Simon is the type of guy that is super hard on himself for not seeing things instantly, but I just know if he was watching me struggle with a medium difficulty he would be very supportive and excited when I'd figured something out he'd done in his head 30 minutes before. 🥰
@@altcommand lmao. when he does that, i always wonder how long it will take him to see. will it be 5 seconds? 5 minutes? find out on tomorrow's rendition of CTC
His explanation of the green and pink cells being the same was beautiful, given me a newfound appreciation for these puzzles as that genuinely blew my mind
I'm confident that an avid watcher could make a fairly easy puzzle that would take Simon 40 minutes, just by using the techniques that he loves to explain in detail.
I love how setters signal that you're doing things correctly. The break-in set theory, once you find it, is clearly signaled by the setter putting 1234 in one half and 6789 in the other. This is a classic sudoku, so you can arbitrarily permute the digits, meaning that low/hi split was clearly done just as a "you're on the right track, keep going" little thumbs-up from the silver, and I always find those beautiful.
@@koomber777 I'm talking about Simon's break-in using SET (starting at around 12:15), where he identified that the 2x2 squares in the corners were the same as the 16 cells around the edges, then realized that the first set had 8 digits and the second set had 8 *different* digits, so between the two he actually knew all 16 cells in *both* sets, and could start doing logic on that. Because this is a classis Sudoku, which digits were where didn't actually matter; the puzzle could have swapped all the 1s and 7s and still been exactly the same, for example. In particular, Simon's logic would have worked exactly the same if, say, the 2x2 squares held 1,4,5,9 and the edges held 3,6,7,8; every inference he made would still have been correct. But SudokuExplorer went out of their way to make sure that the 2x2 square only held the values 6-9, while the edge cells only held the values 1-4. This is the sort of thing that makes it *really obvious* you're doing something the setter intended, rather than just flailing about randomly, because if it was random the values very likely wouldn't have formed such nice obvious sets like "the low digits" vs "the high digits". These little hints from the setter are always fun.
One of those things that reminds me that a well set Sudoku is a lot like level design in a video game. Little things that are invisible to the average solver (or below average, hi) but which subtly nudge us in the right direction, and it's telling how many of the setter videos come down to setters explaining how they give that guidance.
About a month or two back, I decided that I was tired of always needing to resort to trial-and-error in harder difficulty sudokus. I'd been playing them for years, but, try as I may, I was almost never able to do the harder ones without an abundance of trial-and-error, and it always just felt like cheating to me. I had always been told, after all, that the entire POINT of Sudoku is that you shouldn't NEED to "guess". Sudoku is supposed to be a logic game. Guessing isn't logic, right? So I finally decided that there's no shame in admitting that I could benefit from some help and I started looking up videos on TH-cam so I could learn from the pros and I found Simon's channel here (among a couple of others too, but I keep coming back to this one because I love his disposition, his explanations, and his adorable little quips). I figured, "I don't need to reinvent the wheel on my own. Surely, greater minds than mine have already invented the wheel, the frame, the upholstery, and the engine. I might as well benefit from that." I'm so glad that I made that decision. In this past month or two, I've learned about X wings, Y wings, XY wings, other wings I don't fully understand quite yet, 3D Meduas, XY Chains (which still feel kinda sus to me, tbh), and I think a few more things I'm forgetting off the top of my head. Now, thanks to this video, I've discovered this MIND BLOWING concept of set theory, which feels like an absolutely insanely powerful tool. My skill level has increased several orders of magnitude in these recent weeks thanks to these videos. Just yesterday, I learned about swordfishes, and then realized that I'd actually reinvented them on my own, and that I'd been using them several times during these last few weeks without knowing that they were a named strat. I guess what I'm saying is, thank you so much for this amazing channel. I love this content, and my love for Sudoku is stronger than it's ever been. Happy new year. ♥
@@SimoneBellomonte My PFP is an AI's rendition of an RL photo of me. And I'm not sure which AI it was because it was a friend who generated it for me. I'm sorry if that's a disappointing response, but that's what it is. I'm afraid I have no sauce for you, sweetie. ^^```
(Yes I'm late) I believe that that was close enough to him putting in the wrong seven and thinking five, that he still _knew_ he put a five in that row
There a comic book character in Indian comics called Chacha Chaudhary. The main selling point of the character is that his brain works faster than the computer. I used to read it a lot when I was a kid. Seeing you solve a puzzle that a computer couldn't solve, reminded me of him. Thanks for the nostalgia.
It isn't a case of the computer couldn't solve it. It is a case of the computer hasn't been programmed with that particular technique and has been programmed with other techniques. The computer seems to have no problem at all solving it when it isn't crippled.
Computers will dominate any human at simple arithmetic. Once you have an algorithm for solving the puzzle, the computer will have it solved before the frame has rendered to the screen. What humans are really good at is critical thinking. We can predict patterns and test them in meaningful ways. Computers can't. Now, computers can be programmed to brute force things, and this is probably a puzzle the computer could brute force very quickly (given standard solutions to narrow the options). And artificial neural nets can "learn" tricks through what amounts to brute force. But we still have them beat at creating new algorithms because we have the capacity to cognitively understand what we're looking for. And the computer can only learn tricks if we teach it what it's learning to begin with.
Some indian brains for maths are quick on the recall I dont know if they use shift register thinking, I can do most 2 and some 3 digit additon substraction and multiplication by memory recall but beyond that, I dont know, maybe they have deficiencies elsewhere.
efficient brute force solving any simple sudoku is a long-solved problem. when you hamstring a computer by forcing it try to approximate what a human would do, then occasionally you can get a leg up on it. but the computer's method is far superior.
@@chris5619 To be fair to Simon, besides spending a bit more time looking for "weak" cells and X-wings (and friends), I think that he would have followed this solve pretty closely even without knowing that the computer had issues. He can be overly humble sometimes. :)
This looks like magic the first time you see it and you wonder how anyone in the world would be able to come across it themselves, but once you've done some puzzles with SET and the ring, these equivalences start popping out visually a little easier. This specific one with the 4 outer boxes and 4 perimeter rows was featured in a few puzzles in the last few months so it's not altogether unknown, but there have been some pretty unintuitive SET groupings combined with more advanced steps like swordfishes that were particularly nasty to make good progress on.
@@AlDunbar it wasn't fun when I cut off my finger, and it was even less fun when my father made me sew it back on cause he wasn't taking me to the hospital
I appreciate Simon's desire to find an easy way to visualize every tricky geometry based layout, but the builders are looking for ways to make that impossible. I, for one, will celebrate every solve I can do using any technique up to and including Marks thesis that if you can look ahead several moves without filling in the grid and backtracking if you hit a wall, it's fair game. The only problem, I lose track very quickly doing that! Mark can seemingly fill in half the grid mentally and find the weak cell. Not cheating, just amazing memory.
If the builders were looking to make finding the geometry impossible, they wouldn't arrange them so perfectly. Remember they could swap any of the first 3 rows or columns between each other, any of the second 3, any of the last 3, or swap the big rows/columns, without affecting the validity, but making a mess of the green/purple shapes here. Luckily they did not.
I am constantly flummoxed by the genius and eloquence of this man which he puts on display while occasionally chiding himself for a lack of perspicacity in both. Standards that I can only gaze at with awe. Thanks for what you do, Simon!
his content is amazing but it is very niche, he tries his best with thumbnails and clickbait but surprisingly not that many people wanna watch someone solve sudoku for half an hour... i most certainly do but js
you cannot possibly reasonably call your channel Cracking the Cryptic and be responsible for teaching me how to solve sudoku puzzles and identify these amazing techniques and sit down for hours and hours solving this stuff and then spend almost 40 minutes on a really hard puzzle and then say that you CHEATED and that LUCK WAS INVOLVED simply because you RECOGNIZED IN THE BEGINNING THAT THERE MIGHT BE GEOMETRY INVOLVED (which there was because that's how you're meant to solve it) sir, I think you are an inspirational force and I love you
I love playing Sudoku. This one is way over my head. I really didn't understand the techniques Simon was using, but I'm happy for him that he finish it.
...Remember when there was a debate on if a puzzle would be fair to the solver if it required using even the Phistomefel Ring in some circles? I don't think that was even before the pandemic - I'd already been watching the channel for a while and I started late 2019 or very early, pre-pandemic, 2020. At this point, that variant you used here isn't even novel, with the basic principles behind proving it (SET) being needed in some cases to draw seemingly arbitrary equivalent sets. Sudoku seems to be moving ridiculously quickly these days.
This "phistomefel" equivalence has actually been known in classic sudoku for many, many years under the name SK loop (named after Steve Kurzhal) which is why I'm surprised to see it appear on the channel.
@@jovi_al +1. This definitely isn’t a “breakthrough” technique. Seems like just a standard SET pattern to me. Hell, I don’t like SET and yet I’ve still made a puzzle with this exact pattern.
I spotted the phistomefel variant early... I spotted the high/low pairs in the corners.. then got bogged down... :( went into pencil Mark mode despite promising not to (although only a small number of cells had more than 3 Marks)... then spotted the 13 pair on row 5... I then ended up with 12-23-34-14's all over place and the whole thing ended pretty quickly once I started tidying up... quickly = I only took only 2 or 3 times as long as Simon!
If I didn't play Sudoku, I'd still watch it to get my addiction for English accent and turns of phrase satiated. (My grandmother kept her Lake District accent until she stopped speaking at all at age 90). She would "hot" things on the stove. She was a saint on earth in my mind.
The geometry lesson was invaluable - takes solving to a new and beautiful level. If ever there was a video that merits a second viewing, this is it. Thank you so much! Bravo!
Rules: 02:39 Let's get cracking: 5:00 And how about this video's Simarkisms?! Sorry: 4 Good Grief: 3 Goodness: 3 Bobbins: 1 Useless: 1 Apologies: 1 FAQ: Q1: How do you do this so fast? A1: I'm not made of flesh and blood, but of sand ... Q2: Why don't you include 'XX' and 'YY'? A2: Please tell me what you'd like me to include and there's a good chance I'll add it! Q3: You missed 'XX' at 'YY:ZZ'! A3: That could very well be the case! Human speech is hard to understand for computers like me, especially British sometimes! Point out the ones that I missed and maybe I'll learn!
l've done some testing using Andrew's solver, and it can only solve (without forcing chain strats) once the 5 in box 7 is deduced. Even then it's quite hard going, involving a good deal of "Extreme" strats. If you fully exploit the green/purple logic to take the digits up to 29:00 as given, however, the puzzle solution is rated merely as "gentle". (The main difficulty remaining is the deduction at 34:00, which it labels as "XY chain".) So the green/purple logic really does seem to be the difference between this this puzzle being very very hard and being approachable.
Andrew's isn't a great solver, but once you have the 5 in, then a single Alternate Interference Chain and either W-wing or WXYZ-wing should be able to resolve it, with all other steps being basics. The AIC and WXYZ-wing are what Simon found, the W-wing is similar to the WXYZ-wing and technically slightly easier, though they're of similar difficulty. I myself didn't spot the wings and used another AIC instead. There are also better sudoku solvers out there, such as YZF, which can actually spot (some) SET techniques, including the one used in this puzzle. Also, contrary to what Simon thinks, AICs aren't _that_ difficult, and if you familiarize yourself with them it's certainly possible to spot them with regularity. The issue they have is that you have to learn what strong links are before you can really understand them, and links are (in my opinion) not a very intuitive way of looking at sudoku. But once you've done that, the only issue is that there are a crazy amount of places that _might_ have an AIC, and it's up to you as the solver to find the useful one. Kind of like y-wings (bent triples) in a grid with a ton of bivalues everywhere.
@@Leyrann I agree with your point about AICs, they are very easy to spot, even easier than hidden pairs/triples, especially in bivalue cells. I use them so much I actually kind of lost the ability to spot hidden pairs and triples to the point that they annoy me.
"8 may be the most profligate digit in the grid." That's exactly what I was thinking. Except, when I was thinking that, I had no idea what the word 'profligate' meant.
I love watching these and seeing the red bar getting longer and longer. The anticipation of a huge acceleration in solving right at the end as the logic falls into place is extraordinary
You might feel like you cheated a bit because you knew what to look for, but for a TH-cam Video this was the best course of action. This way the viewers could see a Sudoku solving program get stuck, and the video wasn't as long as it would have been had you gone in with no "hints".
I doubt it would be even 10 more minutes. SET has moved up in Simon's solve pattern, and with so many puzzles getting solved by using SET lately this just reinforces it. A while ago Simon may have wondered if a puzzle needed SET to break into it, and would hesitate a bit before giving in and doing the Explanation, and then finding the break in; now he will spot it and sometimes even discard it much quicker.
I appreciate the fact that you apologized for being completely ineloquent, and then you tried to correct your eloquence, and bring it into some sort of reasonable order. I can only imagine the amount of courage and self-awareness that must have taken, for you to not only realize such a thing, but to acknowledge it, and then, even have the courtesy to apologize for it, that really means the world to me. You are as great of a person as you are a sodoku master, and the kind of man I’d hope to impregnate my daughter someday, if I had one. I honestly can’t even put into words what a true honor that would be, to be able to call you my grand-babydaddy. I can tell you are going to make some lucky old man very proud someday. Thank you so much, and God bless.
When I saw the beginning of this and I saw the puzzle I said I'm wondering why Mark is not doing this one. Then it goes on to explain that they should put it into a computer and show the computer can't solve it without bifurcation. The challenge was to solve it in a logical manner. It was then clear why this puzzle was not given to Mark...LOL
A simple explanation for this trick if you accept the Phistomefel ring already is that it's the same after swapping row 1 and 3, 7 and 9, and same columns. You end up with the ring! Swapping single row and columns within the same group is always fine in regular sudoku, as well as 3x3 groups.
I´ve seen a lot of your videos and I understood the logic behind all of them. I like puzzles, but I haven´t studied anything about them. I can confidently say that it has never taken me so long to completely understand the logic behind a puzzle...this is incredible!
This channel is the soul reason I picked up sudoku. I found this channel through my dad, and I'm very glad he has shown me this. I very much enjoy watching these videos
I am hopeful that when Simon finishes The Witness he'll turn his attention to Baba Is You. Far less likely to give him motion sickness, to boot. ...That or Mark gets in on Streaming as well and starts with Baba Is You.
Never really had time for puzzles ... Then I retired and found sudoku. Recently, discovered this channel and blown my mind with the possiblities of sudoku. Crazy fun... Notations-- who knew?
That chain can be explained instead with the "almost locked set XZ" strategy. You have 2 almost locked sets (N+1 digits in N cells) sharing a single digit that can be in at most one of them: set1: {r2c3, r2c5, r2c9} set2: {r5c5} The digit 3 can only be in one of them. This means you can remove any digits from the grid which would force them become locked sets (a triple and a naked single) that is not a 3. r5c3 sees all the 1s in both sets, so the candidate 1 can be removed from that cell, otherwise it would force both sets to contain a 3 which is impossible.
Its wonderful listening to you. You remain persistent in the face of uncertainty and beautifully explain your logic. You are amazing at ferreting out the important clues.
I usually try all the puzzles before you attempt them.... I stared at this one for well over an hour and got nowhere. Seeing the geometry (and the proof) was beautiful. Love your videos, especially your way of explaining - it's better than any other I've come across so far!
I wanted to tell you, I started watching your channel because of your "Baba Is You" play through, but then watched all of "The Witness", and now I've watched this, and I truly understand your brilliance now. What amazing logic. I've been okay at your typical Sudoku, but I've never seen one this challenging or satisfying before. Keep up the amazing puzzling work!
28:00 for me!! I can’t believe I solved this without guessing!! I’m pretty sure I didn’t find all the logic I needed to understand the whole idea of this puzzle, but I found enough to make my way to the end without using bifurcation.
I am only an occasional puzzle person. I saw the "Geometry" and the lacking of any digit having 3 entries so I copied the starting box and paused the video. ~34 minutes later I watched the rest of the video to see I had indeed solved it by rationalizing where numbers could NOT go. I have no clue about what you were talking about with naming patterns to look for and I don't do that whole possible number in the box thing. Just working it out in my head. In the end I managed to solve it correctly and also thru watching the video now understand how I work things out and can give some of my methods a name. Gonna go look for more troublesome puzzles on your channel for sure. Thank you.
I love the explanations of how Simon has other puzzles on the back burner and we might never see this. You do realise the presence of this video is one huge spoiler.
I solved it starting from right after you found that first five, took about twenty minutes I think. The technique blew my mind after hearing you explain it. The technique has many variations if you just pick rows/columns, 3x3 squares of the same quantity and get rid of the overlapping parts. I actually used one such variation in my solution to this puzzle. It was very fun.
Well, I was able to find the seven in the bottom corner in box 9, was able to spot the symmetry in the corner boxes, but tapped out fifteen minutes later.
This was the video that taught me about this type of geometry, and I started working on this puzzle again, forgetting I had done it before, and I'm so happy I found the geometry pretty quickly.
Absolutely amazing solve Simon. Your channel is on the cutting edge of revolutionizing sudoku as we know it with SET. Enough to change all the wikis and computer solvers. Also, XY-chain is what you found at 35:00 point that eliminated the 1.
The channel is certainly bringing a well-deserved spotlight onto the setters who are doing the thing you say, which Mark and Simon are usually quick to point out themselves.
You say "revolutionizing sudoku as we know it with SET", I say "destroying Sudoku with SET" because it will push away a great number of people. I would go so far as to say it will do more harm than good if the goal is to get people interested in Sudoku or to make it fun for people. I have only my gut feeling, but I suspect the number of people who enjoy puzzles involving SET are a small minority of puzzle solvers.
I must be in the small minority. Until watching this channel I never imagined there were these kinds of techniques or even a logical path (rather than brute force) to solve most sudokus. I'm not even close to being able to spot and use SET in an attempted solve myself but I appreciate Simon's passion and his excitement when he sees a novel application of a method like this. I know a lot of people say they find these videos calming but I also find them really inspiring and a reminder that the human brain is (sometimes) capable of achieving tasks that a computer still cannot.
Correction, he found a WXYZ-wing. Though, that's basically a chain that is short enough to have a name. There was also a W-wing that shared a bunch of cells that accomplished a similar breakthrough.
@@nomore6167 And no one is forcing any of the people who don't enjoy SET to use it. Some people make hard sudokus for dedicated audiences, others make easy sudokus for casual audiences. Surely you can enjoy one without putting down the other?
I fed it into my SAT Solver... no issue whatsoever. So, unless Skynet is knocked up in an hour using C# or JS or Java, by a gaggle of first year uni undergrads who still think recursion is a _'pretty neat idea'_ ... we might have a problem : )
I have been doing very easy generated sudokus in the bus for years now, and in an effort to go for a fast time I've stopped using pencil marks. This forced me to train my memory, and I believe it's now helping me think a couple moves ahead. Which is to say, I have poor sudoku solving skills, and I do cover my screen with pencil marks when I try my hand at some of the challenging ones, but now I can at least follow along your videos and understand how brilliant some of those puzzles are :) And I think this geometric approach is exactly what I was missing to solve a challenging sudoku I got stumped on a couple months ago 😮
The high/low and even/odd thing isn't really useful in classics though, since the actual value of a given digit in any given classic is irrelevant (that is, you could just e.g. swap all 7s for 2s in the clues and it would be essentially the same puzzle with those same digits swapped in the solution)
@@HunterJE Just because a relabelling of the sudoku is just as valid doesn’t mean a human won’t notice groupings more easily if they’re of the form I described.
@@HunterJE The high/low grouping is done by the setter to take advantage of the human brain’s tendency to see patterns even when they don’t actually mean anything.
@@ragnkja the point is, it doesnt matter to a computer Even if the computer were to be able to recognize SET, it wouldnt care about high low groupings at all, it would just recognize them as a group of 66778899 and a group of 11223344, which doesnt overlap, thus it would include thats the whole 16 digit group. If it were any other numbers, it would be able to do the same thing but with different numbers, only a human might have problems with that.
@@masked_mizuki Agreed. With high/low or odd/even you are just dividing the Sudoku cells into two disjoint cells (no shared numbers). So it could be extreme (1289) and middle (34567), or kropki numbers (123468) and non-kropki (579) . A computer would not have any problem dealing with (1269) and (34578) while we probably would, because we don’t see a clear reason for it. All of these techniques are just ways of dividing the sudoko numbers into two sets. Which by the way is the normal definition of bifurcation!!!!
I was pleased I was able to solve this before watching Simon's solve. As far as I can tell, the "finned Y-wing" to eliminate the 1 at 35 minutes in is a necessary step in the solve. I completed the puzzle to a far greater extent than Simon did before I reached a deadlock in the end game that I couldn't break without using that step.
There was some extra nice logic! Like the number 5 in the corner boxes is going like a steering wheel round the grid, so does also the last remaining high number (6-9) which had to go into a white cell in each of the corner boxes. Even if we do not know which high number will go into the white cells, we know that there must go exactly go one extra high number in the outer columns and rows. So the last high number in the corner boxes must go in one of the white cells next to the number 5 or it has to go in the other state of existence where it will need to go in the opposite side in one of the other two other white cells. Once we notice this we can look at the effect. Assume that the remaining high number is not next to the number 5. In that case it has a effect on outer columns 1 and 9. We know that there are two high numbers in those column in the right-top and left-bottom box and that those numbers are 6 and 8 since these corner boxes contain already 7 and 9. And this as an effect on row 5: in the green cells of this row now there cannot go a 6 and 8 because of the logic explained, so the green cells must be a 7-9 pair which cannot because of the 7 given in that row. The same conclusion can be drawn apply if we look at the top-left and bottom right box where we then miss the numbers 7 and 9 in the outer row’s 1 and 9. Therefore there must be a 6-8 pair in column 5 which cannot because of the given 8. By this logic we know that the remaining number in a white cell therefore must be next to the number 5.
Simon, a little suggestion, when explaining SET that has "double-counted" digits, I feel it's easier to understand and easier to see if you do it in two steps in this case, you would first look at the horizontal stripes, remove digits that are both in green and purple, and explain: "now, purple contains exactly the same digits as green, plus 2 full sets of the digits one to nine" then you could look at the vertical stripes and do the same process as normal, ending with the same pattern
Hmm, Actually I have a hard time understanding your version and how your version is different, maybe cause I'm not fluent in English. But I understood Simon perfectly. He is really good at explaining things! I really like listening him speak :)
@@sandraraituma That's because my comment is not the explanation, it is a suggestion on how to make the explanation. if Simon were to explain it this way, he would show it on the screen and he would do it with his words, I'm sure you wouldn't have any problem understanding it then. The biggest difference between the two ways and the reason I think this one is better is because you don't get "2 greens, 1 purple" squares, which are always hard to explain, and that Simon has to leave for last to explain them separately.
Another way is to do exactly as Simon does now, but using a separate colour for the rows and columns. Then the corners show 3 colours, which make it clear that they are double counted.
Your way more clearly explains why the corner squares are colored green in the end, but needs extra explaining how purple and green are equal. I do like your explanation a lot. I'm sure some students will prefer yours and others will prefer Simon's.
Ha! I got it! You looked for geometry, but I just noticed the number patterns being reversed/juxtaposed. Pattern Awareness really helps on this one. I noted the 1,2,3,4 sets in the center aisles(?), then the radial nature of the numbers on diagonals, then realized that whole boxes were reversed, but also slightly jumbled. Then just went about solving. I got it all done and found the center/right 1's and 3's were jumbled. I noted which parts were seemingly well-mirrored, erased everything else and started from that point. Different methodology, same result. The geometry knowledge certainly helped you get if faster, and without an errored answer, but I was really happy to solve this on my own then come back to your video to learn the geometric approach.
The best thing about these videos is hearing you get more excited when you start to understand or "get" something, I know that feeling when reaching a breakthrough so well
Great video, I never knew about that beautiful geometry trick. I had initially found more digit pairs than you though, and after you found the pairs 13, I used the same logic at the top which allowed me to find the digit pairs 34 in the second square. That gave me the 3 and 1 from your pair, and the rest of the sudoku pretty much solved itself, nothing tricky after that.
Every time you spot some of the crazy clues I couldn't even think of, I wonder what the video be like if you had eye tracker showing the way you scan sudoku.
Wow that was super impressive. A lot of it went over my head, but all the parts I got were very clever. This channel always amazes me. Also I love your voice and calm demeanor. Keep up the good work!
41:16 ... took me about 9 minutes to spot the break-in, then I had somewhat more roundabout ways at two points (one where Simon deduced the 9 in c9, the other when reaching the quintuple in c2), but in the end, I made my way over the finish line. Nice classic!
Your brain is amazing! I do soduko all the time and only found this video by accident. Your comments on geometry made me think. I'll be paying more attention to the geometry in my puzzles in future
I haven't finished watching the video, but I'm currently at 34:57 and you can see the beautiful pattern of numbers surrounding the puzzle. The groups of 597, 163, 824 repeated on Column 1 and 9 of the puzzle. Same with the group of 685, 394 and 127 on Row 1 and Row 9. Really genius!
This puzzle is really hard is you haven't been watching Simon playing with digit sets recently, but reasonably straightforward if you have. I quickly realised something was going on with the boxes Simon marked in purple, and Simon has used the digit set pattern this puzzle relies on several times recently.
28:14 Hearing him say he trusts his pencil marks right after clearing an errant 8 from the middle square of the top column made me feel some sort of way. That said, I'm just in awe of the logic on display here, and the explanations that go with it. It's extremely difficult to communicate your thoughts that clearly. What an incredible puzzle.
I hope some of these cool techniques people have used to design puzzles that you solve end up in competitions Also, I really think the creativity of puzzles has sky rocketed ever since you and Mark started this channel up. You’ve done absolutely amazing for the world of sudoku
Bro sees the most high level and logical answers that take me a bit to see and understand, yet I also find myself screaming at my phone saying, "IT'S RIGHT THERE, YOU WERE JUST LOOKING AT IT!"
34:40 A W-wing is most likely the simplest way to resolve the rest here, (Eithe)r r3c3 or r5c3 is a 1, both of those cells see a 1-3 pair r2c7+r5c5, so one of those must a 3, both of those see the 3-4 pair in box 2, ergo r2c5=4.)
Very nice video. The first time I became aware of Sudoku. BUT: You said that the computer couldn't solve the problem. That spurred me on to give it a try. Took me one day to implement a Rust program to solve the given Sudoku. Was a lot of fun. But solving this without a computer is truly phenomenal.
As we Aussies like to say: You bewdy, what a ripper!! Two months ago I would have had no idea how to proceed beyond pencil marking the possibles. But I have seen Mark's explanation of the Phistomefel Ring and its variant a couple of times. And that got me started with this puzzle. It took me more than an hour (oh alright, 77 minutes) but I persevered, kept turning the steering wheel and eventually got there.
Extremely weirdly, everything the computer needs to solve this puzzle without bifurcation is the 5 in box 7, So I guess all that high/low digit thing was just to find places that couldn't be fives.
This was impressive! I try to do these puzzles without notation just to exercise my mind. I’m so glad I didn’t try that with this puzzle and decided to just watch you do it.
JESUS, TAKE THE WHEEEEEEEEL. That's the only way I would have gotten anywhere in this one. Beautiful solving, I'm going to have to go back and watch the explanation of the purple/green thing again.
Really enjoyed this, fascinating to see human vs. computer... reminds me of ST:TNG when they shut down the computer to have Picard manually navigate the ship to safety 😆 BTW On a video some time back someone commented that he appreciated you starting to take more time after puzzles to give your final thoughts and sum up your take on the puzzle, and I really agree there. Thanks for another great vid!
Simon is the type of guy that is super hard on himself for not seeing things instantly, but I just know if he was watching me struggle with a medium difficulty he would be very supportive and excited when I'd figured something out he'd done in his head 30 minutes before. 🥰
You HAVE to try the eye tracking software while doing a sudoku puzzle so we can see where your looking in real time
No, no....we would all get dizzy.
Everywhere but the 7 next to a 7
@@altcommand lmao. when he does that, i always wonder how long it will take him to see. will it be 5 seconds? 5 minutes? find out on tomorrow's rendition of CTC
Before you make such a request, think about the consequences. Have you watched "Queen's Gambit", or maybe Hikaru streaming?
@@victorfinberg8595 You are absolutely correct. I've seen a couple of Hikaru's videos with that tracking feature and it's bloody annoying.
His explanation of the green and pink cells being the same was beautiful, given me a newfound appreciation for these puzzles as that genuinely blew my mind
Little easier to just view it as 5 columns and 4 rows, remove box 5 to babalance it back to 4 sets of 1-9 each then remove the 1s that are shared
Tried not to panic when you wrote the 7 instead of 5 up there, haha! This was great to watch, love your videos! Thank you!
At 28:23.
Same!
Same here
Who would have though watching a sudoku video could be so nerve-wrecking and exciting 😅
he even said five out loud but put on a 7
A 40 minute video for a classic Sudoku, this is gonna be interesting
I'm confident that an avid watcher could make a fairly easy puzzle that would take Simon 40 minutes, just by using the techniques that he loves to explain in detail.
@@timothymcdonnell1186 I can vouch for this what used to be hard I just seem to fill in now with much less effort.
It was indeed
I love how setters signal that you're doing things correctly. The break-in set theory, once you find it, is clearly signaled by the setter putting 1234 in one half and 6789 in the other. This is a classic sudoku, so you can arbitrarily permute the digits, meaning that low/hi split was clearly done just as a "you're on the right track, keep going" little thumbs-up from the silver, and I always find those beautiful.
I recognise every single word in this post but understand none of it.
@@koomber777 I'm talking about Simon's break-in using SET (starting at around 12:15), where he identified that the 2x2 squares in the corners were the same as the 16 cells around the edges, then realized that the first set had 8 digits and the second set had 8 *different* digits, so between the two he actually knew all 16 cells in *both* sets, and could start doing logic on that.
Because this is a classis Sudoku, which digits were where didn't actually matter; the puzzle could have swapped all the 1s and 7s and still been exactly the same, for example. In particular, Simon's logic would have worked exactly the same if, say, the 2x2 squares held 1,4,5,9 and the edges held 3,6,7,8; every inference he made would still have been correct. But SudokuExplorer went out of their way to make sure that the 2x2 square only held the values 6-9, while the edge cells only held the values 1-4. This is the sort of thing that makes it *really obvious* you're doing something the setter intended, rather than just flailing about randomly, because if it was random the values very likely wouldn't have formed such nice obvious sets like "the low digits" vs "the high digits". These little hints from the setter are always fun.
One of those things that reminds me that a well set Sudoku is a lot like level design in a video game. Little things that are invisible to the average solver (or below average, hi) but which subtly nudge us in the right direction, and it's telling how many of the setter videos come down to setters explaining how they give that guidance.
Game design is a true art form
@@koomber777 English as second language moment
About a month or two back, I decided that I was tired of always needing to resort to trial-and-error in harder difficulty sudokus. I'd been playing them for years, but, try as I may, I was almost never able to do the harder ones without an abundance of trial-and-error, and it always just felt like cheating to me. I had always been told, after all, that the entire POINT of Sudoku is that you shouldn't NEED to "guess". Sudoku is supposed to be a logic game. Guessing isn't logic, right? So I finally decided that there's no shame in admitting that I could benefit from some help and I started looking up videos on TH-cam so I could learn from the pros and I found Simon's channel here (among a couple of others too, but I keep coming back to this one because I love his disposition, his explanations, and his adorable little quips). I figured, "I don't need to reinvent the wheel on my own. Surely, greater minds than mine have already invented the wheel, the frame, the upholstery, and the engine. I might as well benefit from that." I'm so glad that I made that decision. In this past month or two, I've learned about X wings, Y wings, XY wings, other wings I don't fully understand quite yet, 3D Meduas, XY Chains (which still feel kinda sus to me, tbh), and I think a few more things I'm forgetting off the top of my head. Now, thanks to this video, I've discovered this MIND BLOWING concept of set theory, which feels like an absolutely insanely powerful tool. My skill level has increased several orders of magnitude in these recent weeks thanks to these videos. Just yesterday, I learned about swordfishes, and then realized that I'd actually reinvented them on my own, and that I'd been using them several times during these last few weeks without knowing that they were a named strat. I guess what I'm saying is, thank you so much for this amazing channel. I love this content, and my love for Sudoku is stronger than it's ever been. Happy new year. ♥
Pfp (Profile picture) and / or Banner Sauce (Source [Artist])? 🗿
@@SimoneBellomonte My PFP is an AI's rendition of an RL photo of me. And I'm not sure which AI it was because it was a friend who generated it for me. I'm sorry if that's a disappointing response, but that's what it is. I'm afraid I have no sauce for you, sweetie. ^^```
I love how at 29:00 he looks at the row with the two 7's and sees that the remaining are a 34 pair.
That made me laugh too. I think he was going through the digits in his head and once he couldn't see 3 and 4 he stopped looking and put them in.
it was supposed to be a 5 it would have ended with the same result
He actually said 5 but wrote in a 7
(Yes I'm late)
I believe that that was close enough to him putting in the wrong seven and thinking five, that he still _knew_ he put a five in that row
@@informadentpatientenberatu9293 this gave me anxiety 😁
There a comic book character in Indian comics called Chacha Chaudhary. The main selling point of the character is that his brain works faster than the computer. I used to read it a lot when I was a kid. Seeing you solve a puzzle that a computer couldn't solve, reminded me of him. Thanks for the nostalgia.
It isn't a case of the computer couldn't solve it. It is a case of the computer hasn't been programmed with that particular technique and has been programmed with other techniques.
The computer seems to have no problem at all solving it when it isn't crippled.
Is the comic Ulbrella Accademy by Gerard Way?
Computers will dominate any human at simple arithmetic. Once you have an algorithm for solving the puzzle, the computer will have it solved before the frame has rendered to the screen. What humans are really good at is critical thinking. We can predict patterns and test them in meaningful ways. Computers can't.
Now, computers can be programmed to brute force things, and this is probably a puzzle the computer could brute force very quickly (given standard solutions to narrow the options). And artificial neural nets can "learn" tricks through what amounts to brute force. But we still have them beat at creating new algorithms because we have the capacity to cognitively understand what we're looking for. And the computer can only learn tricks if we teach it what it's learning to begin with.
Some indian brains for maths are quick on the recall I dont know if they use shift register thinking, I can do most 2 and some 3 digit additon substraction and multiplication by memory recall but beyond that, I dont know, maybe they have deficiencies elsewhere.
efficient brute force solving any simple sudoku is a long-solved problem. when you hamstring a computer by forcing it try to approximate what a human would do, then occasionally you can get a leg up on it. but the computer's method is far superior.
I don’t understand what he does, but i love watching this man get excited for filling numbers
27:19 "So this is probably the second hardest won digit in Christendom"
I got a good chuckle out of that one
That was absolutely bloody phenomenal! How the heck Simon found the break through was off the scale clever! The setter is beyond understanding!
I mostly agree, but Simon himself said he "cheated a bit" by knowing that he had to look for something more on this one.
@@chris5619 To be fair to Simon, besides spending a bit more time looking for "weak" cells and X-wings (and friends), I think that he would have followed this solve pretty closely even without knowing that the computer had issues. He can be overly humble sometimes. :)
This looks like magic the first time you see it and you wonder how anyone in the world would be able to come across it themselves, but once you've done some puzzles with SET and the ring, these equivalences start popping out visually a little easier. This specific one with the 4 outer boxes and 4 perimeter rows was featured in a few puzzles in the last few months so it's not altogether unknown, but there have been some pretty unintuitive SET groupings combined with more advanced steps like swordfishes that were particularly nasty to make good progress on.
@@chris5619 if that's cheating 🤣🤣🤣
Sudoku: The most fun you can have with nine digits without cutting off a toe.
or a finger/thumb!
@@AlDunbar it wasn't fun when I cut off my finger, and it was even less fun when my father made me sew it back on cause he wasn't taking me to the hospital
@@IamRelint It's lucky you were studying microsurgery as a child.
@@nagualdesign lmao
8 friends with 9 toes, endless fun playing tic-tac-toe, using digits!
"You rotten thing ! Bobbins !!" One just gotta love Simon's vocabulary 😃
Yeah when I get really stuck I start saying things to the puzzle like "You know, I hate you. You really suck."
@@fubaralakbar6800 As long as it makes you feel better 😉
@@ChrisBreemer zamn you sound like eric cartman's mom
31:50
Speaking of - what on Earth is he saying at 3:35 ? Goodlifisms?
Knowing nothing more than the basics enough to solve easy and some medium classic Sudoku, this is absolutely mind blowing.
I appreciate Simon's desire to find an easy way to visualize every tricky geometry based layout, but the builders are looking for ways to make that impossible. I, for one, will celebrate every solve I can do using any technique up to and including Marks thesis that if you can look ahead several moves without filling in the grid and backtracking if you hit a wall, it's fair game. The only problem, I lose track very quickly doing that! Mark can seemingly fill in half the grid mentally and find the weak cell. Not cheating, just amazing memory.
I get three steps and forget where I came from. Two Steps is fine, that 3rd and onwards is no mans land, here be dragons.
Mark is Dr. Strange in that regard!
I can't do that. So, I mark a cell in RED and then look ahead.
My memory of numbers has definitely increased since doing thousands of sudoku puzzles.
If the builders were looking to make finding the geometry impossible, they wouldn't arrange them so perfectly. Remember they could swap any of the first 3 rows or columns between each other, any of the second 3, any of the last 3, or swap the big rows/columns, without affecting the validity, but making a mess of the green/purple shapes here. Luckily they did not.
I am constantly flummoxed by the genius and eloquence of this man which he puts on display while occasionally chiding himself for a lack of perspicacity in both. Standards that I can only gaze at with awe. Thanks for what you do, Simon!
Quite an amazing puzzle. I could follow the logic as Simon explained it along the way - but no way I could ever solve this on my own!
CTC deserves far more than 400K subs. I’m rooting for 1M!!
his content is amazing but it is very niche, he tries his best with thumbnails and clickbait but surprisingly not that many people wanna watch someone solve sudoku for half an hour... i most certainly do but js
nah, go for a hundred milllion
edit: get the whole world to sub
you cannot possibly reasonably call your channel Cracking the Cryptic and be responsible for teaching me how to solve sudoku puzzles and identify these amazing techniques and sit down for hours and hours solving this stuff and then spend almost 40 minutes on a really hard puzzle and then say that you CHEATED and that LUCK WAS INVOLVED simply because you RECOGNIZED IN THE BEGINNING THAT THERE MIGHT BE GEOMETRY INVOLVED (which there was because that's how you're meant to solve it)
sir, I think you are an inspirational force and I love you
He didn't cheat. He literally followed instructions given by the solver. You people are snowflakes.
I love playing Sudoku. This one is way over my head. I really didn't understand the techniques Simon was using, but I'm happy for him that he finish it.
...Remember when there was a debate on if a puzzle would be fair to the solver if it required using even the Phistomefel Ring in some circles? I don't think that was even before the pandemic - I'd already been watching the channel for a while and I started late 2019 or very early, pre-pandemic, 2020. At this point, that variant you used here isn't even novel, with the basic principles behind proving it (SET) being needed in some cases to draw seemingly arbitrary equivalent sets. Sudoku seems to be moving ridiculously quickly these days.
This "phistomefel" equivalence has actually been known in classic sudoku for many, many years under the name SK loop (named after Steve Kurzhal) which is why I'm surprised to see it appear on the channel.
In some circles no ring is allowed. God, I love what people have become. Open season for me.
@@jovi_al +1. This definitely isn’t a “breakthrough” technique. Seems like just a standard SET pattern to me. Hell, I don’t like SET and yet I’ve still made a puzzle with this exact pattern.
I spotted the phistomefel variant early... I spotted the high/low pairs in the corners.. then got bogged down... :( went into pencil Mark mode despite promising not to (although only a small number of cells had more than 3 Marks)... then spotted the 13 pair on row 5... I then ended up with 12-23-34-14's all over place and the whole thing ended pretty quickly once I started tidying up... quickly = I only took only 2 or 3 times as long as Simon!
As soon as he highlighted the 1234's that formed sort of an outline of four 2x2 regions, I immediately saw the trick
12:30 apologizing for not being eloquent must be one of the most British things 🤣
This is one of my favorite channels on TH-cam and I don't even play sudoku lol
If I didn't play Sudoku, I'd still watch it to get my addiction for English accent and turns of phrase satiated. (My grandmother kept her Lake District accent until she stopped speaking at all at age 90). She would "hot" things on the stove. She was a saint on earth in my mind.
The geometry lesson was invaluable - takes solving to a new and beautiful level. If ever there was a video that merits a second viewing, this is it. Thank you so much! Bravo!
Rules: 02:39
Let's get cracking: 5:00
And how about this video's Simarkisms?!
Sorry: 4
Good Grief: 3
Goodness: 3
Bobbins: 1
Useless: 1
Apologies: 1
FAQ:
Q1: How do you do this so fast?
A1: I'm not made of flesh and blood, but of sand ...
Q2: Why don't you include 'XX' and 'YY'?
A2: Please tell me what you'd like me to include and there's a good chance I'll add it!
Q3: You missed 'XX' at 'YY:ZZ'!
A3: That could very well be the case! Human speech is hard to understand for computers like me, especially British sometimes! Point out the ones that I missed and maybe I'll learn!
might be interesting to see what digit was pronounced the most
@@NoNameAtAll2 yeah
l've done some testing using Andrew's solver, and it can only solve (without forcing chain strats) once the 5 in box 7 is deduced. Even then it's quite hard going, involving a good deal of "Extreme" strats. If you fully exploit the green/purple logic to take the digits up to 29:00 as given, however, the puzzle solution is rated merely as "gentle". (The main difficulty remaining is the deduction at 34:00, which it labels as "XY chain".) So the green/purple logic really does seem to be the difference between this this puzzle being very very hard and being approachable.
Andrew's isn't a great solver, but once you have the 5 in, then a single Alternate Interference Chain and either W-wing or WXYZ-wing should be able to resolve it, with all other steps being basics. The AIC and WXYZ-wing are what Simon found, the W-wing is similar to the WXYZ-wing and technically slightly easier, though they're of similar difficulty. I myself didn't spot the wings and used another AIC instead. There are also better sudoku solvers out there, such as YZF, which can actually spot (some) SET techniques, including the one used in this puzzle.
Also, contrary to what Simon thinks, AICs aren't _that_ difficult, and if you familiarize yourself with them it's certainly possible to spot them with regularity. The issue they have is that you have to learn what strong links are before you can really understand them, and links are (in my opinion) not a very intuitive way of looking at sudoku. But once you've done that, the only issue is that there are a crazy amount of places that _might_ have an AIC, and it's up to you as the solver to find the useful one. Kind of like y-wings (bent triples) in a grid with a ton of bivalues everywhere.
@@Leyrann I agree with your point about AICs, they are very easy to spot, even easier than hidden pairs/triples, especially in bivalue cells. I use them so much I actually kind of lost the ability to spot hidden pairs and triples to the point that they annoy me.
Simon calling Phistomefel Ring basic... I remember when every PR video had him in awe lol :P :P
"8 may be the most profligate digit in the grid." That's exactly what I was thinking. Except, when I was thinking that, I had no idea what the word 'profligate' meant.
Profligate: adjective
(Pr*u*-fill-gu*y*-tat)
To be filled entirely and exclusively with a food item, typically beans
@@pantlooner9601 Yeah, I figured it was something along those lines. Thanks.
8 may be a digit in the sudoku :)
I love watching these and seeing the red bar getting longer and longer. The anticipation of a huge acceleration in solving right at the end as the logic falls into place is extraordinary
You might feel like you cheated a bit because you knew what to look for, but for a TH-cam Video this was the best course of action. This way the viewers could see a Sudoku solving program get stuck, and the video wasn't as long as it would have been had you gone in with no "hints".
I doubt it would be even 10 more minutes. SET has moved up in Simon's solve pattern, and with so many puzzles getting solved by using SET lately this just reinforces it. A while ago Simon may have wondered if a puzzle needed SET to break into it, and would hesitate a bit before giving in and doing the Explanation, and then finding the break in; now he will spot it and sometimes even discard it much quicker.
I appreciate the fact that you apologized for being completely ineloquent, and then you tried to correct your eloquence, and bring it into some sort of reasonable order. I can only imagine the amount of courage and self-awareness that must have taken, for you to not only realize such a thing, but to acknowledge it, and then, even have the courtesy to apologize for it, that really means the world to me. You are as great of a person as you are a sodoku master, and the kind of man I’d hope to impregnate my daughter someday, if I had one. I honestly can’t even put into words what a true honor that would be, to be able to call you my grand-babydaddy. I can tell you are going to make some lucky old man very proud someday. Thank you so much, and God bless.
When I saw the beginning of this and I saw the puzzle I said I'm wondering why Mark is not doing this one. Then it goes on to explain that they should put it into a computer and show the computer can't solve it without bifurcation. The challenge was to solve it in a logical manner. It was then clear why this puzzle was not given to Mark...LOL
Every time you do a fantastic job of solving these and yet apologize every 30 seconds. You are a master at these, own it!
A simple explanation for this trick if you accept the Phistomefel ring already is that it's the same after swapping row 1 and 3, 7 and 9, and same columns. You end up with the ring!
Swapping single row and columns within the same group is always fine in regular sudoku, as well as 3x3 groups.
I´ve seen a lot of your videos and I understood the logic behind all of them. I like puzzles, but I haven´t studied anything about them.
I can confidently say that it has never taken me so long to completely understand the logic behind a puzzle...this is incredible!
"Steering wheel! Steering wheel! Somebody tell him to give it to me" - Kimi Raikkonen
This channel is the soul reason I picked up sudoku. I found this channel through my dad, and I'm very glad he has shown me this. I very much enjoy watching these videos
Please play "Baba Is You" one day, I think you'll find it absolutely beautiful. :3
Yes
I am hopeful that when Simon finishes The Witness he'll turn his attention to Baba Is You. Far less likely to give him motion sickness, to boot.
...That or Mark gets in on Streaming as well and starts with Baba Is You.
God, Baba is You. I came away from that game convinced that that is what experiencing a stroke must feel like
I almost forgot I have still not yet finished this well built game. Its level design hit my soul.
i'd hapilly watch him play through that game.
Never really had time for puzzles ... Then I retired and found sudoku. Recently, discovered this channel and blown my mind with the possiblities of sudoku. Crazy fun... Notations-- who knew?
The extra 7 in box 3 was making me irrationally nervous until he fixed it
After years of searching, finally I found the perfect voice for getting sleepy 😴
That chain can be explained instead with the "almost locked set XZ" strategy. You have 2 almost locked sets (N+1 digits in N cells) sharing a single digit that can be in at most one of them:
set1: {r2c3, r2c5, r2c9}
set2: {r5c5}
The digit 3 can only be in one of them. This means you can remove any digits from the grid which would force them become locked sets (a triple and a naked single) that is not a 3. r5c3 sees all the 1s in both sets, so the candidate 1 can be removed from that cell, otherwise it would force both sets to contain a 3 which is impossible.
Absolutely agree. I couldn't understand why Simon had the slightest doubt about that being a "fair game" deduction.!
This just sent me down an hour long rabbit hole learning this technique. Fascinating.
Its wonderful listening to you. You remain persistent in the face of uncertainty and beautifully explain your logic. You are amazing at ferreting out the important clues.
"we are still the bee's knees, sometimes".... true wisdom!
The look on his face when he knew he had it was awesome! The slight smile with big and happy eyes, well done Simon, that was a hell of a puzzle!
This is the new Kasparov vs deep blue
Except Kasparov only lost and drew to Deep Blue. Simon beat this computer!
I usually try all the puzzles before you attempt them.... I stared at this one for well over an hour and got nowhere. Seeing the geometry (and the proof) was beautiful. Love your videos, especially your way of explaining - it's better than any other I've come across so far!
Amazing as usual, Simon. I’m going to watch this again as I really need to understand set theory. Always enjoy your solves. Keep up the great work!
I wanted to tell you, I started watching your channel because of your "Baba Is You" play through, but then watched all of "The Witness", and now I've watched this, and I truly understand your brilliance now. What amazing logic. I've been okay at your typical Sudoku, but I've never seen one this challenging or satisfying before. Keep up the amazing puzzling work!
28:00 for me!! I can’t believe I solved this without guessing!! I’m pretty sure I didn’t find all the logic I needed to understand the whole idea of this puzzle, but I found enough to make my way to the end without using bifurcation.
I am only an occasional puzzle person. I saw the "Geometry" and the lacking of any digit having 3 entries so I copied the starting box and paused the video. ~34 minutes later I watched the rest of the video to see I had indeed solved it by rationalizing where numbers could NOT go. I have no clue about what you were talking about with naming patterns to look for and I don't do that whole possible number in the box thing. Just working it out in my head. In the end I managed to solve it correctly and also thru watching the video now understand how I work things out and can give some of my methods a name. Gonna go look for more troublesome puzzles on your channel for sure. Thank you.
I love the explanations of how Simon has other puzzles on the back burner and we might never see this. You do realise the presence of this video is one huge spoiler.
I solved it starting from right after you found that first five, took about twenty minutes I think. The technique blew my mind after hearing you explain it. The technique has many variations if you just pick rows/columns, 3x3 squares of the same quantity and get rid of the overlapping parts. I actually used one such variation in my solution to this puzzle. It was very fun.
Well, I was able to find the seven in the bottom corner in box 9, was able to spot the symmetry in the corner boxes, but tapped out fifteen minutes later.
This was the video that taught me about this type of geometry, and I started working on this puzzle again, forgetting I had done it before, and I'm so happy I found the geometry pretty quickly.
Absolutely amazing solve Simon. Your channel is on the cutting edge of revolutionizing sudoku as we know it with SET. Enough to change all the wikis and computer solvers.
Also, XY-chain is what you found at 35:00 point that eliminated the 1.
The channel is certainly bringing a well-deserved spotlight onto the setters who are doing the thing you say, which Mark and Simon are usually quick to point out themselves.
You say "revolutionizing sudoku as we know it with SET", I say "destroying Sudoku with SET" because it will push away a great number of people. I would go so far as to say it will do more harm than good if the goal is to get people interested in Sudoku or to make it fun for people. I have only my gut feeling, but I suspect the number of people who enjoy puzzles involving SET are a small minority of puzzle solvers.
I must be in the small minority. Until watching this channel I never imagined there were these kinds of techniques or even a logical path (rather than brute force) to solve most sudokus. I'm not even close to being able to spot and use SET in an attempted solve myself but I appreciate Simon's passion and his excitement when he sees a novel application of a method like this. I know a lot of people say they find these videos calming but I also find them really inspiring and a reminder that the human brain is (sometimes) capable of achieving tasks that a computer still cannot.
Correction, he found a WXYZ-wing. Though, that's basically a chain that is short enough to have a name. There was also a W-wing that shared a bunch of cells that accomplished a similar breakthrough.
@@nomore6167 And no one is forcing any of the people who don't enjoy SET to use it. Some people make hard sudokus for dedicated audiences, others make easy sudokus for casual audiences. Surely you can enjoy one without putting down the other?
My phone couldn't find anything better than that xy-chain at the end. That is just mental. I couldn't solve it even given the break in. Awesome solve.
"How do I feel?", Simon asks. Well, I feel like I just stared into a pure crystal of mathematical geometry for 39 minutes. Very nice.
my problem was I was restricting my solutions to have 1 to 9 not repeating across the two diagonals !
In other words, you're high on crystal math?
@@captaindapper5020 Nyuk nyuk. :)
The symmetry of this puzzle is top class.
Thanks to you simon, i won sudoku competitions ❤️ thank you
Wow! Congratulations!
Classic sudoku’s are hands down my favorite videos
Man vs machine... Skynet better behave or Simon will humiliate it
I fed it into my SAT Solver... no issue whatsoever.
So, unless Skynet is knocked up in an hour using C# or JS or Java, by a gaggle of first year uni undergrads who still think recursion is a _'pretty neat idea'_ ... we might have a problem : )
I have been doing very easy generated sudokus in the bus for years now, and in an effort to go for a fast time I've stopped using pencil marks. This forced me to train my memory, and I believe it's now helping me think a couple moves ahead.
Which is to say, I have poor sudoku solving skills, and I do cover my screen with pencil marks when I try my hand at some of the challenging ones, but now I can at least follow along your videos and understand how brilliant some of those puzzles are :)
And I think this geometric approach is exactly what I was missing to solve a challenging sudoku I got stumped on a couple months ago 😮
Fantastic! You are an excellent and entertaining teacher as well as an amazing solver!
Love the shout out to Little Britain in the thumbnail.
Two things that solver can’t do that you do regularly: grouping the digits into highs and lows or odds and evens, and set equivalence theory.
The high/low and even/odd thing isn't really useful in classics though, since the actual value of a given digit in any given classic is irrelevant (that is, you could just e.g. swap all 7s for 2s in the clues and it would be essentially the same puzzle with those same digits swapped in the solution)
@@HunterJE
Just because a relabelling of the sudoku is just as valid doesn’t mean a human won’t notice groupings more easily if they’re of the form I described.
@@HunterJE
The high/low grouping is done by the setter to take advantage of the human brain’s tendency to see patterns even when they don’t actually mean anything.
@@ragnkja the point is, it doesnt matter to a computer
Even if the computer were to be able to recognize SET, it wouldnt care about high low groupings at all, it would just recognize them as a group of 66778899 and a group of 11223344, which doesnt overlap, thus it would include thats the whole 16 digit group. If it were any other numbers, it would be able to do the same thing but with different numbers, only a human might have problems with that.
@@masked_mizuki Agreed. With high/low or odd/even you are just dividing the Sudoku cells into two disjoint cells (no shared numbers). So it could be extreme (1289) and middle (34567), or kropki numbers (123468) and non-kropki (579) . A computer would not have any problem dealing with (1269) and (34578) while we probably would, because we don’t see a clear reason for it. All of these techniques are just ways of dividing the sudoko numbers into two sets. Which by the way is the normal definition of bifurcation!!!!
A chocolate teapot quintuple of 12/24/34/39/19 in column 2. I never thought I would see the day. Well played, SudokuExplorer. Well played.
I was pleased I was able to solve this before watching Simon's solve. As far as I can tell, the "finned Y-wing" to eliminate the 1 at 35 minutes in is a necessary step in the solve. I completed the puzzle to a far greater extent than Simon did before I reached a deadlock in the end game that I couldn't break without using that step.
There was some extra nice logic! Like the number 5 in the corner boxes is going like a steering wheel round the grid, so does also the last remaining high number (6-9) which had to go into a white cell in each of the corner boxes. Even if we do not know which high number will go into the white cells, we know that there must go exactly go one extra high number in the outer columns and rows. So the last high number in the corner boxes must go in one of the white cells next to the number 5 or it has to go in the other state of existence where it will need to go in the opposite side in one of the other two other white cells. Once we notice this we can look at the effect. Assume that the remaining high number is not next to the number 5. In that case it has a effect on outer columns 1 and 9. We know that there are two high numbers in those column in the right-top and left-bottom box and that those numbers are 6 and 8 since these corner boxes contain already 7 and 9. And this as an effect on row 5: in the green cells of this row now there cannot go a 6 and 8 because of the logic explained, so the green cells must be a 7-9 pair which cannot because of the 7 given in that row. The same conclusion can be drawn apply if we look at the top-left and bottom right box where we then miss the numbers 7 and 9 in the outer row’s 1 and 9. Therefore there must be a 6-8 pair in column 5 which cannot because of the given 8. By this logic we know that the remaining number in a white cell therefore must be next to the number 5.
Simon, a little suggestion, when explaining SET that has "double-counted" digits, I feel it's easier to understand and easier to see if you do it in two steps
in this case, you would first look at the horizontal stripes, remove digits that are both in green and purple, and explain:
"now, purple contains exactly the same digits as green, plus 2 full sets of the digits one to nine"
then you could look at the vertical stripes and do the same process as normal, ending with the same pattern
Hmm, Actually I have a hard time understanding your version and how your version is different, maybe cause I'm not fluent in English. But I understood Simon perfectly. He is really good at explaining things! I really like listening him speak :)
@@sandraraituma That's because my comment is not the explanation, it is a suggestion on how to make the explanation.
if Simon were to explain it this way, he would show it on the screen and he would do it with his words, I'm sure you wouldn't have any problem understanding it then.
The biggest difference between the two ways and the reason I think this one is better is because you don't get "2 greens, 1 purple" squares, which are always hard to explain, and that Simon has to leave for last to explain them separately.
Another way is to do exactly as Simon does now, but using a separate colour for the rows and columns. Then the corners show 3 colours, which make it clear that they are double counted.
Your way more clearly explains why the corner squares are colored green in the end, but needs extra explaining how purple and green are equal. I do like your explanation a lot. I'm sure some students will prefer yours and others will prefer Simon's.
@@bodemeister118 Using similar colours (red and orange for instance) might help make that clearer.
Ha! I got it! You looked for geometry, but I just noticed the number patterns being reversed/juxtaposed. Pattern Awareness really helps on this one. I noted the 1,2,3,4 sets in the center aisles(?), then the radial nature of the numbers on diagonals, then realized that whole boxes were reversed, but also slightly jumbled. Then just went about solving. I got it all done and found the center/right 1's and 3's were jumbled. I noted which parts were seemingly well-mirrored, erased everything else and started from that point.
Different methodology, same result. The geometry knowledge certainly helped you get if faster, and without an errored answer, but I was really happy to solve this on my own then come back to your video to learn the geometric approach.
Simon is better than any old computer!
Your ability to explain these higher level techniques is outstanding, makes it really fun to follow along
This sounds exciting!
The best thing about these videos is hearing you get more excited when you start to understand or "get" something, I know that feeling when reaching a breakthrough so well
Looking forward to see how Simon outfoxes the computer!
Great video, I never knew about that beautiful geometry trick.
I had initially found more digit pairs than you though, and after you found the pairs 13, I used the same logic at the top which allowed me to find the digit pairs 34 in the second square. That gave me the 3 and 1 from your pair, and the rest of the sudoku pretty much solved itself, nothing tricky after that.
Every time you spot some of the crazy clues I couldn't even think of, I wonder what the video be like if you had eye tracker showing the way you scan sudoku.
you'd be dizzy af.........
Wow that was super impressive. A lot of it went over my head, but all the parts I got were very clever. This channel always amazes me. Also I love your voice and calm demeanor. Keep up the good work!
41:16 ... took me about 9 minutes to spot the break-in, then I had somewhat more roundabout ways at two points (one where Simon deduced the 9 in c9, the other when reaching the quintuple in c2), but in the end, I made my way over the finish line.
Nice classic!
Your brain is amazing! I do soduko all the time and only found this video by accident. Your comments on geometry made me think. I'll be paying more attention to the geometry in my puzzles in future
No "Let’s get cracking!"? :-O
I haven't finished watching the video, but I'm currently at 34:57 and you can see the beautiful pattern of numbers surrounding the puzzle. The groups of 597, 163, 824 repeated on Column 1 and 9 of the puzzle. Same with the group of 685, 394 and 127 on Row 1 and Row 9. Really genius!
This puzzle is really hard is you haven't been watching Simon playing with digit sets recently, but reasonably straightforward if you have. I quickly realised something was going on with the boxes Simon marked in purple, and Simon has used the digit set pattern this puzzle relies on several times recently.
28:14 Hearing him say he trusts his pencil marks right after clearing an errant 8 from the middle square of the top column made me feel some sort of way.
That said, I'm just in awe of the logic on display here, and the explanations that go with it. It's extremely difficult to communicate your thoughts that clearly. What an incredible puzzle.
I hope some of these cool techniques people have used to design puzzles that you solve end up in competitions
Also, I really think the creativity of puzzles has sky rocketed ever since you and Mark started this channel up. You’ve done absolutely amazing for the world of sudoku
Bro sees the most high level and logical answers that take me a bit to see and understand, yet I also find myself screaming at my phone saying, "IT'S RIGHT THERE, YOU WERE JUST LOOKING AT IT!"
34:40 A W-wing is most likely the simplest way to resolve the rest here, (Eithe)r r3c3 or r5c3 is a 1, both of those cells see a 1-3 pair r2c7+r5c5, so one of those must a 3, both of those see the 3-4 pair in box 2, ergo r2c5=4.)
Nice! (Btw pair is used for a pair of cells rather than a single cell with 2 candidates)
I have no idea why TH-cam brought me here, but this was fascinating. I had no idea sudoku could be like this!
I cannot believe I just spent 40 minutes watching somebody else play Sudoku.
Very nice video. The first time I became aware of Sudoku.
BUT: You said that the computer couldn't solve the problem. That spurred me on to give it a try.
Took me one day to implement a Rust program to solve the given Sudoku. Was a lot of fun.
But solving this without a computer is truly phenomenal.
As we Aussies like to say: You bewdy, what a ripper!! Two months ago I would have had no idea how to proceed beyond pencil marking the possibles.
But I have seen Mark's explanation of the Phistomefel Ring and its variant a couple of times. And that got me started with this puzzle. It took me more than an hour (oh alright, 77 minutes) but I persevered, kept turning the steering wheel and eventually got there.
That was incredible. I doubt I would have ever worked out all those deep details of the solution.
Extremely weirdly, everything the computer needs to solve this puzzle without bifurcation is the 5 in box 7, So I guess all that high/low digit thing was just to find places that couldn't be fives.
This was impressive! I try to do these puzzles without notation just to exercise my mind. I’m so glad I didn’t try that with this puzzle and decided to just watch you do it.
Anyone else hear Simon's voice when doing their own Sudoku puzzles, sorta narrating out what's going on?
I give a running commentary, as though someone was watching...
JESUS, TAKE THE WHEEEEEEEEL.
That's the only way I would have gotten anywhere in this one. Beautiful solving, I'm going to have to go back and watch the explanation of the purple/green thing again.
Really enjoyed this, fascinating to see human vs. computer... reminds me of ST:TNG when they shut down the computer to have Picard manually navigate the ship to safety 😆
BTW On a video some time back someone commented that he appreciated you starting to take more time after puzzles to give your final thoughts and sum up your take on the puzzle, and I really agree there. Thanks for another great vid!
Very proud that my first thought was phistomefel… how well you have trained us! X