Extreme Sudoku: Human Logic Trumps Computer Guessing

[@DesmondAltairEzio]

the sudoku grader has the toughness score for this puzzle as Extreme: 525 If you grade it after putting Simon's first digit it downgrades to a Gentle/Easy: 61 amazing

[@Schilani]

That's kinda ridiculous to read. Just one number being the difference between "nigh impossible" to "approachable"

[@Playmaker6174]

I mean, it feels so badass when you use such a powerful technique that even computers can’t figure it out

[@HonkeyKongLive]

It's amazing. Once that 7 is there even just watching on my phone I can rapidly solve, but before the 7 is there I have absolutely nothing.

[@davidissel7980]

I tried the puzzle before watching the video and got nowhere. At all! Then, I read this comment and watched the video until he placed the first digit and stopped the video. I was easily able to solve the puzzle after placing that one digit. Amazing. However, his logic was still baffling. :)

[@FryGuy1013]

@@Playmaker6174 It's not the computers can't figure it out. I put this puzzle into my Z3 solver and it spits out the answer in less than a second by brute forcing it. The solver Simon used is one that tries to solve it in a "human-like" way, by only applying rules that humans use.

[@arielmaoz306]

The one thing I like the most in your channel is the excitement in your voice when you discover something imprtant, it is just like a child finding a fire truck for his birthday and that just make your videos even better. and again, I really love your content and Im so happpy that you upload so many videos!

[@grahamrskelly6042]

Yes! in this trying year the world needed something a bit of joy. What a Channel, what a Channel!

[@GiveupforJesus]

His excitement is contagious. The good kind of contagious lol

[@no-feetmcgee5577]

"About a million Goodliffes--I mean, bifurcations..." wowwww the shade XD

[@vakilian]

Literally laughed out loud. My friend asked me what was so funny and gave me a curious look when I responded "its just this sudoku strategy video"

[@margaretmcnarry4298]

Laughed out loud when Simon said this!

[@DipanGhosh]

Yes, these jabs are getting out of hand...

[@olanmills64]

daaaaAAAAAAaaaaaammmmnnn!

[@honigschlecker1]

Yeah - that was hilarious. 🤣

[@Alex_Meadows]

"Do have a go yourselves!" Haha, no, I don't think I'll be doing that.

[@paulcook2961]

Absolutely you should. It took me 10 minutes and I normally take 30+ minutes on the classic sudokus published here. By the way, I have solved ALL the puzzles published this year APART from a few classic sudokus. They are the hardest to me. Came back to watch the video and I didn't spot any of this clever odd/even stuff and didn't need to. Just had to do a "non-computer-like" trial right at the start then it was easy. The thing about the computer solve is really interesting and Simon's odd/even colouring is really interesting but it would be a shame if that put you off.

[@Henrix1998]

@@paulcook2961 now do your trial and error on paper

[@paulcook2961]

@@Henrix1998 That would be unhygienic!

[@AFastidiousCuber]

@@paulcook2961 So you're saying you bifurcated? What was your guess?

[@SadisticSenpai61]

@@AFastidiousCuber That's what I did. As the 1/7/3 in box 3 all had only 2 possible positions and the placement of the 1 would determine where either the 7 or the 3 went, I started there. It was pretty easy after I was able to place the 1. It still took me 21 minutes, mind. I'm hardly a speed solver.

[@futurefox128]

Ok, from what I'm seeing here my understand is: this was basically MEANT to be solved by humans => Thinking of two groups in terms of even vs odd is so much easier than to do the same with seemingly random groups. What I mean by that: If you think about it, the creator could have chosen to simply permutate the digits. After all "even digits" in classical sudoku just refers to a set of 4 distinct digits, while odd refers to a group of 5 other digits. So they could have made it much harder by choosing another set of "4 vs 5" which don't correspond to even and odd. It would make absolutely no difference for the computer solver, but for a human, it would probably make it MUCH harder to see the pattern there and deduce something from it. Edit: Btw the same is true for classical sudokus that use groups of "low digits vs high digits". This is basically a super hard sudoku with an easter egg for humans. Mad props to Simon for spotting it though!

[@AFastidiousCuber]

You're right, and I think writing a program to detect this kind of thing would be difficult because you'd have no idea what rows/columns and what digits would be involved. The only way I could think to check for this sort of thing would require looking at every possible subset of the digits missing from every subset of the rows/columns. There's 9 columns, 9 rows, and 9 digits, so a brute force search would have to check (2^9)*(2^9) choices for the columns and (2^9)*(2^9) choices for the rows in the worst case, for a total of 524288 cases. Still though, a modern computer could probably do this fairly quickly, especially since it is highly parallelizable.

[@futurefox128]

@@AFastidiousCuber What you are saying is very basic stuff for "brute force". A computer even with a bad CPU can solve that kind of stuff usually in less than 1ms (1 millisecond). It's the advanced tricks you have to use that make this one really outstanding. The algorithms here, even those used by the AI are genius... and if you think about it, there was someone who actually coded this, a human being: ANDREW STUWARD. So this person that coded it is a genius too by my definition.

[@AFastidiousCuber]

@@futurefox128 I meant that it would be difficult to come up with an algorithm which could detect this efficiently without a brute force search, not that the brute force search would be difficult to implement. I imagine most of the algorithms that Andrew implements in his software are brute force with some minor optimizations. Though, finding a more efficient algorithm probably would only save a few fractions of a millisecond at most, so I suppose it really isn't that important. It would matter more if you were interested in detecting this pattern on general n^2xn^2 boards, but in that case I suspect this would become an NP-Hard problem.

[@roland9189]

Yep, you are entirely correct

[@xaostek]

It does feel like this puzzle was laser-targeted at Simon, as he's been shown to be a fan of using odd-even logic even in places that don't require it. Perfect person to showcase this puzzle!

[@jeythegrey]

I'm also lost for words about how you were able to find this nice deduction just from looking at the puzzle... how do you lift your head in the morning with a brain that big?

[@Kelters]

Simon's grey cells are filled with only odd digits. That's how.

[@garretttoombs2259]

Probably the most underrated comment!

[@jeythegrey]

@@Kelters well done sir, well done! :]

[@GrahamFirst]

🤣

[@niceman9605]

@@Kelters this is kind of verbal intelligence

[@LexicographicalPedant]

I feel like I could see Simon in the street and not recognise him. Im just so used to seeing him from a higher angle, while he makes British noises

[@maverickstclare3756]

I like how he doesn't look like himself in every other photo :)

[@kayleawilson]

Bobbins lol

[@LexicographicalPedant]

@@TPH250290 yes of course. If you noticed, I said, “recognise”, not “recognize”. Now, it’s not perfectly distributed between British and American English, unlike something like “colour” and “color”, but that’s the only example I found in my comment.

[@jsharvey1961]

"British noises" ROTFLOL :-)

[@anthonybailey4530]

There's lots of good-natured ribbing re bifurcation in both video and comments, but I want to offer praise instead: what a fantastic and insightful idea Mark had for how Simon should present this puzzle! The resulting video worked so well. Felicitations to you, Goodliffe!

[@GrouchierThanThou]

@@jpryan90 I can never understand why people have a problem with using uniqueness. The uniqueness of the solution is just as much a part of the puzzle's setup as any other rule. For you could easily set up a sudoku with more than one solution and make it the puzzle to find all possible solutions.

[@stevenape377]

@@GrouchierThanThou It depends on what question you want to answer. If you view the only goal as finding the unique solution, then you're right of course. But if your goal is also to be able to verify that a puzzle has just one solution, which would be important if you are a puzzle setter for instance, then you can't use those techniques. Techniques that don't use uniqueness therefore are a bit more generally useful. Everyone can make up their own minds whether they care about that or not.

[@koomber777]

I understood all the words in this video and have absolutely no idea what just happened. Magic.

[@brianarsuaga5008]

I like the royal we in "the computer could not deduce what we're able to see here," as though I was at all able to follow along

[@Mephistahpheles]

That's one hell of a compliment, "Let the computer try it first."

[@rickwoods5274]

"All the normal techniques I know are completely and utterly hopeless. With that, let's get cracking!" I admire your relentless optimistic perseverance :)

[@susanne5803]

Best way to deal with life ...

[@sniebe]

Beautiful solve, but am I the only one who doesn’t mind it when Simon’s videos are longer? Love the enthusiasm and patient explaining of logic, even insane logic like this one

[@derekjc777]

But the longer videos are usually harder sudokus. Much better watching the shorter easier ones if you’re learning. The technique in this one is quite obscure so surprising it was such a short video, particularly with the prelude of the computer solver going haywire! But it’s a good example of an obscure technique making what initially looked like a hard puzzle into a relatively simple one. So this may be a bit complicated for a beginner. I’ve seen Simon use this kind of technique in a couple of other puzzles, possibly also by Sam, so it wasn’t completely new, but the first one I watched was eye opening; although it logically made sense it added extra constraints across the puzzle making it easier to solve. I think the first one was called A Brand-New Technique for Classic Sudoku.

[@sniebe]

I learn just as much from the longer videos, plus I love following Simon struggle through the harder solves, his relief and excitement at the end is very infectious. I am not complaining about the video length, just trying to convey that I could watch him solve all day long and still be happy. Good thing I only found this channel four months ago, I have lots of old videos yet to watch.

[@ChrisWCorp]

What a crazy technique applied on a classic sudoku.

[@GrahamRSteele]

Wow. I think the person that needs to take a bow, is you, good sir. That one piece of logic at the start (not wanting to give anything away) was a stroke of genius. The puzzle opened right up after that.

[@tomcollyer641]

I'm not sure if anyone reads my comments any more, or whether people have been following the discussion on my blog that Simon very vaguely alludes to - but suffice to say you did not need to do MSLS (we definitely need a new name for that) to solve this puzzle. It is humanly solvable in an even more simple manner than is displayed here - all you need to do is go one step further from Phistomefel's theorem into Fred Stalder's intersection theory. And I guess we've already seen a couple of puzzles like this which demonstrate much the same thing - which is not to say that this isn't beautifully executed by Sam (as it always is when he has particular idea in mind)

[@samcappleman-lynes6914]

Whenever you make a comment or post about this bleeding edge stuff I'm reminded of the parable of the blind men and the elephant - both of us are looking at the same object but never seeing quite what the other sees! In fact, I was really hoping you would comment here because I was sure you'd have another way of looking at the puzzle. Maybe I need to think a bit harder about the intersection theory stuff...

[@tomcollyer641]

Sam - the required intersection fir this one is actually one of Fred’s examples! This is probably worth me blogging with pictures and stuff, but using that you can immediately deduce that the 10 empty cells in the odd row/odd column intersections must contain the 6 even digits in the even row/even column intersections, and then 4 more evens from a (1-9) set. So you get they are even by counting up to 10, rather than 20 :-)

[@samcappleman-lynes6914]

@@tomcollyer641 Wow! That's super-duper neat! It even gives you the odd digits in the even row/column positions too! Is "Fred's theorem" to MSLS as "Phistomefel's theorem" is to SK Loops? Probably. What a fascinating time for Sudoku.

[@philipnewmansudoku]

@@samcappleman-lynes6914 (and Tom), ultimately the "hard" part of both MSLS and Fred's approach (and Trevor's, for that matter) is the same - identifying that the puzzle splits into two groups of digits, rows, and columns. I don't know that Fred's and Trevor's visualizations actually have any more (or less) solving power, but they're beautiful ways to see it. Here's a harder (though less pretty) example. (Andrew's solver gets absolutely nowhere with this one.) 1 . . 4 . 6 . . . . . 2 . . . . . . . 3 . . 5 . . . . 8 . . 9 . . . 6 . . . . . 7 . 3 . . . . . 6 1 . . 4 8 . . 5 . . 9 2 . . 9 . . . . . . 8 4 . . . 1 . . . . 9

[@philipnewmansudoku]

And Tom, MSLS was originally developed back in 2012 by David P Bird (who has also put together an Exocet compendium) - his original name for the techique was "Sharks", because they eat all the fish. ;)

[@djh0151]

As someone fairly new to sudoku I am agog. I have followed the channel for a little while and some of Simon's logic is mind blowing. I long to be able see that far outside the box. Amazing solve.

[@jameswiebe8956]

I do believe that we are watching the birth of a new sudoku logic. The Tatooine puzzle was an interesting one-off, but this shows that you can make an entire puzzle around it. Genius, Sam.

[@andrewnelson2525]

One of the most charming aspects of these videos is that Simon can make the most brilliant leaps of logic and amazing insights, and he is ... humbled by the experience. Humbled!

[@ChrisWCorp]

I watch Countdown but I've never heard of Sam.... Oh no, wait. I watch Cats Does Countdown. That's right.

[@adityajogalekar2376]

haha me neither

[@prashanthsaravanan9289]

I am you

[@PH34RB]

I love the game, but man after watching 9/10, regular countdown is like watching paint dry. It made me really appreciate brit humour and wit.

[@9MRSG]

Lol

[@yishsaur7657]

My time for this one: Just 0:04 for looking at it and saying: No

[@rolfremie9634]

Idea for the new software: highlight selected cell by drawing a red border around it instead of colouring the cell. The purples turning orange when selected confused me the entire time.

[@Zombie-lx3sh]

Or just make them yellow instead of applying a yellow filter on top of the underlying color. Highlighting the cells' borders would be terrible.

[@rolfremie9634]

@@Zombie-lx3sh agree, I realised later that borders aren't useful for highlighting multiple cells

[@ghosty918]

Stripes also work fairly well for highlighting multiple boxes

[@GamerBadger82]

25:18 there's something special going on with this puzzle if you imagine it wrapping around from right to left (like a cylinder) the orange squares are alternating 6-8, 2-4, 2-4, 6-8, 6-8. Then also there’s something about the distance between 1-9 (0,3,0,2,3,2,0,1,0). Maybe it's just the grain of the puzzle, but it feels like i’m seeing a little of the construction methods?

[@tzampini]

Wow! Recognizing this odd/even arrangement, especially when odd/even techniques are rarely used (if ever) in sudoku, is a stroke of genius on your part. Bravo!

[@TikeMyson69]

Imagine if he let his friend write his biography. All the wild sudoku parties and stuff.

[@paulcook2961]

Would a sudoku party have exactly 45 guests?

[@TikeMyson69]

@@paulcook2961 405 guests. They could make a people sudoku.

[@robb1267]

There are a lot of 'naked singles' jokes here.

[@derekjc777]

Only nine people allowed in each room. Who will be the extra “odd” gooseberry?

[@michaeljarcher]

Non-Stop Biofication. But plenty of "Cracking"

[@donalodonoghue7554]

Beautiful puzzle and Simon’s logic is impeccable, as always. For us mortals, however, there is a 245 bent triple r1c8, r2c1,7, which leads to a naked single in c9 and no need for bifurcation.

[@alvaropallete]

20:24 Human logic: let's put 1s pencil marks in the same row of 1 in box 6. Just kidding, this video is a good demonstration of the new technique shown some days ago. Bravo Simon

[@catwoman7462]

I've watched a few of these videos over the past few days and have learned a lot of tips. I managed this grid in just over 23 minutes without watching the video! The best tip for me was to only have two pencil marks in each box. Usually I'll have a box filled with pencil marks.

[@Rubrickety]

I'm looking forward to Simon's new culinary/sewing show, Cooking with Bobbins.

[@Anne_Mahoney]

First recipe: parsnips. Buttered.

[@Varksterable]

@@Anne_Mahoney Cooked with gas.

[@dp1381]

What an awesome puzzle! I cannot comprehend how people are so smart that they can set sudokus like this. There's no way I would have figured out the trick without the video, but I wanted to give the puzzle a try once I knew the trick. So as not to totally copy Simon, I began by subdivided the grid into odd and even ROWS rather than COLUMNS. Once I determined where the odd and even digits go in the blank areas of the grid, I deleted the colors I used to initially subdivide the rows and noticed something lovely that is easy to miss in Simon's grid: the blank areas of the grid get colored in to complete the checker board pattern present in the array of given digits, and the cells alternate odd-even-odd-even along the diagonals!

[@ChilapaOfTheAmazons]

What I got from this video is that bifurcation is a perfectly legitimate technique. 🤪

[@LexicographicalPedant]

As a Computer Science student learning Artificial Intelligence (AI), this was a pleasure to watch. Although I do not know the specifics of the Sudoku solver, it is often possible to think of some test case where the AI is fully stumped. A good tip is, most AI algorithms work under the assumption that the other player plays ideally. So, if you can find a way of figuring out a way of playing a non ideal move without handing it an obvious victory, you can beat some AI’s. Its about finding the right non-ideal move.

[@imogenoliver]

Well all I can say is that I’m glad I’m not the only one who found the computer solver thing completely mad! 🤯

[@richardfarrer5616]

Well, don't think I'm trying this one myself despite the comparatively short video. Edit: Wow! I vaguely noted that the odd numbers aligned fairly well and that was as far as I got. That is superb. Now all I have to do is work out when the technique is useful. Kudos for measuring difficult techniques in Goodliffes too.

[@mendelsonja]

I don't think it was measuring difficult techniques in Goodliffes. It was measuring bifurcation techniques in Goodliffes.

[@richardfarrer5616]

@@mendelsonja A good point. I misspoke.

[@waynemv]

I paused the video at 13:01, with only a vague idea how to proceed. But I considered Simon's hint, figured out which cells must be even, determined that a certain cell must contain 7, found certain other cells must be odd, figured out other cells that must be even, found more digits, and then an hour later was done with the puzzle. I probably could not have gotten it without the hint, but that was enough. It was a great puzzle! Now I'm about to resume the video to see if Simon's solve was similar to mine.

[@honigschlecker1]

Actually, I'm pretty amazed that Simon didn't knew the AIC technique. Honestly, I'm using this pretty often.

[@leeprice133]

In general both Mark and Simon seem to have a blind spot for AICs.

[@honigschlecker1]

@@leeprice133 And probably rightly so - since they are usually twice as fast as me. 😉 Although in this one - I had almost the same tempo as Simon.

[@juliusseizer514]

Simon I have been watching the channel for a few months now, and you never fail to astound with that amazing mind of yours. First class. And thank you for bringing all these techniques and perspectives to us all - you have certainly helped me get much quicker at solving which makes it all the more enjoyable.

[@zackvolturo8032]

Anyone notice how the even odd highlights are perfectly symmetrical with the given digits at the start? Amazing.

[@frederikjn]

Couldn't solve it... at all... No idea how to start :) You're on another level man :)

[@hariman7727]

I solved it... by making an incorrect assumption that correctly placed a 7 in Box 3.

[@TheKelliestKelly]

This is the first puzzle showcased on your channel that I solved completely by myself! It took me 38 minutes and 31 seconds. I feel very smart now that I'm watching the video and hearing Simon's commentary on the computer doing it. When I was solving, I hit I point where I was like, "Okay, I'm gonna have to watch the video to finish now." But then I noticed something in box 6 (I forget what) and I was, "Well, hold a minute," and eventually I got it! Yay sudoku :)

[@TheKelliestKelly]

I was confused by what Simon was doing so I went back to my solving which I still had open. I hit the undo button all the way until the puzzle was blank again and I realized I made an error with my first move. I thought there was only one possibility for "1" in box three: row 2. When I went back through, I saw that both rows 2 and 3 were possibilities for "1" in box three. I got super lucky that that ended up being the correct position!

[@Merlin1908]

When you started looking at those columns, I immediately went "Surely Stalder's intersection theory is worth a look here..." and stopped the video. Turns out I was right: Using it on both rows and columns 1,3,5,7,9, you get all the odd/even information and more because the cells with even row+column already have to contain three ones, a three, a five, and a nine beyond the given numbers, which already fills in all the open cells in that arrangement, and similarly you get that all the empty cells with odd row+column have to be even, specifically containing two twos, two fours, three sixes and three eights.

[@grahamrskelly6042]

Oh and also I really did enjoy this video, watching the computer solve it, Kudos to Mark for suggesting this to Simon. What a great video.

[@Draedaja]

"no bother at all"? Well, I'd say... some bother. Also I love "Goodliffe" as a unit for bifurcations used to get a digit xD

[@Varksterable]

Unfortunately, as a unit that's the practical equivalent of using parsecs to measure the distance to your local shops.

[@he1ar1]

i looked up a 3d medusa. It certainly is a Mark technique

[@brandengagne9134]

I tried it. Got lost quick. Couldn’t get a digit. Watched the video. Stunned by the logic at the beginning and then it became so easy. Incredible work by Simon. I love the enthusiasm you have when you discover something that will help. The perfect British accent just tops it off. Absolutely incredible.

[@PaulO-mv6ku]

Nice to know how "we" beat the computer. Well done, Simon - simply stunning logic.

[@laurv8370]

Things you learn on CTC: "This can't be a W!" :D Brilliant puzzle and brilliant solving! (nope, I could not do it without backtrack).

[@brianarsuaga5008]

Accidentally came back to this three years later and... knocked it out. I've learned!

[@djmonkeyking]

Simon. Youre a legend. Discovering CTC over since lockdowns started has been one of the best side effects. Thanks to to you both.

[@Samish30]

After a second look at this week’s video where Simon introduced this amazing technique I was able to do it on my own !! What an elegant solve, beyond sudoku that’s poetry we’ve got here. Hats off to Sam ! I used a slightly different way, watching for the 20 odd numbers in raws 2, 4, 6, 8, it merges immediately with Simon’s method. I love this channel more and more every day, thanks for that gentlemen !

[@sanctionbuster]

As you said i had to do something different, I noticed there were lots of 1s, 3s and 5s. So I highlighted all squares that couldn't be any of them. I saw 2 options for 1 in row 2. Took a punt, ie a "Goodliffe" on column 8 and the rest slowly fell into place.

[@stripypurplepanther]

I tried the same thing. Once all of the positions where 1,3&5 could only be in two places in a box/column/row, I tried 1 in the two possible places in column 8, in one place the logic stalled after a few moves, but in the other it just kept going and unwound the entire puzzle.

[@athaya2992]

i was stunned the entire time watching the video. crazy pattern recognition man!!

[@brodiekane1390]

simon is such a genius for spotting this so quickly. It only took him a couple minutes from start to start counting the even digits in the rows.

[@ChocolateJesii]

"After a series of about a million Goodliffs." Haha

[@johncrotty169]

Savage call out bah gawd

[@adrianhead6272]

Human logic - "1" can only go into one of two cells in box three... one of those options fails. The other solves the puzzle. Completed in 7m05s

[@1002l]

not a clue on this one until simon explained the odds even, NEVER would have thought of that in a million years, very well done, superb solving

[@nickgidzak2804]

i think i have watched about half of your videos while playing along... and you are great help. i start a video.... and open the link to that days puzzle and play along. of course i get a 5 min advantage over you.... because you have your preamble (to be honest i don't really care about the back ground of the person who created the puzzle). So i start the puzzles... and when i get on a roll i pause the video (i often find other things that are obvious to me... but how you solve them im blind to) and i dont unpause the video untill i get stuck. today i got stuck on how to start. your help and insight is alwasy invaluable. so i normally get half way though the video before it becomes obvious. but i know without your help they would never be solved by me.

[@mustafapotur3420]

i get the logic after i watched 2nd time the entire solve. what a brilliant puzzle! and what an übermensch puzzle solver mark is. thank you all that this channel exists!!

[@nana6510]

Do you use "Übermensch" in British language? You know it's a very old German word, got famous by Nietzsche. Greetings from good old Vienna!

[@RoderickEtheria]

Tried this before watching it. Didn't have a clue what to do to reduce complexity, watched some of it, learned a bit more, managed to solve it without having to watch it fully. This is definitely a powerful technique.

[@brandonfisher5303]

Wow had to watch you show the logic for the rows and columns twice but it was incredible. Such amazing logical deduction in a number puzzle. Not only thanks to Sam for building it, but thank you Simon for explaining it so elegantly

[@alanhaysom8702]

Finally after watching your channel for a few days I had a go at this one.....Yay!!!!!... I did it...took me 41 mins but still beaming....lol

[@fugueoffiber]

The audio is fine on your laptop! I have noticed that I often have to turn my volume up for your videos, and when an ad pops up it is extremely louder than the video. I recently found your channel and like watching a video when I'm anxious, your gentle voice and British Dad charms calms me every time.

[@bulboushogwash]

I am about to admit something that may shun me from the sudoku community... first, I fully annotated the puzzle (gasp i know i know im a fraud), then, I decided to try out a random possibility and ran with that and it seems I may have accidentally solved the puzzle in close to record time !! Simon and Mark, if you see this, I know you have raised me better--you have raised me to think and apply logic and reasoning, yet i have failed you. I promise to do better next time...

[@TheAveryFilms]

just wow.... my mind is blown... I solved it rather quickly once Simon spotted that 7... I was clueless how to spot anything... had pencil marks like crazy... said forget this... started watching simon and his coloring... my jaw dropped... as soon as he said odd/even, I was like WTF! ... and was on the verge of seeing the 7 when simon pointed it out... then I was on my merry way. brilliant spot simon... so glad i watch this channel so I can learn

[@burmanphd]

I'm new to your videos. I've only watched a dozen or so, and I've been following KZbin's algorithm's suggestions. So while I loved your delight in cracking it, I missed how you came by the insight that allowed that. Because you knew something about... the constructor? ...you were able to hypothesize... something? And it worked out. (Huh?)

[@Jodawo]

That was unbelievable. That could have been an easily 15-minute puzzle for you. You spent over eight minutes showing what the computer would do. I think some really good video would be watching Mark watching this video for the first time. After seeing the computer do its calculations to figure out this puzzle and when I saw how long this video was going to be I thought for sure this was not going to be a done video. I am so glad I was wrong.

[@SudokuManiacs]

That was simply brilliant Simon... You have proved that there is always something new to learn even for seasoned solvers like us :) Simply beautiful.

[@neljakaksi]

I felt so good having solved this in about half an hour before watching the video. Then I watched the video only to realize I must have made a mistake that by dumb luck led me to solve the puzzle... That is some amazing logic and I can't begin to understand how anyone could come up with that just by looking at the sudoku for a while!

[@balkthor]

This is up there with the Miracle Sudoku at the beginning of the year in terms of greatest puzzle solves and analyses ever.

[@poopsiexpants]

Man, I felt proud of myself for solving this in 30min. And then I see you do this strategy of odds and evens and knock it out in a third of the time. Gonna start learning art I guess :(

[@slowfreq]

Time to try the puzzle for 5 minutes then give up and watch the video for the dozenth time

[@michaelhoffman2011]

would not have thought to do such a technique... great solve... Good job.

[@Coyotek4]

OK ... I am just absolutely *astounded* by the way Simon solved this one.

[@jdyerjdyer]

MSLS did break this one wide open, but to see which to use is the hard part. I tried many different combinations of rows and columns with two and three of the odd digits noting that these were the most common, but sadly I had to take a hint from you to see that I needed to use all of them in 5 columns to locate the even digit placements. Very interesting tool and I've definitely used it a few times to make difficult puzzles easy, but this is a first for using 5 digits at once! Mad genius! Simply mad!!!

[@LightDhampire]

I needed the video's help with setting up the MSLS, but then it was a straightforward solve.

[@unperrier5998]

Wow impressive puzzle and solving. Contrats to both of them!

[@nekogod]

Audio and video are fine! Beautiful puzzle. At 23:00 that 9 was already resolved because the 2 orange cells could only be even.

[@charleychetto5247]

Great solve. I can only assume the biography 'friend' is Simon's Best Man, whose speech was worthy of the name!

[@Nyledam89]

Finally solved one without help. :) Took me 26 minutes and I'm really pleased with that.

[@junkmail2505]

After he explained that the purples needed the maximum amount of events it was surprisingly easy to solve the rest. Took me only about 20min after the coloring.

[@moonglum101]

This puzzle is all kinds of awesome. When I had a go at it my feeling was that odds versus evens was a relevant factor but I couldn't identify why until I saw Simon pick out the five odd numbered columns and start to think about where even digits could go n them. Bonkers! What a puzzle! I was in a state of disbelief after getting the first digit and then another and then another. More puzzles like this would be most welcome.

[@user-gq4lo2cz9p]

What an amazing puzzle! I actually do think I used a completely different break-in with the same technique: 1. I high-lighted column 2,4,6 and 8. 2. I looked at the digits 1,3,5 and 9 as I noticed that they allign similair a lot. 3. If you count how many of these digits can be in all rows of columns 2,4,6 and 8, you find out that there are exactly 16 possibilities for these digits and therefore that at least has to be true. 4. In particularly 6 cells become restricted: R2C8;135, R4C2;15, R6C2;19, R6C4;139, R8C4;159, R8C6;19. 5. This allows to use the 7s in box 1 and box 5 to use them on box 4 and do some more regular sudoku with them. 6. Rather surprising, the 7 in box 3 was also the first digit that I found. From here on I guess it was just going on with sudoku. Though I'm very proud of my solve, you're way of solving this looks like a much more intended way on looking at these digits. My break-in is probably coincidence. Furthermore, I hope that I don't need to use this technique in a sudoku where I don't suspect that this technique is necessary for solving it! :) I'm also very curious that if a computer would be familiar with this algorithm and is efficient in finding it, weather it would rather find Simon's break-in or mine.

[@Kinada]

Took a brief look at this and decided to just watch the video, stopped when he talked about there being 20 evens in the 5 columns and had a go at it from there. Solved it in a bit over an hour and a half with a short food break in the middle. Knowing where to start off was very powerful and the puzzle even felt easy to understand at that point.

[@rebeccanorth6349]

Logical path wins every time...❤️❤️❤️❤️ your enthusiasm & excitement Simon 🤙

[@balthazarbeutelwolf9097]

Took me 37 minutes. Started off classically. Then spotted 3s were heavily resticted on the right-hand side, with one very forcing chain. Tried that to rule it out, but it actually solved the puzzle.

[@AndreAy1975]

Solved it after the seeing the start of the video, where Simon beat the computer. Great idea!

[@hippophile]

After you worked out the parity issue for the rows I spotted the same was true for the columns. And the puzzle was suddenly dead easy!

[@ArloLipof]

Fantastic solve! 🤯

[@BigAsciiHappyStar]

A tough but fair puzzle. The break-in is “gettable” for a solver who knows what he’s doing. Moreover, Sam CL achieves this in a classic Sudoku with no extra rule-sets, and there is no unintended solution path (as far as I can tell). My only regret is not having discovered Tom Collyer’s excellent blog sooner. This puzzle alone proves that Sam CL can mix it with the likes of Mitchell Lee and Phistomefel.

[@Colin_Holloway]

I just came back to revisit this one and found that with newer techniques this was actually a lot easier! There's a Phistomefel Ring on 1's to give the first number, which gave all the 3's and then it was just simple X-wings to finish! I find it fascinating that puzzles that weren't computer solvable 3 years ago are almost trivial now.

[@SadisticSenpai61]

Woo! I got it in 21:36! Ofc I also got extremely lucky with my guess/test choice. As the only two choices for a 1 in box 3 would also force a 7 or a 3, I decided to start by guessing with that number placement as it would let me place a number no matter which position turned out to be invalid. Then once I had the 1 placed, it all just went from there pretty easily.

[@potatoskin5168]

I thought I knew Sudoku, then I watch your videos... I have no idea what's going on but I am intrigued

[@TheofanisIII]

The techniques the solver is using are not actually bifurcation, they're chains of strong and weak links between candidates. The first one specifically is a loop, turning all of the weak links into strong links, which eliminates all of the candidates that can see bot the beginning and the end point of each link.

[@chrisclark4813]

Just finished the Pacman Puzzle, took a while but I got there. Fantastic channel, great how you two guys compliment one another (skill wise). I love Sandwich Sodokus, (guess they're slightly easier), is there a way Sam could provide a blank sheet with spaces to add outside digits? I could then play any Sandwiches I could find. Your Channel would obviously still be the Go To, but you guys are becoming a service provider for thinking people. Please keep up the great work. (Give Victoria a ring and have a go on 'Only Connect'.)

[@bosoerjadi2838]

I used brute force and a lucky guess. Solved it in 12 minutes. 1. I filled in all possible-digits in each possible-squares. 2. I noticed the 67 in D7 and the 367 in D9. 3. I noticed that if I'd choose to put a 3 in B9, all other 3s would immediately follow suit. But more importantly I'd have two double pairs (24 and 67) in block DEF789 which would bring much more clarity. 4. If I would encounter an impossibility, I'd reset and would know that the lower 3 in that utter right column would be the one. And go from there. Except without any double pair. So I guessed that B9 should be a 3, crossed my fingers., After all 3s were eliminated I started exploiting the double pairs to identify singles. And to my pleasant surprise every single I found created a new double pair to be exploited for singles. Smooth sailing that way, all the way till the end. I spend most time deciding what my first guess should be. Strangely, I'm not feeling guilty at all for guessing. Because I feel that this puzzle was meant to drive people who purely rely on logic and advanced techniques stark raving mad. And now I'm going to enjoy watching this video. (I'm always curious whether the sudokus that involve guessing turn out to have more than one valid solution) Edit. I arrived at the same solution. I'm surprised at the reasoning using odds and evens and impressed by how you've arrived at it. I felt the same joy you did when it turned into a ridiculously simple puzzle. Except that mine was driven by relief. Yours by the confirmation that your newfound method had actually worked.

[@mikesummers-smith4091]

"Unfortunately, I'm not really well-versed enough with multi-linked locked sets." At last! Something we have in common.

[@ryfors]

I just wish I understood what Simon was saying ^^' This theory is beyond me

[@Il_Dilettante]

I saw the odd digits but didn't understand that they interacted with the evens, but after following his video just to the part where you mark the even digits in the rows, it was absurdly approachable, and was the first puzzle I think I've ever verbalized my appreciation for (in my head)

[@lesternielson9280]

Absolutely Brillant!

[@daniellassander]

I wouldnt have a clue where to even start lol, really smart solve man!