An UNBELIEVABLE Sudoku Masterpiece

[Music] [Applause] [Music] hello and welcome to wednesday's edition of cracking the cryptic and today on screen we have a puzzle i am intrigued by um this is by a constructor called a frayed knot i think you can see on the screen the spelling of the spelling of that um obviously sounds like something a bit different um but this got an interesting story behind it we had an email a few days ago from the constructor the dying fletchman basically saying that this puzzle is a complete masterpiece it's been published on our discord server and um anyway mark had a look at that email and decided he'd give it a go and mark has is well he basically rang me up and said i have to do this puzzle right now because it is apparently a complete work of genius um so well it sounds brilliant doesn't it so i'm gonna i'm gonna attempt it in a second i'll read the rules in just a moment before i do that please do have a look at our kickstarter book if you haven't had a look at it already it's um it's going to be the best sudoku book of all time i mean no doubt about that and you can read more about it on the screen if you follow that link um we have um been looking at artwork believe it or not over the last couple of days and we have um one possible um piece of artwork we'd like to include in the book a sort of way of presenting the puzzles and that's over on the kickstarter now so if you want to if you want to check that out do have a look at it if you if you do support the book we will of course take your opinions on it into consideration also i should mention a little bonus for those of you who sponsor the channel on patreon uh the times crossword championship is coming up very soon uh it's being run in a slightly different way this year because of covid and it's going to be an online event which um which basically means they'll release three puzzles onto the internet and it will be a race to see who can solve all three of them the fastest so if you're a touch typist you're at a massive advantage compared to mark and me um anyway mark is now in full practice mode and he's recorded a solve of him solving three times crosswords as fast as he can uh so if you like well if you want to see frankly genius at work uh do have a look at that video it is uh fairly impressive let's just leave it at that um now what are the rules for a frayed knot puzzle let me read them to you what we've got is normal sudoku rules apply circle digits equal the sum of all digits on their attached arrow so that's completely standard arrow rules digits may repeat on arrows i mean obviously those squares can't have a repeated digit because they're all in the same box but that digit could be the same as that digit for example um and then finally no two cells which are chestnuts move apart may contain the same digit so the way that works is let's imagine that square is a one then one well if the one was a chess knight it could jump to all of these yellow cells and uh therefore none of the yellow cells can contain the digit one you cannot have a digit separated a night's move away from itself um so that's all the rules do have a go at this i mean this is a very rare thing um uh that mark gets this excited about a puzzle so i'm looking forward to trying it let's get cracking and see how we do if you want to have a go of course click the link under the video as usual um so you can see we've not been given we've got seven arrows which is not a great deal and one long arrow here that's length four oh actually okay that's weird isn't it that looks like a long arrow to me but it's actually the same length as that arrow and that so in fact these arrows are all of length for it's just the optical illusion that sort of um makes them look like they're all of different lengths so right so let's look at this you can see these three cells on this arrow are all in box four so they can't all contain the same digit so the minimum i could make those yellow cells add up to would be six so the minimum that this cell can be would be six in this plus if we put a one there that would be seven so this has to be at least seven whoopsie um that has to be at least seven um this one is the same i think because it's got three digits in column seven so again the minimum i could include on those three cells would be one two and three that's six plus one so this is seven eight and nine as well those are separated by a nice move ah in fact loads of things are separated by night's move ah that's interesting look at these four cells they are all a knights move apart so this square this circle here cannot be the same as those two and in fact that one sees both of those and ah yeah okay so they all see each other really well that one this one here doesn't see that one that's the only possible repeat um but these three have to all be different numbers uh anyway let's i don't know what that means sorry um this arrow ah this arrow is less powerful that's annoying look this one has three arrows in the same column this one has three arrows or three cells on arrows on the same box this one doesn't this could have repeated digits it could have two repeated digits and that means look we could do ones and twos which is annoying because that means this can be a six um so we are if we'd have got this down to seven we would have known these would have been a seven eight nine triple which would have been rather nice but we can't um this one has to be at least six because all of these three cells are in the same line this one ah that's interesting these three digits all have to be different as well because this cell sees that cell by the night's move rule so these are all different so this has to be at least six otherwise it would have been possible you could have had i guess something like that and this could have only added up to four but that is not possible here this one must be at least six that one is only a two cell arrow so i'm ignoring it sorry two cell arrow but uh yeah you're not interesting at this point um okay so so we've got lots of interesting communication we've got any digits ah i tell you what we could do there must be a one in one of those three cells because otherwise this would be two three and four as a minimum two three and four add up to nine plus one is ten and that would have to be a ten and it can't be so there must be a one in one of those three cells similarly there there must be a one in one of those three cells sorry i am now a bit stuck what we meant i mean i can see or at least it feels like there is an awful lot of interrelationship between these three arrows well these three circles and the arrows that they're on ah okay yeah here's something we can do with this arrow um these can't all be different digits so although we know those are different it's not also possible this is a different digit because if we did that we'd have to have one two three and four along the arrow and that would have to be a ten so i know that that there is a repeated digit on this run of um on this arrow and it must be this one this must repeat in fact in fact we can do better than that this repeats with that one exactly that one that's interesting because obviously these can't contain a repeated digit they're all in the same box so we know that the repeated digit is this one this one sees that one by sudoku and it sees that by night's move so those two squares are the same which means i'm going to color this because look now we know that there is a purple cell in one of these three cells and we might be able to do stuff with the knights move here now not quite i don't think no okay but that's can we do the same with this one yeah so yes we can look exactly the same logic this cannot be one two three and four so it must have a repeated digit the repeated digit has to be here this time and this cell sees this by sudoku and that by knight's move so those two are um repeated digits on this arrow now ah yeah look there's a purple and a blue cell in box five so these can't be the same repeated digits there are different repeated digits and the blue maybe the blues work better there must be a blue in one of those three ah and a blue in one of those three um okay now let's try the same on this one this no this is no good this is no good because this can have two repeated digits on it we've already looked at this that you know you could have one two there and then one two there although i mean although if if this is a repeated digit it would have to repeat with that cell because it can't repeat with this one that's a nice move away so you could have repeated digits there and there and or here and here this one obviously sees that cell so it would have to repeat there so ah that's annoying i would love to be able to eliminate um if we can eliminate six from this cell oh yeah you can you can you can you can right okay look if this the only way this can be six is with ones and twos repeating but the problem with that is for this arrow it's not for this arrow it's for this arrow this would have to be a minimum of three and four um because if they if these cells can't be one and two they have to be three and four but these are in the same line so they would have to be a minimum of one and two and one plus two plus three plus four equals ten so actually we can say um we can say that this one is a c it cannot be six and if it can't be six we now have this triple going on which definitely feels to me like it's intended um now so this sorry i'm just trying to get my head around what this means maybe i'll have to do the same thing here if this is one two three four it breaks obviously so that we know that there is at least one repeated ah yeah okay all right so there's at least one repeated digit along this along this arrow let's ask could there be two repeated digits now all i need to do to reject that hypothesis is to all right let's let and we need to look at this i can't quite see it but what i'm thinking is if that this doesn't this yeah i can do it i can do it right okay look um sorry i'm not being very articulate i'm now going to be articulate here we go with um articulation so if those two squares repeat each other let's look at that um so let's imagine these two squares are the same um same digit now the critical thing i think is that this green digit whatever it is cannot be pink or purple and it cannot be blue now why is that well it's because this square sees both of those things so it can't obviously be the same digit so if green repeats uh well yeah if yes if green repeats it would have to be a different repeated digit to purple or blue now what about if this repeats what about those two squares repeat if these two squares repeat this one sees purple this one sees blue so again we would have another different digit to purple or blue now obviously this orange can't equal green because they're in the same line with each other so now we'd have four different repeated digits along these arrows how is that ever possible because if for example if i put one on this one and two on this one now these have to be different digits so i could put three here and four here but that is never going to work you can never have a repeated four on any of these because they're all four cells long and if i have a repeated four and i put the minimum in the other two cells i will get at least to ten which is impossible so i don't think ah now this is useful this is definitely useful but i don't actually know if i can do anything with it which i know is perhaps no that's that's not quite what i meant but what i mean is that i've now convinced myself that there are there is only one repeated digit in these yellow squares there cannot be two and that repeat but the problem is i don't know where it is it could be those two it could be those two but whichever it is it is a different repeated digit to these ones and we know it can't be a four i'm getting somewhere here i am getting somewhere so now the repeated digit the repeated digits that are purple blue and whatever repeats on this one have to be ones twos and threes because you can never repeat a four on a force for on an arrow of length four so so if you've got if we've definitely got a repeated three in one of these positions i'm just going to put this one in just i don't know which one which one of these is repeated it's either this these two or these two but i just want to i just need to think about this so if we have a repeated three yeah whichever one of these is the repeated three is associated with the nine because it will have to be two threes plus a one and a two it that's all it can be which doesn't matter which of these circles is the nine it must have well put it differently it doesn't matter which of these circles contains the duplicated three that circle must be a nine now does it work the same way with the twos then is the two have to be the eight yeah it does yeah because you can't have a third two so yeah so whichever one is the two has to be associated with a one and a three i don't know what the order of this is this is just for exposition so this in this iteration that would be a nine this would be an eight this we know would have to be a different digit would have to be a seven we know the repeated digit would have to be the one and we can't have another one so we'd have to have a two and a three so actually that that that actually would work i can't see immediately why that's broken but okay obviously the problem with all of this is that we don't know we don't know which is the we don't know which is the nine we don't know which is the eight we don't know which is the seven but we do now know what the repeated digit is on each of those on each of those arrows and i don't even know in this one whether these are the repeated digits or these are so there's a lot i don't know but there's a lot i'm finding out as well and i apologize if i'm missing something straightforward here uh but i'd well i could be um now now now this is good though this is good because i can go further than this because now now i know there is no four ever on any of these arrows because i know exactly how the nine composition must be made up i know exactly how the eight composition must be made up and i know exactly how the seven composition must be made up these arrows all contain the digits one two and three okay well that's a little bit interesting i mean look for example this square now has to be higher than four this this one that one has to be higher than four or not higher than four it has to be at least four actually this one is better than that one because this is a three cell arrow so this square has to be a four five or a six it can't be higher than six because the minimum i could make those two squares would be three ah that is in fact these now have to be one two or three because once this is at least four you can't have another four on the line or you will well you can't obviously have another four in here because it will repeat four in the box and if you put five with it you're going to get to 10 so these are one two or three this square as well oh this is getting very interesting look this square has to be at least four for exactly the same reason and this is a three cell arrow and again i can't now repeat a high i can't have another four or a five in these two squares so these are one two and three that gives me a one two three triple in this box no oh my god no look it does more than that it this little funny arrow here is seen by this one two three triple so this has to be at least a four and we know all of these are different digits so again i've got to go one two and three in those two cells and now i've got a one two three triple up here oh good grief no look there are all sorts of things going on in this puzzle now so something i've just noticed is that this square has to be a one two or a three and it's not purple and it's not blue so this has to be this has to be the green digit whatever green turns out to be now i'm going to delete the greens from there because i need to work out which of these is the repeated digit but if this is green ah look if this is green this is purple so this is green oh look what color is that well the answer is it can't be blue because that's blue it can't be purple so it has to be green and once we know this is green we know it's the repeated digit and therefore it has to have a friend there and now this square can't be purple we know this these are blue and purple now so this is purple this is blue this has to be purple because it sees a green and a blue look look we've got purple purple that's a night square away from a purple so where does the purple go in those three squares it must go at the top this square sees green and purple so it's blue look this is unbelievable this is unbelievable this blue sees both of those squares this one by night smooth that one's in its column so that's got to be blue and that's therefore got to be purple because there's a green in its column this therefore has to be green look where does where does purple go in those three squares it can't go in this column so it must go here we've almost we have now done all the purples that fit we have now we don't know what purple is we don't know whether it's one two or three but we now know what whichever it is it appears in those squares in this grid that is absolutely beautiful um ah blue must go here because blue cannot be seven eight or nine blue must be in one of these two ah okay well we can see therefore it must be in this one blue can't be in a circle because even if it was three that would make those two have to be one and two and more importantly one of them would have to be purple which it can't be so this is blue where does where does blue go in box seven it doesn't go there it doesn't go there it doesn't go there that's a nice move away so it's got to go here that means this ah that square's green we could have done that before that square's blue green has got to find a home in the middle here which and it can't be there so green goes here have we done all of so i've done all purple i think i've done all blue as well so i've just got green can i do all the greens um well that can't be green that can't be green that can't be green so green it goes there and we get a sort of i don't know a flag shape down here blue green and purple and now now that square is green so now we've actually managed to position in this grid all of the ones twos and threes even though we haven't got a clue what they are i love that i don't know about you guys i absolutely love that um now the challenge i suppose is to understand how this allows us to solve the puzzle this square can't be six anymore can it because at the minimum i can now make those add up to a seven so that has got to be removed now that's interesting straight away because we know that whatever this is it cannot reappear in those two we know that this was a triple on seven eight and nine so these two squares now are the same color these but these these must be the same so perhaps we have to go about the grid highlighting all the sevens eights and nines now this square can't be a six because it has a 4 on its arrow same is true of that one so uh so maybe i have to color these two in different colors so i will make that one um what shall i make it decisions decisions these are the things i don't really like orange maybe i'll make it yellow if i make it gray i'm worried that oh it does it makes the thing disappear so i'll make that one orange okay so we're gonna have yellow orange and red for the sevens eights and nines oh okay so look where does yeah this is quite cool the central box now whatever this is it let's imagine this was a seven just for the sake of exposition this now would have to be an eight nine pair and where would that eight nine pair have to go in box five that it would have to go in those two scrap squares because we know that um everything else is a low digit so so these two squares are sevens eights and nines but we don't know whether they are yellow or red do we uh maybe we do but i don't think i know i can't see how to tell no i can't see how to do that um [Music] right what what am i meant to do now then i don't think we know enough about we don't have enough sevens eights and nines in the grid to i mean apologies if you guys are seeing something here that i'm not but can we use any of these arrows so this one is equal to oh no hang on i've got an idea like oh yes yes red these two cells have the same total but they both include a purple and a blue look purple blue so the sum of the two greens must be the same as whatever i put in this square now that's interesting because if the sum of these two greens is equal to the sum of this well equal to this square this square must be even so it can't be five and there are and now if we know that basically whatever i put in the the green so two lots of green is equal to that you can't obviously green cannot be one anymore because it has to equal four or six so green now is not one that's not one that's not one um can we do any more with that oh yeah oh no no yes we can we can because if this is two twos one and three would make eight if it's two threes it has to be nine with one and two so this is not seven once we know the repeated digit is two or three it must be associated with eight or nine so okay um so that means that one's not seven so this is eight or nine still don't know how to oh hang on look i've got a four five six triple in um in box five i've got seven eight nine there and a one two three there i didn't know i didn't think of the green as being a two or a three which maybe i should put it in so it's a bit clearer um put some digits into these colored squares so now look at box five you can see those have to be four five and six ah got something right these are four five and six now if you've done a lot of knight's move sudoku you will know that when you get these triples in the middle of boxes like this you should always look at those two squares because what can they not be anymore and the answer is four five and six if that's a four it rules four out of all of those positions so it can't be the same is true obviously for five and six in these two cells and that that is beautiful because that means what can these two yellow squares be they can't be one two and three there's ones twos and threes in their boxes and they can't be four five and six so they are seven eight and nine and that now now i might be able to do better coloring because i can see that one straight away has to be yellow because it can't be orange or red so that one's red which means it's not seven this is eight or nine now all i've got to do all i've got to do oh look ah yeah okay look where does red go in this box it can't go in those squares it can't go in this position because 8 plus 2 would be ten so this square is red and it must therefore be eight or nine now oh beautiful now now do sudoku on on the red in this box it can't be red here because that's a nice move away so this is red and this is eight or nine that now this is great because now this one can't be red so this must be red and that's eight or nine which means this one must be yellow red must go here by sudoku red could be in either of those two cells yellow is in one of those two cells i think yellow is in one of these two cells we haven't done very well with orange actually um okay ah oh no oh yeah where does where does red go in this box oh that is red it was highlighted i had it it made it look yellow sorry that's no use at all so red must be in one of these two and red over here must be in one of those two i think we're done with reds uh unless i can get one of these two cells disambiguated using something else so how am i going to do that i will have to oh i know how i can do that simply what's that one that's got red and yellow in its box so that's orange that means there's an orange in one of those there's an there's an orange in one of these two that can't be orange because it's this is getting really complicated um ah but that's still good yeah let's actually follow that chain through this is orange so the orange in this box is in one of those two cells that means that orange in box two can't be here because of this orange and it can't be here so the orange in box 2 is in exactly one of those two positions now look orange is in one of those orange here this must be orange so that's a 7 8 or a 9. ah look at this orange where does orange go in uh in box nine this square is gorgeous it rules out those three and that one so it can only go there that's got to be orange now now this must be orange oh nearly um that can't be orange there must be an orange in one of those two ah that's interesting there must be an orange in one of these two and there must be an orange in one of those two now they are in the same columns of the grid so the orange in column three has got to be in one of those two cells okay so is that useful it probably is useful i just can't quite see how i don't really even know how to notate this i'm running out colors and that square's got to be a four five or a six i can see that just looking along this row [Music] how long have i had 36 minutes that's quite a long time but this is this is not easy at least not for me [Music] um i use this arrow oh good grief oh this has been here for a while sorry sorry ah look we've looked at this already if um if this is a nine what is the repeated digit in these two squares we know it's got to be three well so that means a three here would be associated with a nine here and this would be a six but in exactly the same way what would happen if this is a repeated two we know that two has to be associated with an eight here so this square is always six whether this is two or whether it it's three it doesn't matter because the two um the relationship between the green and the red is always sort of constant um so sorry i should have seen that the moment i got these two but i didn't um but that's still still let's forgive me because that does give me that cell that's a four now um now that means that's not four so this square's got to be a five or a six this is really interesting look whatever this square is it won't be in those two squares so this square is also therefore the same as this one and therefore by sudoku the same as that one so those three squares are all the same color therefore that's not a four five or a six sorry it's not a four it is a five or a six now what do we do now oh yes yes i can do something th this um can red be nine if red is nine what do these two squares have to be if red is 9 these have to be a 2 3 pair which they can't be because this is a 2 or a 3. there must be a 1 in these 2 squares and once there's a 1 this has to be 8 and once it's 8 all of the reds have to be eight they are all eight and this is a one three pair therefore and therefore this is two so now we get the two over there of course so green is now two we can fill in all of the greens and actually this this puzzle could it could become a bit more straightforward now because i could find myself able to fill in huge swathes of it um quite quickly now with eights must go there eights must go in one of those two i shouldn't have said that should i i'm now going to come a cropper and it's gonna all stop um i can remove two i suppose from everything else i should maybe do that that's a bit tedious but i will do it um oh yeah yeah look this one this arrow now comes to our rescue can this be a three if this is a three that's a five and this is a ten so purple purple is a one and we get all the ones done now now blue must be three because we've not found a three yet so all of those get done and suddenly we might be able yeah look look this arrow now what what is this arrow it's got a two and a three on it so the minimum i can make i need this to be a minimum in order to keep this down to a single digit number so orange has now become a nine which means yellow must be a seven this is just a work of art isn't it this this puzzle is a work of art that can't be a nine anymore therefore this can't be a six so that's a five therefore this is an eight so uh we don't know i suppose i can make that red therefore so that was which means that one's red and that one's an eight remove the pencil mark move the pencil mark and okay so this is a five or a six now have i actually done all of my arrows now i think i might have done i think i have in which case this should just be a sudoku with a knight's move constraint um i say just be um [Music] so this is four six and seven i don't know how to do that this one is five six and seven that's not a six ah this is useful if six is in those squares and it is it can't be here because it's a night's move away from that so this becomes a six that finishes well it doesn't finish but it means those two down there are a four five and there's a five here so this is not five that's four five that's not four anymore that's not four anymore because of the knights move this is a four um oh look there's a five six pair in this row so this must be a four seven pair i don't think i can see anything and knights move away from that these two squares have got to be six and seven these three squares have got to be four five and nine that's not nine that's not four that's not four either look because of this four here that means that one must be four which i will accept with gratitude there must be a four in one of those two cells now what next maybe those two five six and nine that does not look useful i mean i'll fill them in but i don't think that's helpful at all oh i think i'm now missing something fairly straightforward because otherwise this is going to be an absolute brute to finish oh look not yes i am nines here and here i mean that can't be a nine so we get a nine there i should color it in make myself feel cleverer um now nine is here look so let's color that one in nine cannot go oh yeah nine can't go there because it's a nights move away it can't go there because there's a nine here so this is a nine color it in that's a five that's a four that's a nine color it in that's a seven um that's a seven by sudoku these squares are four and five yeah the four is seeing that square so these squares are four and five the seven is seeing the seven and the four down there that must be a seven and a four therefore these two squares have got to be five and six surely something something must be seeing one of these i'm sure and how about the sixes and uh six and sevens are easy so the seven and six gets resolved and now there's just going to be one pesky five or one pesky six ah there it is that six is seeing that square and i think now we are going to be able to solve the puzzle and what a puzzle this is i mean it is very well it's very common on cracking the cryptic that we we are faced with puzzles that are extraordinarily clever but this really is extraordinarily clever i mean absolutely stunning and i think i've got it right and how pretty is it as well uh i know now i must put the sevens in otherwise people will get cross um so let's make those yellow and i should just oh i've got sixes in grey as well so i'll do the sixes too just so that everything's um everything's in order so it's just fours and fives i've not filled in i think um but afraid not that is some debut that is some debut uh an absolutely startlingly brilliant puzzle i absolutely loved it um and thanks actually to mark for insisting i did it um i hope you enjoyed watching me solve it i hope you managed to get through it i really hope so because i'm really looking forward to the comments and we'll be back later of course with another edition of cracking the cryptic you

Channel: Cracking The Cryptic

Views: 154,290

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Id: Jk2ko0-eP7c

Length: 46min 4sec (2764 seconds)

Published: Wed Nov 04 2020