The Greatest Discovery In Sudoku History?

[Music] thank you hello and welcome to Wednesday's edition of cracking the cryptic and I hope you all had a good Valentine's day yesterday uh and in fact the puzzle on the screen is yesterday's puzzle because Mark is up to his nefarious tricks and he sent me a link to today's puzzle which you'd like me to open live on webcam so why don't we do that now and we'll click this and we'll click this and we'll see matrical by fafford fafford um what's the whoa whoa whoa whoa whoa whoa well that's not got a lot in it that's not nine by nine four five that is hang on hang on I got what is going on that is 11 by 11 it looks square there's not much in this grid draw all right let's read the rules Madrigal by fafford draw nine none overlapping three by three boxes and place the digits one to nine in each box okay digits cannot repeat in a row or column cells outside the boxes should remain empty Maverick's just taken off maybe Maverick's going to start re-emerging onto this onto the scene and the cracking the cryptic videos digits within a cage must sum to the sum to the given total as only one cage this orthogonally adjacent digits can never be consecutive being a one to two ratio sum to five or some to ten that's absolutely ridiculous that is absolutely ridiculous if that is that is amazing I mean frankly that is amazing Madrigal by faff I've never heard of fafford why have I never heard of bafford because fafford appears to have come up with a puzzle of sublime miracle-esque genius I mean it's absolute nonsense it's a um it's what they call these puzzles deconstruction it's a deconstruction puzzle in the sense that we don't know where the three by three boxes live we and we get one cage that that's got to be the most remarkable Discovery in the history of Sudoku if that Souls because that that is absolutely amazing um sorry I'm just a bit lost for words I'm I'm stunned by that I'm just simply stunned I'm also stunned by the fact that I haven't heard of this puzzle is it brand new I've no idea because well there are a number of possible reasons it's possible it's absolutely impossible it is impossible and nobody solved it or very very few people have solved it so Marx is trolling Me by sending it to me that's possible and that might be why I haven't heard of it because uh it's just impossibly difficult but imagine imagine this puzzle has a logical way of solving it and it's been solved by a reasonable number of people and it's achieved a high rating um then I I feel I've been negligent frankly in not having heard of this because this that is absolutely amazing magic why is it called Madrigal I don't know magical sun is to do with church singing isn't it um I'm not sure maybe it well maybe we're about to have a religious experience in solving in solving this puzzle anyway let me let me do some um do some announcements I have just read a most wonderful interview it's in the new New Yorker magazine which um I don't normally take but it's uh it's available this interview online and it's with the legendary will shorts who is a friend of mine will um as many of you will know has been the New York Times crossword editor for well for a long time I think coming up for 30 years I want to say an absolutely Charming Man and um yeah just sort of talking about the state of crosswords at the moment the state of words at the moment all sorts of stuff in there it's just a delightful read so I commend it to you anybody who has an interest in Puzzles I think would enjoy it um birthdays I've got some good birthdays to do today Ender Ender my friend you have a cool name and I understand you're eight years old today this is absolutely wonderful um these these young people who watch the channel um and I understand that you named your friend's dog bobbins that I applaud you for um and your mum Crystal wrote to say that you do watch the channel and you'd like a shout out so end a happy birthday my friend um now George from your wife Anastasia um she described you George as an amazing husband a brilliant friend and a big Sudoku lover and she assured me that there will be cake so you are in for a great birthday and happy birthday George um Liam from your fiance Val and Evie who love you very much um so Liam happy birthday to you and out mapped now your wife Becca wrote to tell us um basically that you are a wonderful husband and I can't actually read out the whole of the message that Becca sent us because it will make all other men watching this video feel entirely inadequate um but I know that you make Becca incredibly happy so uh so Matt you definitely deserve some cake um and then finally Thai Thai you have turned 25 today thank you very much for your email we appreciated it mightily uh it was full of kind thoughts and Ty I hope you get your chocolate cake today so there's some lovely birthdays there and just the other thing is to mention that if you are a fan of the channel on patreon then today is the last day that you have if to submit your solution to the glum hippo fossil hunt and be in with a chance of getting a shout out you still have a few more days if you just want to win the plushie I say just want to win the plushie we have never had a prize that is so soft sort after people are telling us exactly how much they want the plushie um so if you want a chance to win the plushie you have to get your answer in by the 20th so you've got a few more days but if you want to shout out it's got to be it's got to be today and very well done to the following who have sent in correct entries Mike Daniels Dr G Hunter John Jameson skilinsky Andrew montillioni John Andrew McCullough Thomas helm deederick Jessica Friesen and Winnie Schmidt Veena Van Heusen I think Livy Roberts and Nick palotti very well done indeed now I am anxious I have to say to have a go at this magical by fafford um I've read the rules so all it remains to do is to say do have a go at the puzzle yourself the way to play is to click the link under the video as usual now I get to play Let's get cracking um ah how do we do this so there is some rule about deconstruction puzzles isn't there I'm not sure how useful it's going to be in a in a puzzle where we know nothing I think what we're going to have to do is to work out I have a feeling I've done a puzzle before that's got that's had a constraint similar to this and it's very hard to even Constructor box that works like a three by three box that works so maybe that's where we start I was going to wonder about geometry to start because I think assuming this is the same size as other deconstruction puzzles I've attempted before you can prove something like this that those cells have to be in different three by three boxes of the puzzle because otherwise you run out of room to actually put nine three by three boxes in but let's not start with that let's start with um we could draw a box couldn't we let's draw a box in the grid here and let's try and work out whether or not it's easy or hard to construct so we've got to put the nine Sudoku digits in here such that none of them are consecutive none of them are in a one to two ratio none of them sum to five and none of them sum to ten so which is the most restricted digit that's what I'm asking myself um we want something that's effective we want digits that are affected by black crop key dots don't we so we can bring that in so it's either going to be three 4. 4 or 6 I reckon I probably own probably only three or four because three and four are also going to be affected by the sum to five ratio which six and eight aren't two actually might be restricted so what can two be next to two can be 2 can't be next to one three four two can be next to five um I'm saying that glibly like I just it and any I think it's right but it would be quite easy to miss one of these relationships two and six can be next to each other I think uh two and seven can be as two is not that restricted two two and eight can't be and two and nine can be oh maybe I've got to use the eleven I don't know let's let's just carry on for a minute three what can that be next to three can be next or three can't be next it can be next to one I'd keep changing my mind about which way I want to do this three can be an X to one it can be next to five it could be it can't be next to six because that would be in a one to two ratio can't be next to seven but can be next to eight and can be next to nine three is not I don't feel that I'm getting very via four uh no four can't be next to one okay so four can't be next to one two or three off or five also oh it's four four can't be next to six either now 4 can be next to seven we need some digits for it could be let's do because we can't just hide it on its own in a corner it's going to have to be next to something for four can't be next to eight and four can be next to nine right so four only has two partners and that means that four is in a corner because obviously if we put it anywhere else if we put a 4 here we'll have orthogonal connections to three other cells and I don't think four has I'm just going to double check this I don't think four has more than two other partners it could be next to so can't be next to one because those four and one add up to five can't be next to two is in a one to two ratio three is consecutive five is consecutive six is adding up to ten with four seven is okay eight is not okay it's in a one to two ratio yes so four goes in a corner which corner should we put it in let's put it in that corner so four goes there and it must be next to seven and nine now we don't know the order but obviously we can just assign we can just assign an order because we're just trying to work out how this works and if we did it the other way around uh I can't remember if that's the same way around or a different way around but if we did it the other way around we're not changing anything um we're just flipping the grid around that axis these digits are still going to have the same restrictions so what's hard now is presumably this Square we've got to put something in the middle now what we can't put one in the middle because that would go with um nine to make 10. we can perhaps put two in the middle why couldn't that work that might be okay three is impossible that would add up to ten with seven four we've used five is uh maybe possible not sure six is consecutive with seven is the same as seven so we're not putting seven there eight is consecutive with seven and nine and nine reviews so it's only two or five in the middle right let's try two so if we put two here what can we not put next to it we can't put next to it one and three o h r ah so so one three and eight have to hide in the corners and we're left with five five and six hmm that that corner couldn't be one because it would add up to ten and couldn't be eight because it would be consecutive so that would have to be three right maybe we can force this to be incorrect now what were the digits I need to place five and six [Music] um so these are a five six pair set as six can't go next to three because three and six are in a one to two ratio right so five goes there six goes there eight is consecutive with seven wow okay so that might be possible actually I'm just going to note that down here because I want to um obviously there are other arrangements of this in terms of we could um well we could rotate the grid around the two we could reflect it um so there are you know but broadly this is the pattern of the digits that emerges if we put two in the middle but I don't think oh hang on we had the four nine the seven didn't we we're going to delete all of those squares we're going to delete this because there was the possibility that this is five as well now if we put five in the middle what then becomes difficult well probably not much because five can't be in uh a domino that adds up to five with another digit because we can't use zero and it can't be in a domino that adds up to 10 with a digit because we can't use another five so if we do this what's the problem now well one thing that does occur to me is that two is not allowed to be next to one three or eight so two is does that mean two goes in a corner hang on let me think about this because two if I put two there how can I avoid this 2 being next to a one three or an eight I can't do it because one of these squares will have to be a one three or an eight because I can't put all three of them in that Domino yes so two goes in a corner which corner we don't know okay so the two's in a corner one three and eight are not going to be next to it what's the other digit six oh six can't go next to five or seven whoa whoa whoa so six is gonna have to be in one of those two positions so if that was six that no that can't be six because I said I need the six to Shield the two don't I this is really interesting so if if if we are in a world where we put five in the middle we have to put two in a corner and we have to use the six to keep the one three and the eight away from the two which means I think that this can't be two because that would be six and that would be a one three or eight which is not a which means this Domino is broken so we have to put the two here oh no but the other six cut no okay it's simple isn't it it just doesn't work you can't put you can't use the six in the right place whichever one of these I make two I need to hide I need to use the six in an adjacent cell to hide the one three or the eight and because we can't put the six next to the five that's really lovely it's really simple and she sit here but I didn't see it okay all right so look look we've done it well when I say we've done it we haven't really done it at all we have worked out that um ignoring rotations and reflections there is one there is one grid that we are using and that is a relief because that suggests the puzzle might be solvable so we've got to put versions of this grid nine times ah ah but ah this is where the 11th is going to come in isn't it because yes three and eight are not together in this grid this has to be yes this obviously whatever's this is part of one of the grids so so however we orientate this the three by three that surrounds the 11 it does say that does it digits in a cage must sum to the given total so I think we are allowed to assume that this that this is part of a three by three but we can't make this three and eight because three and eight aren't together we can't make them it can't make it five and oh two and nine are together four and seven are together ah Ah that's annoying okay so there isn't just one option for this 11 cage because we could flip this grid upside down put the two here put the nine underneath the three and the four there in some some arrangement that would work or we could put the two on one side and have a 4 7 here sweet that's weird that's actually a bit terrifying because we don't know then we know what the rough grid is we're working with but we can't use the 11 cage to disambiguate we can't use the 11 cage to tell us which version is at least in this one that makes me wonder whether I have got this right at all because what on Earth okay let's get rid of my box here I've got to put nine nine versions of this and when I say versions of it I think there are quite a lot of versions you know if you imagine if we just cycle that grid just twist it 90 degrees or twist it 90 you know we could do that or we could reflect it and then twist it 90 degrees I sort of feel like there are quite a lot of orientations the only thing that's stable is that the two is in the middle so ah sorry I'm not spotting how to do this at the moment I have a horrible feeling that what I'm supposed to I don't want to do that I don't want to do that I was thinking what I've got to do is somehow guess the orientation around this 11. see how we sort of propagate but I'm not even sure I can see how to propagate it around the grid because I I mean even it even if I knew exactly what that looked like how would I then how would I then position the other eight three by three boxes with no degrees of freedom they've just got to be somehow their exact position is known this is absolutely amazing this this is quite simply the most remarkable grid I've ever seen in my life um I think it must be I want to say it's the twos because the twos are they're like the center of a tire aren't they um it's like it's like they've got um we've got a Michelin tire although other tires are also available um surrounding the two so the so the next two wherever it lives in the grid well it's got to be at least a Tigger bounce away from that too I think that's what we can say what do I mean by a Tigger bounce um I mean like uh a long night step or something what I mean is you can't put a two here you can't put two here because because if you do put a 2 here remember the two is surrounded by the Michelin tire and that cell is going to have to be part of both um both three by threes if you make that a two then the Michelin tire that surrounds that two the three you know is that one and this cell is part of two boxes which is um I presume not allowed yeah draw nine non-overlapping three by three boxes so so what we've got to do is position the twos quite a long way from each other the Michelin tire thing means and let's just imagine that was a two for a moment hang on let me just think about this if that's a two we can't put any more twos here or here or here or obviously in there so none of those could be twos now that I don't think anything that's very close to this Michelin tire can be a two either so all of these come out to oh oh yeah okay two obviously I say obviously I've only just noticed it but obviously because two is in the middle of the Michelin tire two never goes in the perimeter of the puzzle so because if we put a two in the perimeter then there would be some cells in that three by three that would be off the grid so none of these cells that's such a pretty pattern that's such a pretty pattern none of these cells can be a two at all wow okay so that's right so I've got a nine by nine here in the middle that has to contain nine nine twos so those cells uh what color should I use Gray it's a bit dark uh yellow that's a bit garish um well just look at the white cells in the grid ignore the green ones well actually I can't ignore the green ones because this is part of it um but this area here that's where all this is the area where all the twos live in the puzzle and it's a 9x9 area I've got to put nine twos in without repeating twos in a nine in a row or a column so this is some sort of yeah okay I've I think I've seen this pattern before um because I have I've done a puzzle with Tigger bounces in it where you've got to keep the digits Tigger bounces away from each other and they um um I can't remember I can't remember how it works it works something like it works something like this you've got to put them you know they go they go like this and then maybe like this doesn't work you see because that's too close to that one it's really restricted there's there's not a million ways that you can you can put digits into a nine by nine such that they are a Tigger bounce away from away from each other there are there are not there are not an infinite number of ways of doing this but what I can't remember is what uh well it's two things I can't remember a I can't quite remember the pattern I want to say it's something like it's something like this and then that one no that's wrong isn't it here that's wrong here because although that's not a Tigger bounce in the sense since it's not a long night's move it's too close to that Michelin tire because then that I can't yeah I can't have them this close on the diagonal um so yeah I'm not doing a very good job of explaining this at all and that's in the same column so let's move that down let's move that down but now I think I'm running out of room aren't I I think the one down here is going to run out of room so I so I don't know what the pattern is so yeah there are two problems I don't know what the pattern is and I can't remember how to justify the pattern anyway but I think that there is a limited number of ways that you can put digits into a nine by nine such that they don't they don't get too close to each other [Music] um I want to say let me just think about that let me in fact I'm just going to I'm just going to outline my 9x9 so I can see it more clearly and I'm going to think about how can I position twos it feels like I want to put you know I want to start with one of them in a corner is what I want to say because I think I think they have to be really efficiently positioned foreign but then that's quite a big tire isn't it I can't put one there I don't know I don't know I don't know about this this is actually quite tricky um how can we do this in some sort of logical manner we've got to I've got to put nine twos into a nine by nine hmm I do yeah I know what I'm going to do I know what I'm going to do I'm going to draw in um I need I need a way of keeping track of the fact that I can't put twos within Tigger bounces of each other except it's a slightly stronger condition than that because I also can't put twos this close to one another either and what that effectively amounts to is I cannot put more than one two into a three by three box if I draw that three by three box there and I say okay I want to put more than one two into it well I can't is impossible because wherever I put the two wherever I put the two twos because they've got Michelin tires around them there will be an overlapping cell now that's really interesting because that tells me that if if I have to put nine twos into this nine by nine but I can only put one two into any one three by three I have got a Sudoku grid which is actually going to be useful isn't it because now at least I can at least I can think about how to put um let me try and do this hang on right so now what I'm going to do is I'm going to get rid of my colors I know I'm not going to get rid of all my colors I'm going to leave my beautiful purple color in and I am going to try and prove that two lives in the corner which is where I want it to go so let's put two in the corner I've just realized I've got rid of my I'm going to have to remember what that pattern was of the digits as well oh bobbins right okay well anyway let's do that in a minute firstly I want to work out how we position these two so I'm going to start with the one in the corner which is I think where we're going to I think this will be the only way that we can keep the twos far enough apart and somehow fill the grid so if we put a 2 in the corner where can we now not put a two We cannot put two into any of those squares or any of these squares um which means that the two the two in this box is in one of those positions which means that I want to say that means that it's not a two yeah that's right isn't it so so this is this is quite hot web we're positioning the twos we have to think about them being uh rotund twos they have to have a Michelin tire around them so if you imagine I put a 2 into one of those cells let's put it there for example it's got a Michelin tire around it so if I put a 2 there is going to hit it which is not going to be correct so in fact given there's a two in one of those cells that cell and that cell are actually not twos at all hang on that would imply that sells not to 2 either for some reason that feels no I think that's right isn't it if that's a two you can't put a two in this box because of the Michelin tires so none of those are twos that's weird that's weird well if that's true surely it's true for those three in this box yeah yeah given so again it's it's slightly hard to visualize uh for me at least but if I put a 2 there let's actually do it that's a two ring it with our Michelin tire whoa no it's not a it's not a sort of prehistoric Tire although that's an even more prehistoric Tire um then you can see wherever I put the two if I try and put two in any of those three cells once I've once I've put the prehistoric Tire around it it's going to overlap so okay so we are getting somewhere slowly so now there's no two in those cells which means we've almost locked the two in here I think it's going to be here I think you get this sort of you know it's like a flying geese Arrangement is what I'm expecting so one of those is a two so none of these is a two um right but do I've got to put a two in one of those so none of those is a two by the logic we did up there and I want to say this hang on none of these is a two either ah broke no I've got this wrong uh ah well it doesn't work it doesn't work with that anyway because look um these can't be twos they'll be too close to our prehistoric Tire here and that means one of those is a two in row six but these are two these these two twos are now too close together even if I put the twos there and there they're going to overlap in this position so I've made a boo-boo here well this is not this is apparently not where we put the two to make this work which is weird that is weird I was absolutely convinced that was going to be right so this square is out of bounds that is not where the two goes now well that's just strange isn't it because that would seem to be the most efficient way that's I'm now thinking that it might not be any Arrangement that's going to work and that means I've done something wrong what have I not understood well one thing that's possible is that I didn't get the when I when I did the three by three I thought there was only one sort of basic arrangement of the grid now if that if I did miss an arrangement then this this is all for nothing but that this is just total nonsense because if obviously it's totally predicated on us have to having to put nine twos in the middle three by three um what should we do let's let's try this one um let's try and put a two here and see see how quickly this breaks but I have fear that these are all these are all going to break um so if this is a two well again imagine we've we've ringed it with our prehistoric Tire I think that one that one uh uh that one's okay isn't it because that this one is okay because that is a Tigger bounce away so once we ring that cell and we ring that cell there is no overlap right so that one is legitimate this there's a two in one of those so there's no two in these uh and no two in that one I think that's got to be right and there's a two in one of these so there's no two in any of these yeah this is just gonna break I think so there's a two in one of those which means there's no two in any of these [Music] um if there's a two in one of those there's no two in one of those haven't broken it yet actually I haven't broken it yet uh so if there's a two in one of these none of those can be a two if there's a two in one of these none of those can be a two there's a two in one of those [Music] so which means these cells can't have twos in them now well now it's interesting for these two cells isn't it because these neither of these can be a two because there's some sort of weird X-Wing going on because there we know that the two in column seven is in one of those two positions and once we've ringed it with a Michelin tire a two in one of these would break the world so there's no two in there now there's no two in there uh so there is ah this is it right so now we've got a two at the top so that can't be a two it's too close so the shape of the Michelin tire is like that these squares become greenified this these two become greenified this one is too close by prehistoric Tire logic that's too close by prehistoric Tire logic so we've got to this oh it's broken again I'm not surprised it's broken again look the two down here is too close by Michelin by prehistoric Tire logic so that doesn't work either unsurprisingly and I think unfortunately this is going to be a a repeated theme Here um because now well I'm going to tell you that if if that cell is not in is not a two neither is that one because that's exactly the same geometrically as this one so neither of these are now possibly possible to be twos um we will try this one we'll try this one if that's two then none of those twos none of these are twos none of these are twos uh that that that that that and that all get ruled out in an instant so this is this is going to break in about two seconds flat isn't it um right so let me think about this so now it's it's quite fascinating actually one thing I will just say is it was was quite fascinating is that the patterns are all slightly different so how how we're breaking the position of the twos they keep changing slightly uh so there's definitely a two in one of those now okay so there is definitely a 2 in column seven in one of those five cells so that can't be two anymore that's not going to be enough is it the same must be true here that's not a 2. um okay I can't see how to break this one as quickly um let me think about this so maybe it's this one maybe this does work that would be terrific if it did I need to stare at this with some sobriety and try and work out I think that the difficulty here is that I can't actually even if even if I knew if I knew that there was a two in this position oh actually there isn't a two in this position is there I can just abandon this straight away I didn't think of this well No this must be right if that's if that's a two well it's definitely not a two in this three by three box because that sells not in an 11 cage it's not in any cage and that would require that digit to be an 11 which I hadn't actually thought about at all oh my goodness well hang on a minute if that's I hadn't thought about this at all um hang on hang on hang on am I going mad I have to put a 2 in every I do have to put a two in every three by three box in my in my hypothetical middle nine by nine I do have to do that because they have to be far enough apart so it is essential that I put a 2 in here but if I put a 2 in there and I put it here the Michelin tire surrounds it that cell cannot be part of the Sudoku Grid or cannot be part of a three by three that would require this to be an 11 that just doesn't work so I think almost I think I'm writing saying actually that's not going to work either is it I don't think anything Works apart from that one maybe so I don't I actually don't think I have to do this um I just hadn't spotted this Rinky Dink in the logic um but I'm going to now claim that's not a 2 by reference to the 11 cage which might be why this 11 cage is here although I rather suspect it's not so let's repeat that logic then can that be a two well if that's a two that's the three by that's the three by three that surrounds the two so ignore the three by threes I've joined drawn in that would be a three by three in the finished puzzle and you can see this Square would not be part of a three by three which is not going to work and that's the same is true for all of those cells so the only option now is this one so this now either this is a 2 or I've broken the puzzle and that is going to be a cause for some consternation but I'm afraid I'm really sorry I don't know what I did wrong but something I have said is wrong um now this is the problem with this is it's too close to the edge it's going to interfere too much with this box because you can literally can't put a two in any of those cells um instantly that so we get a two in one of these which is instantly knocking twos out of all of these it's got to put a two right over here now and now because there's a well clearly this now can't be a two but I think we can go much further that can't be a two that can't be a two nothing we would no nothing none of those can be a two they get too close to these dominoes so now I've got a two over here which means I've got no twos in those I've got a two uh what can I do with that anything the geometry is different isn't it the geometry is different because these yeah it's different from this box it's these two boxes are different from these two boxes um uh ah all right but I can run that logic again because I've got to have a two in one of those none of those can be a two because I've got to have a two in one of those none of these can be a two so there's a two over here no no two up here quite managed to break this yet which is perhaps useful given there are twos here and here we can get twos locked into two by twos but how can we do better than that right neither of those can be a two because if I make these a two I have to put two twos in column nine look because this if that's a two that can't be a two and that can't be a two and by symmetry that's exactly the same logic so there's a two in one of these which means there's two in one of these and now there's no two here and the same is true for this little Domino isn't it because if if there's a two in this Domino those are both twos in row eight so there's no two here there's a two in one of these there's no two here now which means we're going to get some twos but I think this is going to all crack now because that has become a two which knocks that out from being a two puts twos into those that now oh that has to be a two because of this one so that's a two which means that's not a two that's a two that can't be that's a two and that's two so does that work wow wow okay I'm almost tempted to celebrate because that is that is that works well in the sense that these twos are all far enough apart that we don't run into prehistoric wheel trouble so this is well this is ABS this is absolutely magnificent because now now I think we're we're close to solving the puzzle this is so amazing because we literally well once I remember what the ordering was of the two thing was or The Ordering of the thingy was around around the wheel the Michelin tire around the two I mean literally we have these These are the only way this is the only disposition of twos you can put into this grid so this this allows us to draw that the actual Sudoku um so look we can we can I think I've got to get rid of everything here apart from these precious twos I am not getting rid of these we leave the precious the actual twos in the grid we get rid of the um we get rid of the three by threes I drawn to figure out how the twos work and we instead of that we're going to we're going to draw in actual uh let's use black to do the outlining we're going to draw in actual Michelin tires now around our around our real our real twos this is the most spectacular puzzle honestly come on ah oopsie um we're going to do this that's got to be the Michelin tire there we're going to have this and then now we're going to go around the crib now with new purple to indicate that none of these are part of the real Sudoku grid like that and now now we've just got to remember how these work probably this is the one we're going to need to start with isn't it because I think we found out earlier I think that's got to be a 4 7 pair because I think we said that the three and the eight weren't together in in in the in the in the three by three we came up with and the five and the six weren't together so it's only the four and the Seven that were together and I know the order because I can't remember what that three by three looked like but I do know if that was a four it would be next to a two and that's not gonna work because that would be in a one to two ratio so that's it oh and I just remembered it did we did work out that four went into the corner didn't we so that's and that we put the nine on the other side of the four so we've got two seven four nine now what else do we do we worked out something else one three and eight all had to all had to Shield themselves so let's reinvent the wheel so to speak that square cannot be an eight because it would be consecutive that square can't be a one um oh bobbins no that one can't be a three because it would be in a in a domino adding to ten right so that's got to be a one which means this is a 3 8 pair uh eight is consecutive with nine I'm not very good at this am I that's three so there we go now we've got five and six six can't go next to three so that is a real that is a real box to the snoku and let's just think about what fafford has done here Fred I can't get used to that soon but look fafford has used this cage to do two of the most remarkable things you can possibly imagine first a to pinpoint precisely how the twos get positioned and secondly to then fix the orientation of this almost magical Square um now now so we now know that some variant of this lives in every single other um every other Tire we've got to put in the grid so can we lock yes okay so now we can we can approximately lock the orientation of some of these because because we know what the digits are that surround the two and in particular if we view this as a type of propeller um I don't know sorry this is my weird brain working but if I view that as a propeller now imagine the propeller that surrounds that one now if it if it twisted if we twist the propeller slightly so that we put the six here or the nine in in this Arrangement obviously we're going to run into a problem here we can't have the sixes and the nines on the propeller being here and here so these two squares have to be the six and the nine these two squares have to be the five and the seven but what we don't know unfortunately oh we do we do know actually because look this one cannot be one nine because that would break the rules of the puzzle and that so this square is a six that square is a nine oh and that okay that is that is not the same I I thought we were going to get basically just propagated propagated boxes but we haven't got propagated boxes at all now so we know that the six is surrounded by one and an eight and we know that the nine is surrounded by a three and a four and we know these squares now are these squares aren't they they are three five and eight but we know the propeller digit there is the five so we put the five there we put the seven there these are three and eight but eight is consecutive with nine so we know the order three and eight go in at the top so this one I think I think is the same orientation there's not going to be another way of doing this we can't yeah if you think about the six and the nine we can't just suddenly reverse the order and have the nine next to the eight that's not going to work so we've got to go six nine four one here and somehow we need to disambiguate either that digit or that digit or perhaps this digit [Music] um we know this this middle um this middle Tire it's got It's season nine here so the orientation of its propeller has got to have fives and sevens into those squares which means that again we've got six and nine vertically here which again means that the orientation of this propeller can't be such that we have five seven vertically because that's going to then rule that cell out so again here we've got six nine vertically maybe we have to have six nine vertically everywhere then yeah again the propeller here has got to be six nine vertical five seven horizontal Ah that's useful eight can't go next to seven so that's got to be five that's got to be seven so that's different from this one as well strange hmm okay so we know three and eights around the five and we know one and four surround the seven let's put that in and see if that helps me um that one I think can be three or eight can't it is there something here eight and six could go together obviously eight and nine card but eight and six I think cat three and six can't but three and nine can bobbins right okay all right what are those squares then oh this we really don't know because we don't know the orientation of either axis here all right we do know that this R we know this is a 5 7 and we know the sevens on the left [Music] so then we know we've got three and eight into these squares and therefore we've got one and four into these squares so now we know these three digits don't we because they've got to be let's look at the rows three nine and four so we know that's got to be the nine on the propeller and the three and the four we can do because we can't put three next to seven so this is better this this box up here might actually be doable we can put six at the top of it and now this one is identical to that one and identical to that one so this one's a this is five this is ah five this is one this is seven now yeah naughty puzzle are you rotten thing all right I can't see how to do that one either let's have a look at that string of digits you can see there's a again we've got nine actual digits in column four I don't know if I really think of that that must be well it's column four of the 11 by 11. these squares are not one four seven they're not six two nine so they are eight five three and the five is the propeller digit so we go five seven uh eight and nine can't be together so we've got to do that oh that's lovely look look look look that eight can't be next to seven so that's the middle seven can't be next to three come on so now we should be able to do this one because we know the three goes next to the five not the seven and the one goes next to the seven not the eight and that one suddenly got done now now and we and we should be able to get this one now oh it's the same as that one so this is nine this is four this is one this is six now okay so what's going on here 147 obviously seven is the propeller digit four can't go next to six so that goes in that's got to be the other side so that's five so we've got one seven four two five which is this one again so this there's definitely some sort of pattern I mean it's very unsurprising given what's going on in this incredible incredible puzzle um right so perhaps we need we need some magic to be worked here don't we with ones and fours perhaps and this one is threes and eighths okay which is five two seven I know seven and nine surround a four okay so oh no imagine if I can't do it now imagine if there's some sort of ambiguity left in the puzzle that would be uh how upsetting would that be quite upsetting oh hang on there's a four here that seems to say that's got to be a one yeah that seems perfectly legitimate doesn't it that's just Sudoku right so that's forcing the six and the nine to be that way up which forces the three and the eight and now the middle box look that's got to not be nine so six and nine go in and now the orientation of this requires the four to hide in the corner which means that now we should be able to do this shouldn't we we've got to keep the three the the nine and the eight apart and that would how this one's done because that can't be eight three eight um and now we're just copying what pattern is it this one so this is nine this is six this is for this is one oh my God this way that is absolutely amazing Madrigal by fafford fafford an absolute unbelievable genius fafford how did you discover this how on Earth did you discover this I mean surely I'm not the only one who's just thinking this is completely and utterly bonkers it is Bonkers there is literally I mean I always want to just reset the grid to look at it again there is just an 11 cage in the grid and we have got sent over the years loads of puzzles um like empty grid sudokus and they're literally just an empty Grit but inevitably what they tend to come with is a screed of rules you know really really you know difficult rule sets that have to be you know you have to stare at for a long time to make head no tail off this rule set is two paragraphs and they're short paragraphs it's tiny and yet it yields that beautiful said its solution and it is beautiful it's really well it's fairly clear you've got to think about how to construct a three by three it I found the second bit difficult to working out how to think about how to position the boxes but it's actually it's perfectly doable once you once you sort of start to think about it and then it just magically falls falls out that is one of the greatest puzzles you'll ever see on this channel I mean it's one of the greatest discoveries in the history of Sudoku and I look forward to the comments I love the comments especially when they're kind and fafford should be being eulogized to the to the hilt for that one that is absolutely amazing share this puzzle widely folks because this one well they should write newspaper articles about it absolutely loved it and we'll be back later with another edition of cracking the cryptic thank you [Music]

Channel: Cracking The Cryptic

Views: 218,975

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Id: kDPTNACpJuA

Length: 64min 24sec (3864 seconds)

Published: Wed Feb 15 2023