The Sudoku With Only 4 Known Solvers

[Music] thank you hello and welcome to Tuesday's edition of cracking the cryptic um it's not Tuesday is it oh I'm sorry I think I've got the day wrong I've lost track of days saying where's my phone hang on oh it won't tell me tell me what the day is Monday is Monday Monday the 19th hello and welcome to Monday's edition of cracking the cryptic that is not a good start is it oh dear oh dear anyway it's Monday happy Monday and it's possible that that error that deliberate error won't ever be seen because this puzzle on screen is called the 15th day of Christmas by Chris Moore and Mark sent it to me this morning with an enigmatic message that said something like this puzzle is probably impossible and unsuitable for a video but it might be the wording was something like it it might it might have very interesting logic or something and the reason that makes me deeply suspicious is the sort of the might word because that suggests that Mark hasn't solved it um now that might mean he's had a go at it and found that it's just monstrously hard it might mean he's done nothing at all I don't know um but it is it is at least suspicious what I did do is I looked it up on logic Masters Germany after he'd recommended it and I noticed that it's only been solved four times now what I not I didn't only forget the day what I forgot to check is when it was published because if it was published six months ago and it's only been sold four times that means that Mark's having a joke at my expense because this is going to be absolutely impossible um because if it's only been sold four times in six months a lot of people will have tried it and no doubt it's absolutely viciously difficult if it was only published this morning it's been sold four times that has quite a different flavor to it so I should have checked that and didn't but this is as we speak the Sudoku with only four given solvers um which might that it's very very hard we shall see the rules are really short actually so I'm hopeful it may not be quite as difficult as I fear um but what else do I need to tell you about today I need to say very happy birthday to Julia and that's because your best friend Mallory Julia wrote to us and said that you would appreciate a shout out so I hope that you have a brilliant birthday with lots and lots of cake um other than that uh over on patreon we have the Sudoku event of the year coming up and I love the fact that um almost everybody agreed that the world Sudoku Championship was not the Sudoku event of the year the Sudoku event of the year is coming in the next couple of days when we are going to release the very first ever fistmavel Sudoku hunt over on patreon which is going to be oh well I'm looking forward to the comments already let's just put it like that and this is this is a big thank you from us um just um from us to our patrons you keep the channel going thank you so much for your support and this Christmas present we hope um you will you will like it um anyway the other thing we've got over on patreon and you've still you've only got one day they left actually we are creeping towards the 20th and that's the cryptic scriptures of The Secret Snake Society um this um so we've got more correct entries I'll read out some names uh Maddie capelloni Marnie seprovich Branford MD Max Verner Chase Stuart Crichton Roddy danawat oh sorry ridi Dana watt Ashley Hunt Mark Dumont Jerome Duman Denny major Meryl Jensen Ivan Valerie Esmeralda Klein resync and Anne-Marie DeHaan Leonard Sorensen cuddle me Q Craig Anderson and also Stanley gawlik all of you sent in the correct entries very well done and the other thing we've got over on patreon at the moment is my soul of this vicious puzzle by tall cat called Shadow so if you like watching or if you have a bit of schadenfreude in your soul check that video out now let's have a look at what Chris Moore has done I have done a Chris small puzzle before I think I think it was about Saturn the moons of Saturn or something it was a very good puzzle if I'm remembering rightly this is where it's going to be even more embarrassing because I'm gonna have got the wrong Constructor but I think that Chris Moore did a puzzle called something like the moons of Saturn which was brilliant but the rules of this puzzle are as follows normal Sudoku rules apply each purple line contains digits that sum to 15 including the thermometer right so we've got to make sure each of these lines contains digits adding to 15. digits cannot repeat on a purple line so what we're not going to be doing is double seven one presumably or any other iterations thereof um no two purple lines can contain the same set of digits right digits along the purple thermometer must increase from the bulb end so if that's one that's got to be well not got to be but that could be five that could be nine for example they would add up to 15 wouldn't they so that's one way of doing it um and cells separated by a night's move in chess cannot contain the same digits we have a night's move restriction today so if this cell was a one then and it let's imagine where a chest Knight could jump to from this position it could jump to there there there there there there there there there there there Nori Nori so none of these highlighted cells could contain the digit one if the central cell was a one because then there would be a knight's move apart and that's against the rules in this in this puzzle do have a go the 15th day of Christmas so this is late as well isn't it isn't the 15th day the 15th of December or if I got that wrong as well this could be a dreadful video for mistakes but anyway do have a go the way to play is to click the link under the video now I get to play Let's get cracking and see what is going on and my temptation I suspect this is all going to be about night's moves um but what ah okay let's start with something simple actually which is that the two cell lines well how do you make two cells in Sudoku add up to 15. there are two ways so right so I see that digit in the corner is one two three four or five therefore because one of these two cell lines is going to be a six nine pair and one of them is going to be a seven eight pair and however they're arranged they're looking at this digit which has to be low when I say low I mean it can't be six seven eight or nine um right [Applause] so all of the other all of the other lines are three cell lines and we've got one two three four five six seven eight of those which makes me wonder have we got the full set I don't know how many ways there are of adding up to 15 in three digits using Sudoku numbers without repeats as well let in fact let's check that so let's let's try and list them all so if we had a one in the sum we'd need two more digits that add up to 14 so we could have one five nine or one six eight if there's no one in it let's have a two in it so the next two digits have to add up to 13 so they could be four nine um five eight or six seven and if we don't have a two or a one in it then we can have a three in it now we've got two digits to add up to twelve so they're not going to be we can't repeat so we can't do three three nines we've got to do three four eight or three five seven and if we have a four in it and no one two or three then we need two digits that add up to eleven which don't repeat before and don't involve one two or three so that's right so the complete set is eight eight there are eight combinations right so that is immediately interesting to me foreign let me just think about that for a moment so we've so we know that each of these lines contains of one of these combinations we've got two digit ones in the combinations three digit twos oh that's weird you've got what you've got you've got less digit threes in the combat in the combinations then you have digit twos in the combinations but what that surprises me for some reason I would have expected there to be some sort of symmetry about this two digit Eights three digits sorry two digit nines three digit Eights only two digit sevens so it's it is symmetrical but in a slightly strange way fours there are three fours four fives oh right yeah no no okay okay I get this actually I get this this yes the corners of a magic square are y this this is going like this the corners of the magic square so I've looked at this on the channel before um in fact I bet the reason I've thought of this is because I said um the Sudoku with only four given solvers and our biggest video on the channel is a a puzzle a video called a Stoke of the only four given digits uh by odd vandervatoring and that involves a magic square so I've Got Magic Square in my brain and that has helped me because what does a magic square look like uh in Sudoku land well the magic square looks like this there's always a five in the middle of it and there are even digits in the corners um and and The crucial thing the The crucial thing that's relevant to this puzzle is that the magic square in using if you try and make a magic square out of Sudoku digits so let's try and put a magic square into this box so a magic square of course is a is a square where every um every row every column and every diagonal adds up to the same number and I know most of you know this already but because of the secret there is a secret about Sudoku which is the digits one to nine sum to 45. now if you know that and we're trying to work out what the total might be that a magic square in Sudoku adds up to well given that those three rows add up to 45 it's going to be 45 divided by 3 is going to be the total for a row and that's 15. and that's what this puzzle is about 15 numbers so why why is why is this occurring to me as interesting well I know that a 5 goes in the middle of a magic square um I I've proved that many times before but is there a quick way of doing that I don't think I need to prove it do I I mean the proof is the proof that five goes in the middle is that if we were to draw we know that the number the magic number is 15. so if I was to draw diagonals if I was to draw two diagonals one row and one column then I those four lines I've just drawn would add up to 60 because each line is adding up to 15. but this cell is included in every single line it's included in all four lines so we could and we can see that the four lines I've drawn include every single cell of the Sudoku plus this cell an extra three times and every single cell of a Sudoku adds up to 45 so if I take 60 which is the sum of the lines um including the three repeats if I take 45 from 60 I get 15 which I know is counting three lots of this Central cell so that Central cell is a five uh that's that is the most elegant proof of that and I think I have Sam Kaplan lines thank for that because he was the one who originally um wrote to me about it I think so anyway you can put a five in the middle I'm digressing put a five in the middle but the reason that um I realized that magic squares are relevant is that the corners of the magic square are always the even digits um and the way that you might see that is try and put an odd number in a corner and you'll find there's a problem now because now uh this digit here would have to be a one obviously to make that work um and now these two squares have got to add up to six to make this row add up to 14. and the only thing you could put I mean there's simply know nothing you can put in this digit that's going to make this a possible total if you put you can't repeat the one and the five if you put two and four in which are the only other ways of adding up to six this cell is too high so it's it's logic like that that tells you the corners of a magic square are even um now this is the magic bit here let me just put this in we don't know what the order of the magic square is it doesn't really matter but the crucial thing is and this is what triggered it in my brain is that the corner is part of three different sums so when I listed these out and I could see that the two was in three different sums and the three was in two different sums that rang some sort of Bell in my brain so now let's just fill some of this in let's just we it doesn't matter what the order is I just want to sort of show you how this might look let's make that six and that four so in order to make this work that's one that's nine that's going to be three and that's going to be seven and I think obviously different orientations we could rotate this reflected and things like that but but basically that's always the pattern of the magic square so in fact I can and the good thing about this is let's count how many variants of 15 are included in the magic square well is that one two three four five six and the two diagonals brings us up to a grand total of eight so I have managed to represent my my eight lines that I've got to draw into these this puzzle rather than having eight different um lines lines in the Sudoku used up I've just used up one box which is much more efficient and therefore I'm pleased with myself so um and that's why there are four fives there were four fives in the in the combinations because of course the five is used on the diagonal twice that column and that row which is rather cool um now now how is this going to help me solve the puzzle this as the answer is potentially not at all um well it will be a useful Aid Memoir though um but I think we're gonna have to think about the knights move chicory pokery to understand this aren't we sorry I realize I've just stopped talking there I was I was what I was doing was scanning the magic square and trying to see whether um the thermo was in some way restricted uh I don't think it is I don't think it is I'm just trying to understand what the options are um yeah because the seven eight and nine are always in different rows ah yeah okay okay so this the seven eight and nine are always in different rows and Columns of the three by three magic square I almost said Sudoku there but they're always in different rows and columns and so are the ones twos and threes and so are the four fives and sixes over the four five and six on the diagonal ah so I was about to say something that's wrong but it's almost interesting actually I was about to say that there's entropy in the options Ah that's really beautiful nearly so what I was what I was thinking is that any way that you structure three Sudoku digits to add up to 15. because the ones twos and threes are in different rows and columns and the sevens eights and nines are in different columns you're always picking one of the digits one two and three and one of the digits seven eight and nine and one of the middle digits the four five and six which are also in different rows but the exception to that rule is is the combination four five six which which takes the three midly digits uh in the sum and puts them into into a um sequence so every other combination takes a low digit a middle right I've got something a low digit a middle digit and a high digit so that digit I know is a four five or a six I realized that that may seem underwhelming if this is the 456 a variant then that's probably how this wow okay I wonder if that's how this works so imagine this was the four five six Thermo then we would be able to place the digits on it using the thermo the fact we have to increase as we go along the thermometer but we also know that because of the entropic nature that would then exist in all the other lines every other line is made up of a low digit a one two three a medium digit of four five six and a high digit 789 is it using the knights move as well I was wondering if I could lock four five six either on or off some of these other lines now I mean no I can't quite I can nearly do it I can't quite do it this one can I can nearly I think I think it's going to be easier actually to prove this is not four five six because if this is four five six very hard to put a four five or six on this line that cell can't be four five or six because this sees the bulb by Knight's move that can't be four five six because it sees these two in the column and that in its box this one can't be six can't be five it might be able to be four uh no it maybe it can be four that would put a four there in the middle box so actually I can't rule that out what about this one if this is four five six or clearly that can't be any of four five or six but that one could be the same as that one bobbins right okay all right I'm abandoning that I thought that might be a way of learning about how these lines move together no this is always four five or six I don't know even if I completed that thought process when I jumped upon it but this is always four five six because either the nature of of one of these lines is entropic I it has a low a medium and a high digit or it is specifically the sequence four five six in which case this is clearly going to be a four five or a six because it's going to be the five um that so so actually all right so if this thermometer is not the 456 thermometer that is definitely a low digit and that's definitely a high digit um that's that three fours annoying me now because I know that's not right but okay we're just gonna live with that I think I'm going to retain my magic square especially as it took me a while to explain it [Music] um rise okay so it's got to be something else then so what is this something else what we're looking for is some way you can't write you can't repeat a digit on a line can you so I want to say that that means I don't know normally in night's move sudokus it sounds like this this one this one this one and this one maybe let's just take a look at those so that that cell I'm asking I'm trying to work out where that cell goes in box five and that's purely because there seems to be the most real estate in the puzzle is condensed in box five now this can't repeat on its own line we know that oh blimey I don't know that's right I don't like that cell is the key to the puzzle I'm gonna try this one instead uh no I don't like that one either okay let's try a corner one then in in the hopes that this is going to yield some sort of I don't think this is this this feels worse uh this I'm not thinking about this properly I'm not thinking about this properly there's got to be some I've got there's got to be some way of getting into the puzzle um I've got nothing here that digit cannot appear on this one that I've got a horrible feeling this is something to do with exactly the point that we were thinking about earlier which is that you know how many um you know how many twos can you put into these those four lines or something like that or how many nines can you put into them especially when the middle box all those digits have to be different so all of these digits have to be different but we can see from the magic square though that there is no well we can see from the magic square that not only are we using every number at least on at least one line we're actually using every number on at least two lines and we're using some numbers like five on four lines so is it fives that are restricted the problem the problem there the problem I've got with that is that I can well imagine there's some sort of restriction on fives you know I probably can't put three fives or something in in those in these but there's nothing to stop that being a five that being a five that having a five no this is not I'm not thinking about this clearly at all I'm so sorry um okay 26 minutes how long do I give it before I give up on this I suspect that Mark hasn't solved this I suspect this is beastly it's only got four solvers that's probably in several months it's very interesting there's definitely this is the sort of puzzle I like to mull over for a few days and then I might be able to crack crack it or come up with something um I don't think it can be to do in the eyes it's just not to do with the the two cell lines there's something about the three cell lines problem is I can't if there was a cell you know if there was a cell maybe let's just take that cell as an example if that cell and it doesn't work so it's not right but imagine that cell couldn't appear on any of these lines that would be interesting so that would be a real deduction that might be able to yield some sort of trickery but I don't see how I can possibly even there that I still can get some there's going to be some arrangement of these lines that you know you can only have two repeated digits on or something and that's going to matter for the magic square [Music] um I can see I can't have two I can't have a repeated digit in that pattern because that one sees that one by night's move and that one by nice move yeah that's interesting let's just stare at that for a moment or two in the absence of anything better so that Arrangement and I didn't I didn't actually use the um I didn't use the Box logic to prove that you can just see that these set that cell sees those three cells that sells these those three cells of that cell seeds those three cells not through Sudoku logic but through well through night smooth logic and row and column logic is how that works it doesn't use the Box logic so it should also be the case there so those those three digits those six digits all have to be different that's blue believe them that's a bit aggressive I think that's orange then yeah um so right so those six digits are all different so they have to be what does that mean in terms of my magic square that means that they are yeah well it's actually quite that's quite an interesting thought bizarrely you know because they can't be they sort of um they exist either in the rows or in the columns that is weird that is weird I don't know what that means but I do think that's really interesting what I mean by that is what is this combination this yellow combination and the answer is of course I haven't got a clue I'm just going to call it a for a moment now a a is either diagonal well let's try that just for a moment is a diagonal I won't let me do that because these are big numbers but um if a was diagonal on the magic square how would we ever fill those digits in and the reason I asked that question is that these digits cannot repeat any of the digits a so if those digits let's say it was those digits are the a digits how would we avoid this combination having either an eight a five or a two in it which way should we divide our magic square to achieve this wonderful thing the answer is you can't do it but because you can't take a column you'll always pick up a yellow Square you can't take a row you'll always pick up a yellow square and if you try the other diagonal you pick up the five so there is no way that that the a sequence um is is a diagonal now once it's a row let's put just make it the middle row it could be a column let's just make it a row what's this one now well this one now can't be a column because if it was a column it would pick up one of those digits so it's another row so I either this is a row of the magic square and then this is a different row of the magic square well this is a column of the magic square and that's a different column magic square and that is really rather surprising I think I don't forget this is not you know other magic squares are available in the sense this you know we can't now say even if I could you know I I can't assume that this is because we can rotate this we can reflect it so I mean we're not we're not able to to deduce too much from this or all we can say for sure it's that hmm the combination of digits that exist in yellow can it is possible to express them yeah it's possible to express them as two different rows of a magic square it's also possible to express them as two different Columns of a magic square um right so now can I use that on this somehow to create a fish that would be lovely um so there's loads of repeat digits opportunities that's not sensible as a thought um I know all six of these digits are different I know all six of these different digits are different oh wait a minute ah what's that telling me that's telling me something I can't have the same combination oh good grief right okay so that's telling me that there are four digits think right I think I can now state with certainty that there are four common digits between Orange and yellow is that right right just bear with me here I'm not sure about this but I'm going to so let's say that yellow corresponds to rows of my hypothetical magic square so let's just say that it's in fact let's let's divide it let's say it's the top row and the bottom row they that's absolutely possible that the yellow digits would be these these but now we've got exactly the same exactly the same restriction on orange orange is six different digits so where am I putting orange in my magic square and the answer is not in the rows because if I do put them in the rows remember I can't have the same combination so if I made this 816 I can't make either of these eight one six because that's going to repeat the sequence and I'm not allowed to do that so if I try and make this orange that would in theory be possible but now what's the other so let's say this was three five seven oh ah so I wanted to now I want to do numbers three five seven how would we ever make this now work we can't make it work and can't make it work because remember it cannot duplicate a number from three five seven so it's not a combination that's on the diagonals or vertical because that will repeat one of the digits so it needs to be another horizontal sequence to add up to 15 and the only two available have already been used on yellow so that means that this orange is very specifically yeah again it can't be diagonal for the reasons that we said it couldn't be diagonal on yellow so orange is vertical so let's say the Orange is this one and this one you can see that however I I'd divided up the orange I'm going to get an overlap in four positions so there are four common digits between orange and yellow foreign it's so nearly difficult for that one to be repeated I mean there are only six here if that's repeated where is it repeated it can't be there by night's move it's not in the same box as itself it's not there if that's repeated it has to be there but this looks the most restricted digit unfortunately let me think about that for a moment it is I think it's this one this one I don't think is under the same pressure it could repeat in two places uh that's so annoying that really is that's a beautiful it's a beautiful thing oh oh no I was getting excited then I was about to say oh and does that mean that the repeated digits have to be well at least two of the repeated digits have to be even oh golly imagine if it's parity imagine if there's some logic that says that the repeated digits between orange and yellow have to be all the even digits they're going to have to be some even digits because I could only take one column stripe to keep even digits off the repeating digits and then the other one would shift over into a side there oh sorry I realized that was a complete pause there my brain was sort of I was just looking at the pattern and trying to understand so I'm doing it again I'm trying to understand what it means the the other thing is ah right here's another Point actually Which is less well it first blush it's less powerful but maybe it's not less powerful um yeah that is that is a lovely Point actually I'm just think I'm just trying to see whether I agree it's correct right it is correct okay right forget what forget what I've been saying about um about orange orange and yellow overlapping in four cells they do overlap in four cells let's just take one let's just take this one because I can see what it does on this one I'm not sure what it does on that one yet but let's let's let's just take this one now this one I have to put a stripe down the Grid it's that one that one or that one it in terms of uh which combination it's going to be but that means that this one and this one share exactly one digit because if I put it there I don't know which one this yellow is but let's let's in fact let's let's put it in just so just so we can visualize what's going on let's say that this one is eight one six and this one is 492. let's put that one in as well um now if this is 816 it's this stripe but we know that the Orange is vertical somewhere don't know where but it's going to have to overlap with one of these digits because if it's that string then it's one five nine and that would require us to repeat the one but the point is is how can you repeat a digit between those six cells and that is an interesting question because of the knights move constraint so can that digit repeat in yellow which one could it be well it can't be any of them because it sees that one by night's move so this is not repeated this is not repeated because it sees that one in its row that one in its column and that one by night's move so that's not repeated so that must be repeated and where does it repeat well not there it's in the column with it not there it's a nice move away so it must be here so those digits are the same number and that is actually a positive that is an a real deduction if you like rather than just um a weird deduction or a sort of completely abstract deduction that is a real deduction that digit and that digit are the same number which means that in the middle box that digit is very nearly restricted I think it's going to be the same is it in here it's the same in here ah oh you're shocking my straps that is absolutely I've got digits I've got two digits foreign that I've actually got tears in my eyes that is on that is unbelievable setting literally unbelievable if that's how you're meant to do this that is and is if this is designed to do that Chris that is one of the most brilliant things I have ever seen in Sudoku ever because what this is this is ridiculous right anybody who has not spotted this and I'm sure most of you have now because uh actually it's not that difficult to see once you start hunting for blue digits but but pause the video give yourself as long as it takes to understand this you are it is absolutely extraordinary it is absolutely extraordinary um for those of you who managed to do it I'm right aren't I it is extraordinary um because where does blue go well let's start down here where does blue go down here and the answer is on this on this little patch of of purpleness but that logic is the same up here and this is what give it gives it to you it's the same you can't put this as blue because it's going to overlap here so blue is in one of those cells and if blue is in one of those cells how many combinations how many combinations adding up to 15 is blue Party 2 and the answer is one two three four which digit is party to four different combinations that add up to 15. that one so that's a five and that's a five and that is just about as beautiful a deduction as I think I've ever seen in Sudoku that is so cool and that's not five anymore so that's even so those two digits have opposite parity ah I could almost get rid of five off there and that would have told me that this wasn't the four five six um combination oh hang on I know it's I know it's not the four five six combination because the fives are all placed oh right right this is huge this is huge right so so now now we've got to concentrate a bit because we've worked out that the five the four combinations that add up to 15 that include five are on these specific lines so that includes the four five six combination it includes the 852 combination and it includes the combinations that have the odd digits on them foreign does not have four five well it doesn't have it's not the four five six slide and that means it's entropic which means that that digit is a one two or three that digit is a seven eight nine and that's a middle digit and we know that the parity of these is different um but yes this was the other thought I just had which briefly removed itself from my brain but has now come back right we know we know that these are not diagonals they are not diagonals because because we had we worked out they had to be rows and columns because were they to be diagonals you couldn't have not had one of their digits on the on the other part of the bracket if you see what I mean so if that bracket that bracket we know that's six different digits well if we if one of those was the diagonal two five eight how would this not have any of those three digits on it you can't draw a line across the square that doesn't touch one of those cells so it couldn't so that wouldn't work so so these are set right so these digits are odd that's what we've just learned there those digits are this this and this because the the specific combinations that are that combination and that combination are the cross across the middle of the magic square this is just uh this is mine but I am going to sit here until I solve this I tell you that now this this has to be seen has to be seen um right so these are odd now that means that these are the diagonals because they're the other combinations that involve five so one of these is the four five six so let's actually pencil mark it uh one of these is four five six and one of them is two five eight um now I can't use anything in this box to help me so let's not do that I have right come on so now this cell is even because of the night's move constraint so this I mean this even that deduction just Thrills me it absolutely Thrills me because let's think about the nature of this one three seven nine what what are those digits and the crew the only the only thing you need to know not not only are they odd but they're obviously all different because they are those four cells across in the cross of the magic square because one of them is this com one of these lines is this combination the other line is this combination so these odd digits are those cells they are not the same number so that digit sees those this one by Night smooth this one in its row this one it's row this one in its box so it is not one three seven or nine it's not five so it's even there we go that's even that's even these two have to have opposite parity now in order to make sure this line adds up to 15. this s are you oh bobbins that doesn't work I was about to say it's even it very nearly it's probably even but it could be five I think ah well it clearly can't be one three seven or nine it's it's exactly the same as this one it's it benefits from the same uh the same restriction but this cell I think might be able to be five five in the middle box is restricted actually it's in one of two places but unfortunately one of those two places is that one so that's either five or it's even foreign right so what on Earth do we do now do I know what the thermo is now so the thermo is not the cross it's not the diagonals so it's it's this this this or this I think it's one of the other four combinations all of which in exhibit entropy foreign sorry I'm just not spotting this am I what is it then I could I don't know I don't actually know what to do here I could argue about um I've got nothing I've got nothing here what is it going to be then nine where does that right where yeah all right where does that digit go in this box that's a good question I think it's odd and we know that it doesn't go on this line which is a five and two even numbers it can't go there by by the night's move can't go there by Sudoku it can't go there by the night's move so it goes there so those two digits are the same number that is a one three seven or a nine and it's the same as this one so we'll give it a green oh now I don't want to give it a green flash I'll give it a these are the questions aren't they I'll give it a blue flash so that digit goes down here somewhere where it can where it could go on the line still um now come on Simon I had momentum for a moment and my momentum has gone away what about I wish I knew um that's got to go is there is there the same thing here then yeah okay so try and take advantage of symmetry if it might be available to you and it is here that digit cannot go in those cells and again it can't go on the line so that digit and that digit are the same ah and that's different from Gray because those two digits see each other yes we know that the ones three seven to ninths are all different so those two digits are the same I'll use green this time so that's one three seven or nine it's going up here somewhere so hmm what does that mean Green in this box if we know ah yeah okay where does that digit now go in this box box five it's not here doesn't repeat on its own line doesn't go there by night's move it doesn't go here because that's even a night smooth it's not even so it's not that cell so green is in one of those two positions let's just highlight that for a moment so does that matter uh I mean it it might do um if I knew it was that one then I would know that was a seven or a nine and then I would know that was a seven or a nine and then I'd now got grief I'd know that was a two oh hang on does that not add up to no that does work that does work sorry it would be a two that would be a two that's if I can get this cell to be this one so why can't it be that one where would it go here it would go in one of two no that's not good um I don't know I'm sorry I I'm sure that there is something clever I can do here do I know do I know more about these these things than I think I do so I know that this uh yeah okay so I know that the yellows are in the same orientation within the square I know the oranges are in the same orientation within the square foreign s so the ah ah yeah it has a that's a good thought this is a good thought right so so either this one or this one is that strip in I mean obviously the the the the the the point is these might not be yellow the magic square could be different but in principle one of these has to be the horizontal strip completes the grid look that can click that is the third row that's the combination that is akin to the third row that I've not yet placed in in the yellow ring so in terms of again of our hypothetical we know that the oranges are hypothetically in the vertical plane so two of these uh combinations that go vertically are Akin that go around this ring and then the third one what's that going on in my phone that's all right um the third one the one that is not on the orange ring is either this one or this one so that are ah right so that means there is an extra region in the Sudoku there are two extra regions in the Sudoku because either it's these digits plus that is an extra region or it's the these digits plus this is an extra region foreign so what we need to do is to find is to find either in this combination or this combination a cell I've done it I've done it there we go I've done it right what I was going to say I'm going to complete my sentence now my brain my brain or my mouth throat to check my brain did cash that's amazing right great Gray so what I want to imagine is that this combination here this 357 combination is that one I mean you can see it it can't be but that's that's that's not by Design that's just that's just luck that's a five in the middle ignore that let's imagine that that's yellow that's the third yellow uh combination well then we would know that that combination of nine cells was the digits one to nine once each because we'd had all three rows of the Sudoku catered For in these combinations or all three rows of the magic square now how could that be when whatever digit is in Gray cannot exist anywhere within yellow so let's make those yellow and now ask where gray goes in yellow well can't go here it sees this one can't go here it sees this one in fact this gray rules out all of these doesn't it all of these cells which are in the box with that gray also sees that one that one this gray sees those two you can't put gray in yellow at all so it can't be so so this cannot be yellow and if it cannot be yellow which is the third row of the magic square well it's got to be that one so that's yellow and that means this is orange wow and these are these yellows and orange fish that we've now created are two extra region we've got the fish here doing this so that's a fish and this is a fish and the two fish are extra regions by which I mean that we've got to put all of the digits one to nine once each in them foreign and that means that means I've got another ticket is this no I can't use I can't say things like that because it's not true in the moment it feels like it is this is one of the most brilliant puzzles I've ever seen in my life honestly this is just absolutely startling now come back to our thoughts around green and where green goes in this box and in particular the question I want to change I want to change that question Justice where does the green digit go on the orange fish where is the green digit on the orange fish that's the question I want to ask it's not in these cells and it's not in those cells because this is green and that one sees all of those and this green which we know is the same as this sees that one so the green is not in there it's not in here by night's move this is an odd digit so it's not there and we know that green in box 5 goes in one of those two cells so it's not that one so the only cell that can be green is that one so that is green and that's absolutely massive because this is now odd in fact in fact we can do all sorts of things that is a one or a not a one or a three this is not this is now odd and not eight now in order to make this add up to 15 we've got this which is not changing the sort of the parity we need these to be of opposite parity so this this can only be a two and that was the digit that I've got now that's seeing that by Knight's move this digit is now low isn't it because it we're adding five to at least seven so that's got to be not seven or nine this now is seven or nine so we've got sevens and nines all over the place and for our next deduction oh this is gorgeous right look two is now off this line so that is not 285 it's four five six and if that's four five six that's not four five six and is we take the four and the six out so that's got to be two five eight I got interrupted is the school holidays I believe it I've got ah this is not the puzzle I ever wanted to get interrupted on let me just see what I've been doing I've been um doing some stuff with twos fives and eights down at the bottom here so why did I think this was oh yes okay because I got a two here wasn't it I've got a two here I've been away from the puzzle for quite a while actually this is um four five six yes yes okay I've remembered so this this was the diagonal and this is the diagonal that's the other diagonal and that's how I knew that once this was four five six this became two five eight and yes and this all stemmed out stemmed from that absolutely or did it hang on now what where did that stem from how did I get yes yes I got that this was a two didn't I because of this extraordinary stuff that gave me this as an odd digit and then I knew the parity of this one so this two hit right this is just my putative magic square this is not important and I fat yes and I could I constructed the fish yes I've remembered so this was an extra region and this is vertical fishes this is vertical stripes of my magic square this is horizontal stripes of my magic square um okay right so what I've got to do now is to work out which digits are restricted well what I mean is I've got to make sure I put one of each digit on each fish um I was about to get excited about putting this on the top fish saying it couldn't go in any of those positions that's two oh this this shows how much I've I mean that's already on the top fish Simon it's got to go on the bottom fish can it go on the bottom fish easily if it goes on the cam it can go in the bottom fish in a variety oh actually no hang on it can't go there oh so this digit is in one of those three cells is that worth pencil marking of course it is it makes me feel like I'm making progress over and above where I was um right oh come on I am going to sit here I'm going to sit here now I'm going to shoot all interruptions um although that last one I couldn't really avoid it there were children in the room and everything um come on so we've got so what we've probably got to do is to think about all right where does that digit go on the top fish it doesn't seem to be able to be in any of those cells or that one so it's in one of those two so one of those squares is quite a low number and it's that so let's purplify that and purpllify one of those give those a little bit of a shadow to indicate we don't know which of these is purple as that helped the answer is well actually does that benefit from the same problem that digit's also got to appear on the orange fish so it's not in any of those cells it's not an odd number it's not there right so that digit is up there as well so this is in fact if I label this cell with the power of running out of colors a bit here should we get rid of let's get rid of blue I think we can get rid of blue because we've sort of we've sort of used blue now and let's instead blue this digit so where does this digit go on the top fish the answer is in exactly the same positions as the purple so we can get rid of the white blueify this and these digits are from one three four six and eight is that in any way helpful can you put four with audio no you can you can oh dear um so instead of that what could we do we could oh I know what it is I know what it is right it's exactly the same as it is with the fives just looking at the fives then and trying to remember how I knew they were fives and then I remembered the the most amazing logic probably there's ever been in Sudoku that gave us that these were fives but this is orange and this is yellow so they cross in the Square and if they cross in the Square they must have a a digit in common and it's exactly the same pattern this is exactly the same zigzag that this is so that's so that digit is there is that what I'm learning oh please let that be what I'm learning that's going to give me a 2 here as well I think that's correct isn't it if I know that the orange fish is the other dimension to the yellow fish there must be an overlapping digit between orange and yellow so there is a common digit in that spiral just as there was a common digit in that spiral so that is the same we can't repeat digits here can we it's the same I can't don't think the Symmetry possibly breaks let's just check it that can't repeat that can't repeat its view of that so that that digit must be the repeated digit so it goes there so this is now not two uh two is here by a process of Sudoku of all things in box five means that means two is mildly restricted can that be two I'm getting can no two can't repeat on the orange fish so there we go right so actually two is restricted in this box up here one of two places um this digit is odd now because those two are both even so that's an odd digit and it's not five so that's one three seven or nine and therefore it finds a home in one of those cells which is that one wow because we know these are four different digits from our earlier logic that digit is not the same as that it's in the same box as that and the same row as that so those two digits are the same we're going to need another color let's go light green this time um that oh that digit has appeared on both fish all right that digit's over here with maybe we're starting to get to the point where we might have to get rid of this up there um now for on well that can't be right okay here's another point that digit is not able to be particularly low because that would force this line has to add up to 15. so this is one or three this would be at least a double digit number so that is now seven or nine that's seven or nine that means that cell's not not seven or nine anymore so this is I've got a 1 3 I've got one three pair here come on come on I've got come on Simon please uh this feels well yeah okay where does the purple digit go up here that's got to go here now by Sudoku that's purple and it's a one or a three so now I've got a one three a one three that line down here remember that adds up to 15. Let's actually put the options in now six seven eight or nine this is a one three pair so in this column oh I've got oh I've got a seven nine pair here coming off the line so that's got to be a seven or a nine it's one of those two colors what's going on in this column then we know that is it this digit here that's not eight that's going to be too big I've got a 4 6 pair oh my goodness that's got to not be for it this is five or eight that's five or eight that's so nearly you oh that's a five it sees a four six pair five [Music] four six pair that's become become an eight look I've got six seven nine in the column that's becoming eight therefore that's a seven to make the maths work that's an eight by Sudoku oh okay I'm feeling better now so it wasn't although I got interrupted it wasn't at a stage where the puzzle was brutally becoming brutal again this is a five by Sudoku that's an eight [Music] um what does that mean I don't know I can't put another five on an on a purple line I have well and truly busted the fives so five in this box now is might be restricted look or not oh yeah no it is a bit that five reaches in there so there's a five and one of two places that settles my two and five down at the bottom that too Lots the two out of here and plunks it here so now I've got to don't use that to do not use that to that do is very very very misleading um two two goes there just by the power of not not being a knight's move away from self look I'm gonna have to get rid of my magic square the most wonderful magic square in the world uh is it safe to do that is it safe to do that have we extracted every last you know what's the expression from Harry Potter every last Exquisite drop of Agony um I don't I don't know I I think I think I probably have I know the diagonals I've used those they're there and there and I've got two fish left which are basically yeah I think I'm gonna risk getting rid of this [Music] um and that that's that's like saying goodbye oh yeah now I should get rid of it because if that's eight seven we know that's six nine so that could be important um it says rather desperately uh okay this column has got all of the digits in it with the exception of nine oh my goodness me and that nine unless I made a boo-boo here sees that cell which makes it a seven that a nine and by mathematics that's a four and that's a six and by Knight's move that's a six and that's a four and that's a six and that's a nine wow wow wow just just incredible this is this is right that's a seven eight nine triple in that column so these squares are four and six which we apparently don't know the order of um can we do any more maths that's just oh yeah we can't that's a nine so that's a nine that's a one that's a three by maths that's a seven uh one magic square back now to know that could probably work out what this one has to be now uh it's Gotta oh it's got a purple on it so it's got a one on it it's not got a three on it therefore it can't have a four on it because that wouldn't add up to enough so we know that this it seems to have to be one eight six now um and that would be great because it would mean that was an eight because it couldn't be a one or a six how could it be anything else given the options for those squares how do I know oh I know oh I tell you why I know there's a blue on there don't I there's got to be a blue on the top fish and we knew it was there and it's a six so it must go here because it doesn't it can't go there good grief so that's six therefore that's one that's an eight by Magic and maths that's an eight by Magic and maths that's not a seven because it's season nine this is a one three pair so one is in one of two places [Music] um and actually if I had my magic square available I could now work I suppose I can work out these digits anyway can't I I can just use my ring of yellows and that the digits I've not put on the yellow fish yet are three four and eight and three four and eight do as you may have gathered at up to 15. that's not eight that's not eight so that must be an eight this is a three four pair now um which is probably resolved somehow so how many eights have we got lots can I get them all just pausing for a moment while I think about that question um I fear the answer might be no I'm afraid there might be a way of getting them but I can't see what it is so we might have to wait a moment or two and hopefully it won't be longer than that to magically get those other digits now nine is mildly restricted in this box look it's in one of two places I don't think Knight's move trickery is going to help me but nine does help me get that digit because it can't go here because of the night's move so nine oh sorry oh that's great so 9 is now here by Sudoku replacing a pencil marked eight so eight is now in one of those two we've got an X-Wing of eights left this row needs ones and sevens ah so that's got to be one by Sudoku and that's got to be the seven gosh imagine if I do this and then I find that I've got a nice move you know there's something a Knights move away from itself I would probably cry um there's a one in one of these cells right those squares then they've got to be three four and five and I'd love to know what the order of that I know that's not five I I suppose that's gives me a three four pair so that's got to be a five okay fine we might have to do some three four coloring it looks like this is a two five pair and the Knights move doesn't seem to be helping me but that means these squares here have got to be one and six which is resolved I see so that's six that's one that's one so one is in one of three not here because that would break the knight's move constraint again once in one of these two cells one is here one is here one is here three is here come on come on these squares down here are three four and six really resultable that's a seven by Sudoku that's not able to be three um what's going on in the bottom row this this doesn't look oh that's C that becomes a three or a four no no no this is 3C anything no is this two five C in it ah it does that too reaches in there it sorts that out good good okay so can I get oh I can get two in this box that's been available for ages sorry if you've been shouting me about that I tell you if you're shouting at me very much in this puzzle I will feel a bit sad for myself because this I do feel has been at least quite an interesting Journey um like this has got to be a three or a four whoopsie so in this row we need three is four that's a three or a four can't be five so the five in this row gets placed I think I'm just focusing on all the wrong digits at every moment I possibly can 4 6 and 7 in this row so that's got to be four or seven and that has got to be four or six or seven and somehow something needs to reach in here and tell me Well if this was four it would rule four out of both of those so that becomes six or seven now okay um can we reach in here and pick up an eight or a nine from somewhere that's going to resolve this I bet you it's possible what about these squares they've got to be nine and oh nine and seven again uh okay or have I used up all of my lines that's the other thought have I used up all my lines imagine if this would be a disaster uh what about this column that is oh that's it look this three sees that cell so that's got to be the four which makes that the four and that the three and that makes that the seven that's the six that's the four oh come on oh I think I just put four in that cell I don't know what happened but that means look this four six gets resolved by night's move jiggery pokery four goes here and that's three in the corner that is a very very cool three in the corner uh seven and eight are in those two cells and eight is useful seven eight eight nine seven nine that cell down there is a three I think so somehow this uh that's four three four four three come on yes yes foreign person to solve that puzzle there is no way Mark did that there is no way that's what he's done he's had a look at it and he's noted that it's really interesting and he still I know what I'll do I'll send it to gubbins over there and see if he can solve it in a video of no less you rotten thing that was I think we just have to spend a moment though and reflect on the utter Genius of Chris Moore for creating this puzzle that is this deduction here around these fives I I don't know maybe there is another way of doing this but that is one of the most beautiful things I have ever seen in a Sudoku puzzle full stop the 15th day of Christmas this is my Christmas come early a puzzle like this does not come along very often um and what Chris has done here deserves just humble respect it is an absolute masterpiece one of the greatest puzzles of all time I have no doubt in saying that absolutely stunning thank you so much for watching I'm now going to go and play Mourinho probably but later with another edition of cracking the cryptic [Music]

Channel: Cracking The Cryptic

Views: 196,833

Keywords:

Id: Iu9sDHZwjj8

Length: 85min 18sec (5118 seconds)

Published: Mon Dec 19 2022