 18 minute mark.
- adenozine 6y agoI get the feeling that he would be a very impressive programmer.
- jcims 6y agoThis is clicking on an existential level for me. Lex Fridman's podcasts in particular have been sort of forking in two directions lately, one on artificial intelligence, consciousness and just a somewhat muted wonder how the human mind operates and our present lack of understanding of how it comes together systematically to create our experience. The other is about physics and how the experimental and theoretical come together to try to give us a better understanding of the fabric of our universe. For this video, in the former case it shows how plastic the mind can be. I'm probably about the same age as the guy in the video and honestly have been struggling with an experience of cognitive decline lately. To see how adaptive the brain is to not only develop grooves that accelerate analysis in the long form, but also adapt to new rules and constraints almost as quickly is really quite remarkable (and for me personally, encouraging). His quick pattern analysis at the end uncovered the second case for me. This is obviously something we've seen in many other situations as well, but how a collection of 'particles' with multi-dimensional constraints can form order and even crystalline structure from almost nothing. Very fun video to watch. Thanks for sharing.
- tshanmu 6y agopuzzles and progamming - two of the best ways to while away the time.
- yesbabyyes 6y agoThis was great fun! They have a new miracle sudoku[0] up since a couple of days, as well. Seeing him color the potential twos (aside from two wrongly colored squares) and then piece by piece ruling them out almost looked like a game of life, with new patterns emerging. [0] https://youtu.be/Tv-48b-KuxI https://youtu.be/Tv-48b-KuxI
- ropable 6y agoThis video was just fabulous to watch.