The Sudoku With Only Two Rules

[Music] hello and welcome to Tuesday's edition of cracking a cryptic on a truly horrible day here in the UK it is filthy outside um but I am going to distract myself from this awful weather by by indulging in one of life's great Pleasures at least I hope it will be a great pleasure I'm going to have a go at a puzzle called double self-referral by the Dutch Master arand Deering um and I will tell you the reason I'm a little bit nervous about this is that we haven't actually had managed to get this tested um none of the testers could do it um which is it's very unusual for an ARD puzzle Ard was responsible of course for our most popular video ever um the puzzle I think we called it the sedu with only four given digits and throughout the life of cracking the cryptic Arts puzzles have been enjoyed by literally millions and millions of solvers um and they're normally they're so clever because they're not normally brutally hard uh they normally involve a trick or two but once you see the trick they sort of fill in um but anyway no one's been able to do this um so uh I'm taking a small risk but it's it's the least I can do I love Arts puzzles as a rule and hopefully I'll be able to make my way through it even though this might be a long video let let us see uh the rules are really short and it's some sort of indexing thing going on uh in fact let me I'll just read you the rules now so we can think about them when I do the birthdays but it says um normal sidoku rules apply well no it doesn't say that I extrapolated that CU I saw it said Place one to n in each row column and then I real realized it said and marked region once each so that means that we've got um we have got a regular sidoku um so we've got to put the digits 1 to n in every Row in every column but we don't have 3x3 block boxes today or well we actually have one there but we have um uh we have regions look so those squares there should be nine of them and there are so they have to contain the digits 1 to n once each as well um so it has regulars normally have properties that you have to think about to do with things like the law of leftovers if you've ever heard of that in sodoku well you might be about to learn more about it but but the the the the extra rule here you can see we've hardly got any given digits at all so we're not going to be able to solve this as an irregular puzzle unless there is an extra Rule and the extra rule is that when digit Zed is in cell brackets X comma y then digit Y is in cell X comma Zed and digit X is in cell Z comma Y and I haven't got a clue what that means but when we actually do the rules properly we will think about what what that means you'll be you should be able to see it on your screens now and dive into the puzzle if if that is your bent um anyway anyway more more about the puzzle in a moment or two what do I need to tell you well one thing is that we are streaming tonight at 10:00 UK time so it might be about the time this video finishes you can just skip over to the stream and watch Mark and I do battle with this wonderful puzzle game islands of insight it almost feels like it was made for us frankly it is absolutely beautiful and full 10,000 puzzles I think um and I know that the puzzles are hand generated um and there's a whole raft of puzzle makers uh in in the credits um I exchanged emails with Elliot Grant this week about it so I'm really stoked to have another go at that puzzle or that game um and yeah that that should be coming imminently I'll try and remember to put a link on the screen other than that just to mention we've got our patreon uh the best soku Club on on on Earth we have our competition running until the 20th to solve a brand new sidoku hunt that's over there at the moment so do have a go at that and there's loads of extra content as well now let's turn our attention to birthdays and I will start by wishing Diane a very happy 33rd birthday from your husband Cameron uh I know Cameron is making you pasta carbonara and cake today Diane so that sounds quite good um and apparently your Labrador Milo might help with both unless there is chocolate in the cake well Dian frankly I hope for your sake there is chocolate in the cake because that's really the best type of cake Milo can make do with the leftover pasta pasta carbonara but many happy returns it sounds like you're going to have a very good day uh next Belinda it's your birthday today many happy returns um Sim s wrote to us and said uh well said what an absolute Legend you've been um I know Simon's been suffering from nerve pain sounds excruciating for the last couple of months and he is very grateful for all you've done to him all you've done for him Belinda um and uh many happy returns I hope you able to have chocolate cake today um next Nancy has turned 65 today and I know this because your husband Steven wrote in um and the email was headed well to the most caring most beautiful and most patient woman in the world so Nancy you have very appreciative husband there and I hope you have a great birthday today thank you for watching the channel and I hope you get chocolate cake and then Stuart uh it's your birthday today and I know this because your sister Abigail wrote to us uh and I have to thank you um uh Stuart for for converting Abigail to uh cracking the crypto um and this wonderful world of variant soku and then finally I have to I have an apology to make I missed a very important 28th wedding anniversary which happened on the 9th of March and this was um for Jeremy and Stacy over there in Virginia and I was meant to shout this out and I somehow got my diary mixed up uh and I would have shouted it out in about a year's time which is no of no help to man nor Beast um but Jeremy and Stacy I'm so sorry I hope you had a brilliant day and I hope you can forgive me um and um I hope you had a cake and it was it was good cake and yeah sorry um is that all is that I don't want to miss anyone else's anniversaries or birthdays um I think it's everything let's turn our attention to doing some sedu solving I have already read the rules of Arts puzzle but I I just want to think about the rules and try and understand what they mean um so this this second line of the rules with all of this Zs x's and y's in it if digit Zed is in so there's a digit let's say that that's Zed so five is in cell that's row six column 6 isn't it so if five is in cell row six column 6 then digit then s six will be in cell row 6 column 5 six will be in row 6 column 5 so six will be there that's one of the consequences there is a second consequence which is that the digit the digit six again it must be is in the cell oh this oh the cell row five column 6 row five column 6 so that's a six but good grief I might have to do another one of those sorry I'm going to have a think about this one as well um if if this time the digit Z is one if one is in row 9 column 9 [Music] then the nine is [Music] in row 9 column 1 so nine is there so this is indexing sort indexing sorry there's one more thing isn't it I'm I'm just trying to understand how the indexing works here apparently computer programmers just get this instantly unfortunately I never really got into computer programming which might explain why I don't get these things immediately and the digit X which is going to be a nine is in the cell cell that's Row one now row one column 9 so that is also a nine [Music] so okay we do have a go because I'm starting to solve now the way to play is to click the link under the video as usual um but now I get to play Let's get cracking I mean I'm not going to take these out of the grid because I think they're just basically given by the by the actual rules it's almost like these are given digits that we're meant to use to understand how the indexing works why why does that result what's what effectively this is doing this is in row six and column six so this five is saying throw a six I still haven't quite got this you know sorry sorry if this is obvious to everybody I'm going to just put something else I'm going to put a two in there and think about this um so what would I let's think about what I would expect this to do I don't really I'm not really built an expectation I think that is going to do something maybe with maybe it is indexing a nine into maybe there what else is it going to be indexing then maybe a four because it's in the fourth row so so there must be yeah there must be a yes it must be indexing a four somewhere and that four is that going to go in the second row then uh maybe uh CU cuz the original the original yeah the original Zed would be the two yes okay so that is how this works so what happens is you put a digit in you look at the column number that the digit is in so this two is in column number nine and you write nine into that column number in the row you've put the digit in so that would be a nine and then you look at the row number and that's a two and you say okay okay but you put the row number which is four into the second row in the same column I think I think that's how it works and are these these a cycle then do the or does let me just now I'm just going to have a think about this one so Row 2 column 9 let me try and do this without reading the rules so Row 2 column 9 what do I think what do I think this four is saying this four is is no it's it's not a cycle it's not a cycle is it because that four is if I understand the rules correctly that four is saying write a nine cuz this column index is nines into the fourth column so I think it's putting a nine there and that's in the second that's in the second row oh yeah so that that what that one sort of is used up now so that one resulted in that one and that one that one results in those two and this one that this is in the second row so I should put a two into there into the ninth row and it's in the fourth column so I should throw a four into the ninth column and I've already got that so I get an extra two from this now this two is saying write a nine into there that's correct and it's saying write a ah four we've got to put a four in somewhere four because it's in the fourth column in there perhaps so it's opposite that one right and then that one does this just keep maybe this just keeps going so if we can place one digit no it can't keep going soow if row 9 column 2 is a four that's saying right yeah that's saying right this nine in and WR two yeah so so now ah okay so what's happened here is writing this digit in the grid has given us actually six digits Al together and they're all they're all symmetrical um they're all if if we were to I don't know if I can do this hang on let's have a go I don't want that color let's go for that color they're go they're all symmetrical around this diagonal yeah that's that that is forced by the nature of the equation wherever you put yeah you have to keep cycling until you reach the end of the cycle now okay so the interesting thing here so when you ah it doesn't work the same way on the diagonal itself because when you put a digit that's not on the diagonal the cycle it creates is six six numbers but when we put a digit here I'm just going to check does this have a another implication I don't think it does because it has a repeated digit in its equation what I mean by that is if we think about Zed if we read the rules which reply Z XY if you have a repeated digit in Zed X or Y so two of the digits are the same it's not as powerful I think so well let's think about this then so this is saying this is saying hang on hang on hang on this is a six it's in it's in the fifth row so it's saying write a five into the sixth row in its column which I've already got and this five is in row six so the five is throwing it it's in row six column 6 so it throws a six into two positions both in row five and column five that's why the one throws the nine into those positions so everything along this diagonal yeah I think I think all it'll do let's just let's just pick a digit let's pick a strange digit let's put three in there now I think CU that's row 7 column 7 I think that's just going to put sevens into those isn't it so again symmetry across the diagonal but of limited a more limited application the my hypothe hypothesized two here I better to take that out out because that's not correct is it yeah okay actually I'm just going to put it back in again let me just I'm just going to double check that I agree this this must result in symmetry across this diagonal I think row four 9 is a two so basically 4 column 9 is a two it is it is weird but it it does I think I think that is what it causes because that makes row two column 9 or four and once row two column 9 is four once row two column 9 is a four that's telling you to put a N9 in here and a two in here once you put a N9 in here that's indexing the two in its column which so th this is forced as a result of this but putting that in forces this down here exactly opposite it on the diagonal yeah so what you get is this sort of a cycle of six digits for any digit that's not on the that doesn't have a that doesn't have a repeated digit in its coordinate so the positive diagonal just doesn't work the same way does it because this doesn't have a repeated digit on its diagonal on it sorry in its coordinate what about if we pick a digit if we made Row 3 column 7 let's make that a three what's that doing that's throwing seven uh it's throwing let me just s this out it's throwing a seven here I think and that's throwing a three down there so so yeah again because I've got a digit because I've got a repeated digit here within the within x y and Zed I've got a repeated number I end up having to put a digit on the diagonal as a result of that now also yeah and then it's indexing itself oh I see yeah it indexes itself from a column perspective CU it's saying WR three into Row three so it indexes itself but then from a row perspectiv it indexes here which has to have an equivalent which is down here and then this will index itself from a column so again ah right so it's all about it's all this puzzle is entirely about the Symmetry across the negative diagonal which will occur no well there's always symmetry across the negative diagonal but whenever you have any combination of x y and Zed that is repeated it will have a much less profound effect it will effectively only well actually what if that's a three that just does nothing does it that indexes itself three times that's a three in Row 3 column 3 so the cycle there just goes sorry if that's just made a horrible noise down the microphone but it it will just go on forever so the cycle the cycle just ends if you put if you put a three into Row three column 3 if you put a three in the same row number you'll get you'll get that will cause two more digits to appear in the puzzle so that three is worth three digits and if you put a digit like this one row 4 column 9 being at two you can see four 4 9 and two are all different numbers you're going to get six digits as a result of that [Music] um so oh my phone is buzzing that's fine um so what does that mean then what that means is I know one thing I want it to mean but I'm not sure whether what I'm about to say is right or wrong so I'm just going to delay saying it for a [Music] moment I don't know about this I'm going to say it I can't think why it's wrong I'm not I think it must be right okay what I'm thinking what I'm thinking is this if I put a digit anywhere anywhere above the diagonal but not on the diagonal we have worked out that that will cause that digit to reflect across the diagonal so if I put that digit in into the puzzle I will also be able to put that digit and that digit is going to be the same so digits occur in pairs across the diagonal when they are not on the diagonal but there are an odd number of digits to be placed in sidoku so I have to put nine nines into this puzzle I have to put nine sixes I have to put nine fives I have to put nine ones therefore I feel like I have to put one of each digit on the diagonal because otherwise I otherwise I don't see how I can achieve oddness an odd number of each digit clearly I can't just I can't get to an odd number of digits by just posting them on either side of the diagonal because every time I put one in I I cause another one to occur so that means I must have at least one of every digit on the diagonal but there's only nine cells on the diagonal so I must have one of each of those digits on the diagonal I think that's right that feels right and that's interesting so that means I I can't have ones or fives in any of these positions um well apart from the ones that they're already in obviously so right what do we do then do we have to color this that's what I'm thinking now I mean one and nine have to be in there by the by the fact that they have to appear in this region yeah I mean it's it is a little instantly interesting isn't it I mean if I just put one and nine in there those cells that cell for example I don't think that can be a one because if that's a one I think that is going to cause that to be a one and it's in the same region as that one let's just let's just check that that is correct so that is Row 8 column 7 um equaling one now by my understanding of the rules see that is saying that the eight should appear here cuz this is in the eight row and this is in the seventh column so the seven should appear here I think that's what that's saying and you may say ah but you've not got a one here but I will have by the time I exhaust the implications of these two squares so this is saying write an this is in the seventh column so I think it's saying write a seven into here and that's good cuz that is opposite that one and this seven is saying write a one into the seventh row which is there and that is six cells no it's not six cells of cyclical this because we haven't got an eight that's equivalent to this one so something should make this an eight and it should be this I think and this is in yes this is in the eighth column so in its row we have to write an eight into the First Column so there you go symmetry symmetry works as a thing right so that means this is not one okay that's uh no nine um hang on one of one of no I'm wrong so it means there's a nine in one of those four positions by by symmetry across the diagonal but that nine doesn't actually see any of those positions wow okay um this will be why no one's managed to solve this this is this is not easy stuff actually is it it's not it's not I feel like I've done a lot of thinking I've 28 minutes of thinking I've done nothing Beyond just do the things we could do in instantly nine is in one of those four positions so it's in one of those four positions um perhaps what we're meant to do is to [Applause] use the law of leftovers I wonder about that now so yeah I mean well it's it's an obvious point but one in row seven has to be here and so they must have an equivalent which is there is it oh that's another 3x3 I thought sorry I thought there was only one 3x3 in the puzzle but there is another one down here I've suddenly spotted yeah I mean the same it's diff difficult to really know how to do this but these two digits also have to appear somewhere in row seven so they're going to be in there which means they're going to be in there as well um right so no it's actually that's not even true what I was about to say so I'm not going to say it what about the same is true which ones is it it's going to be these have a relationship I think um so this this is classic law of leftovers applying there um law of leftovers is just a sort of a simple uh version of set theory by the way if you've ever wondered how the law of leftovers works um the way to one way to think about it if you're more if you're more comfortable with set theory than you are with other things is to say okay can we describe exactly when we finish this puzzle what will the green squares contain and we can describe that exactly because we know that the green squares will have five sets of the digits one to n in weren't they each of the there's a five complete rows of the sodoku so that's what the green squares will contain now what about if I highlight instead of five rows of the sedu I'm going to highlight five complete regions of the sidoku so I'll highlight those what will they contain well that's those F those orange cells there are just five complete regions of this puzzle so they also going to contain five sets of the digits 1 to 9 now if we remove all the commonality there because all of the cells that have green and orange in them are in both sets we're just left with these so these must be the same thing because we've just we had the same thing we had five sets in in of 1 to n in green five sets of 1 to9 in Orange and I just took out all of the cells that were common and if you take the same thing out of both sets what remains in both sets will still be equivalent so these are equivalent um so these two greens are the same digit as these two oranges right but okay but these are you see what I was wanting to do was to reflect these across the diagonal but I don't know we might yeah we might have to split these up a little bit further actually let's try that let's make that one blue and this one purple and what we're saying at the moment is that purple and orange are the same digits as green and blue but we don't know but we don't know which is which but but by splitting the colors up it's now legitimate for me to say okay well purple we know must be there because it must reflect across the diagonal blue must be here so purple and right and that just does it straight away purple and blue cannot be the same because in this region of the puzzle they exist together so purple which we know is the same as either blue or green is actually the same as green so we can make purple green again um and therefore we know that blue is actually orange so so oh my phone is buzzing uh that's fine okay that is now now we can go further than that because I've not done my reflecting all all my Reflections across the diagonal look these have got to reflect right so blue in this box looks restricted to me it's in one of no it's in one of one place actually that's very interesting okay so this is this is the first moment of during this solve where I've actually felt like I've done something that OD ODS intended me to do um because look uh where is blue blue must exist in this region by sodoku I can rule out lots of cells so it's in one of these three now if blue was here once I've reflected blue across the diagonal I've got two Blues in this box so blue is not there if blue is here and I've reflected it here I've got two Blues in this region and that can't be right either so blue is there and I've actually established a position of blue but we don't know where the digit that blue is right but can we do more sidoku nearly blue is in one of those two squares right and if blue is in one of those two squares by symmetry blue is in one of those two squares H look that that's just just that falls out of normal sidoku I did it by reflecting the blue across the diagonal what about where is blue in where's blue in this region we do know blue and green are different don't we yes so yeah so blue blue blue is in one of those two squares and again we can reflect that across the diag Al can't we so blue is in one of those two squares right and that's very annoying because actually that's that's used up all our blesses we've we've got five Blues actually placed in cells and four dominoes of blue that look very deadly pattern to me so so we're not going to be able to resolve these by reference only to Blue is what I mean we're going to have to have something else interrupting the flow of blue to figure out the patterns we only need one we only need to get one of these because then they'll chain right so let's try green what can we do with green let's try oh yeah yeah yeah yeah where's Green in this box oh no green oh no green has already appeared in it I was getting very excited then I was thinking I could place green here but actually no I can't um well all right let's try green in this box then so green but green could be five couldn't it okay that can't be green because if that's green that's going to put a green there by Symmetry and there's going to be two greens in this box down here so green is not there green is not here so green is in one of those two I think but if it was that one it would reflect and if it's this one it doesn't reflect uh yeah that doesn't matter though does it so there' need to be a reason this can't be green to do with the fact it causes fives everywhere but goly gosh um I don't want to I don't want to go down the route of trying to work out you know if that's a five what does it do cuz it does do things if you know that's a five what's it going to do it's going to say we have to write a two into there I think and we have to write a four into there I think that's what it does and all of the all of the concomitant sort of follow-ups from those things I.E the Symmetry from those things fact that's weird now I think about that that's a slightly terrifying thought that makes me think the only way you're actually going to be able to make progress with this puzzle is by backing into stuff sixes and nines or ones and fives because knowing stuff about twos and fours which might emerge from say getting this was a five well this is always this cell is always doing something with twos and fours because it's in row two column 4 not quite I think this ah I don't think I'm that far away from having an Insight here how do we solve this I'm just going to check whether I can put green into this one green is not in those green is not in these yeah I I can't put it in but I can I can tell you that green green can't go so green by sidoku can't go in those cells I've highlighted now green can't go there because Its Reflection is there and I get two greens in this box so green is in one of those two squares on the diagonal and that's that's it that is it I think because I worked out there could only be one green on a diagonal so I don't I think if I think if I make this five green I can't put green at all in box one but I'm not I'm going to double check that green can't be BL no green can't be blue so these wouldn't be able to be green and if that's green that's green I get two green that's right that's right right so this is not green this is green and that is reflectable to here that's got to be so now I've got I've got four GRE if no I've got six greens oh I'm not going to get oh Bobby I know what I'm going to get I'm going to get stuff in here that is unresolved aren't I botheration I am I am cuz they're going to reflect over there aren't they ah and we're going to going to get this sort of deadly pattern again so whichever one of these turns out to be green we'll fix all nine Greens in the grid ah that was close we were close to having an epiphany okay right so I think what we need to do is to find another area of the grid where we can do well what do what do I think it is it's either going to be LW of leftovers or it's going to be the diagonal I think it's one of those two things and I'm unsure don't really know how to even I don't have any feel for which of those it is and I'm not really doing a very good job as I stare at this grid of working out of working out law of leftover tricks I can see which is a bit interesting that there is six here and that's going to go in one of those three squares by law of leftovers trickery which means it's in one of those three squares where are the boundaries there yes it's okay so maybe maybe six on this diagonal is a place we could think about let's just think about that so what I'm saying uh by the way the LW of leftovers thing I'm noticing here is um draw draw an imaginary line down this this section of the grid uh or if you want to do it by um by set Theory that's a complete box of the sidoku that's a complete box of the sidoku and this is a complete box of the sidoku so those those cells I've highlighted contain three sets of the digits 1 to n I'll try and do it with colors so we'll make those purple it's going to get a bit messy but obviously columns one 2 and three are three sets of the digits 1 to N9 let's make those gray so gray and purple at this point are completely equivalent if we didn't delete or remove from any remove from both sets any cell that is in both sets you can see we' remove all of these and we'd be left with the fact that these three squares are equal to those three squares hence one of these is a six um I'm not actually going to retain that coloring though because I think it'll confuse me but if one of those those is a six I'm allowed to reflect that six across the diagonal there and that's a little bit interesting now in terms of the diagonal cuz the six in one of those three squares knock six out of the first three cells of the diagonal so six on the diagonal it's not here it's not there it's not equal to one is it equal to Blue no it's not equal to blue blue is in the sixes row so six is in either there or there on the diagonal and if it's right I'm just going to highlight those squares for a moment if it's here it's in row four column 4 so it's indexing fours into two places it's four there and four there the sixth row and the sixth column so if that's if that's six these two are fours but four is not useful and if if this is six we're indexing um eight aren't we we're indexing eights into this square and this Square I think so we either it's very complicated because we're either index we either result it either results in a getting eights in the Grid or getting fours in the grid neither have actually very useful digits I don't think [Music] oh hang on I've just seen something I haven't seen before that can't be a one I'm not allowed two ones on the diagonal so one is moved over here can one be green one can't be well I don't think one can be green hang on a minute I don't think one can be green I think I'm getting mad now if one's green that seems to suggest I've got to no I do I have to put a one in one no there is a one in one of these I don't remember how I got how I got this is being green but it does seem to be right I right I think I needed to revisit ones much earlier I didn't realize this at all so one I don't think can go there one has to go here and that's reflectable to there and hang about about I just tried to put an this is huge this is huge for many reasons in fact before we get on to those reasons let me just see can I get one is not green so one is in one of those three squares in this region which is reflectable around in around the diagonal but these are not in the same region so I don't really want to do that pencil Mark CU it'll confuse me okay maybe that's not a straightforward as I thought it might be but no the other thought I had when I got the one here didn't I just say if that was if that hang on how did it work if that's a six I thought I had to put eight into this Square well and yeah that can't be right can it I'm going to I'm going to do this slowly don't trust myself at all but I think if that's a six that is saying because that's row eight colum eight that is saying right an eight into here it is it's definitely saying that that's how these this diagonal works if 6 is in Row 8 column 8 then 8 is in row eight column 6 row eight which is there it's that that we've proved that's a one that's definitely this is not right so this is not orange so this is orange that is six that causes fours to flutter about and appear in the Grid in those two positions unless I'm going crazy uh no comments please about me already being that way inclined it's been said before um now right well now I'm going to repeat the trick this remember what we said we said those squares were the same as those squares so I'm going to I'm going to write four into one of those I'm going to write four into one of those now I can't put four in any of those squares that square I could maybe go in the middle so four is now in either that's can four be blue no no I've definitely seem to have a blue square looking at four four is not equal to five so four can go in the middle of the Grid or there now what does that mean I could make those both orange just so that we've got consistency of coloring [Music] um so one of these purples is four and if it's here it's saying put eight into there and there if it's here it's saying write five into there and there right uh well I don't know what to do with that but I would note that that's completing our triumverate here isn't it so if we do write fives into those two squares then I think we're also writing fives into these squares or one of these three squares we'd also I think get fives in those squares I'm not sure about that but that's just where I was what I was playing with with sidoku in my mind just now 3 four five six seven we'd have two more fives to place oh and they're going to go in these 3x3 in the corners ah okay um right maybe I've got to maybe I've got to think again about ones I'm not sure I think it might be ones it might be nines I'm going to try ones first um I did get because I did manage to get ones over here yeah and I haven't thought about ones since I realized this was one I haven't think thought seriously about ones since then where is one for example in that region not there this one pencil Mark says not here this one says not there one is in one of those two squares I think let's actually pencil Mark that with a color and both of those should reflect across the diagonal into well that's quite interesting because because that reflection across the diagonal puts one in this position or this position now that means this can't be a one because if that's a one neither of these could be a one and we couldn't in the end once we work through all of the the weirdnesses we couldn't put one into this box so that is not a one one is now in one of two places and its equivalent then is one of these two places [Music] um if one's there if one's there then again that's that's part of this triumverate isn't it oh but we've already have one on the diagonal so that's maybe not surprising so if that's a one that's a one one two 3 four 5 six 7 8 nine oh yeah okay uh I have a the other bad feeling I'm having now about this puzzle is I think it's one of these puzzles you could just get terminally stuck on what I mean by that is that I suspect this has a very very linear path this it doesn't feel like there's you know there's multiple deductions that we can make at any one point feels difficult now can we do anything with nine was the other digit I was going to think about but I'm I don't really like the idea of thinking about nine I have to say where is do we think nine is going to end up being green it could be couldn't it it's a 50/50 chance nine is green in box three or box seven um do we know where the nine I don't know oh that's in that is interesting actually that is one point I've just deduced okay where where is nine in this funny region here it's clearly not in its own column it's not it's not one it's not five it's not six it could well be green but it's not there I've just noticed cuz if that's a nine I think that's saying right five into that cell and that's in the same region as I've got a five in so I don't don't think that can be a nine so nine actually is restricted in this box it's got to be in one of two places I think probably in green now if if nine was there well that would mean nine was there that would mean nine was here so we'd have you get these these sort of incred patterns emerging in the grid that this would mean nine wasn't [Music] green so nine be in one of those squares nine would be in one of those squares can nine be blue no nine can't be blue so nine wouldn't be blue actually where is nine in box one in this situation it's very hard to put it in I think it might oh no maybe it could be here one of those two I think not sure about that actually that might be incorrect although no it can't be in that one it would be in that one so that would be a nine which would make that a nine I think [Music] oh hang on now I've got no hang on I've done something wrong cuz I seem to have two nines in the same row I don't understand why I did wrong there that was that was complicated may maybe I'm just going to think instead about where nine is in this box oh no cuz I don't know whether Nine's on the diagonal or not this is very confusing this is very confusing indeed um can I do anything with this at all I'm beginning to think not um well dear if that's weird okay let's try something crazy and this what I'm about to say might be absolute bobbins but I just noticed something really odd there where is nine in this box I'm going to claim it's in one of those three four squares including it could be green okay so it's definitely in one of these now by by symmetry across the diagonal therefore nine the equivalent one of those I'm going to claim is in one of those sort cells now I don't think it matters which cell you pick for yellow now nine always ends up in green let me explain what I mean by that now this is this is really quite complicated but so possibility one is that yellow and green are the same so obviously then nine ends up in green so what we have to and prove is okay well what happens if nine is not in this cell do we know actually hang on I don't like I don't like what I've done there I've got to be very careful about this because I don't want to I don't want to indicate that there's any ambiguity about the fact these two are green okay these two are definitely green let's remember that as well so let's go back to this these two are definitely green so if yellow if if the nine is on this green cell obviously nine is green everywhere okay so this one is not the interesting one so let's take it out of there so what happens if nine is in one of the yellow cells now if nine is in this yellow Domino this yellow Domino ref F across the diagonal to those squares and those two squares being a nine will mean that is not a nine and the nine in this box will be in green so the Paradox is you can't do that because that's already green so you can't put nine in these it just doesn't work because it puts nine in green and therefore that should be nine by the logic we've established earlier so these are not able to be nine now what happens if this on the other hand is nine well if this is nine remember this is the equivalent of these so that would be nine so if you make that nine that's nine and then n nine is green again so nine is always green there might be a better way of seeing that but that seems that seems quite beautiful so all of those are nine which means these are not nine nine h no bobbins well yeah so we we have proved that nine is green here haven't we that is what we've just done and therefore nine is not there so so we can actually pinpoint nine everywhere in the grid that is now nine and that is in that is in row three column 3 so that's throwing a three here and a three here and all of these nines are throwing digits around the grid but we're just going to have to work out what those digits are right so where do we start with that should we start with this one let's start with this one Row 2 column 4 is equal to 9 so this is saying this is saying throw a two down here into blue and it's saying throw a four into here because this is in the fourth column and that's got to have an opposite which is let's not get this in the wrong place that's going to be there the two needs to have so two is blue so we can fill in a load of twos that two is on the diagonal and that is in row 7 column 7 so that is putting a seven here and a seven here now did we get all of the knowledge we possibly could from this so we got twos and fours and their opposites and the and the nin we did get six digits from that which is what we would expect to get good good now okay but we didn't use for example this Square we haven't used this nine yet so this nine is in row five row five column 8 so it's saying throw the eight in this row into the into this position throw the five in the column into this position that says five there eight there by Symmetry and that's all the digits we're going to extract from that one but we've also got this one as well so we're still making more progress we've got this one to do and this is in row 6 column 7 so that's saying in the row um be so easy to make a mistake here I think it's this is in the seventh column so I think it's saying put seven in here isn't it and it's saying it's in the sixth row so it's saying put six in here fill in the equivalence across the diagonal and the beautiful thing about that is it does seem to have filled in row N and column 9 somehow in the most peculiar way um what was what was our purple digit going to be was that I can't remember what that even was now um I don't remember what are these this is a three four pair so that's three or four by symmetry across the diagonal so that is a three or four was that one of the things we thought it was going to be if it's a three what's it doing it's putting an eight here and an eight here if it's a four the eights move up into those two positions we don't know very much about eight so we've only got this little poorly eight in the grid um right so we might not be able to do that let's let's try the diagonal we need to put 3 4 7 and 8 into it yeah okay let's fully pencil Mark that diagonal 3 478 I can see four can't go into those squares cuz we've got fours pencil marked already now this Square definitely can't be what's what region is that in that's in that region with a seven and an eight so that can't be seven or eight that's a 3 four pair on the diagonal so there is now a 78 pair along this diagonal and this one is indexing ones and this one is indexing twos well uh that doesn't work oh there's a seven here so definitely it's already resolved that's eight that's seven seven is indexing ones so there's ones in those positions now eight is indexing twos so there's twos in these positions two is blue ah there we go okay so we finally resolve the twos we've got to put twos into those two positions by sodoku they lose there Flash and have we done all the twos in the puzzle one 2 3 4 5 yes we have CU we have got the two on the diagonal as well have we got all the ones in the puzzle no we haven't but we might be able to do better better with ones now cuz we just got some ones as a result of that seven uh let's think about that we need we've got five ones in the grid so we need four more where is the one in this box one one of two places I'm going to claim and both of those are reflectable I'm not sure if we can do that maybe this column is a better place to look CU we've got this three four pair so we need sixes sevens and eight in yeah where's seven in this column I don't think it can go in those squares so I think it has to go there and now these squares have got to be six and eight now I've not used the power of this one that's going to result in a seven here but also let's think about it so that's saying that is in the eighth column so it's saying put eight here and it's in the fourth row so it's saying put four here so 4 three four go in that becomes a four as a result of that little Escapade this is saying put eights into the third positions which gets a sixes and six by symmetry over there that's a five so that's a five I'm not sure whether we should be focusing on um symmetry stuff or just almost sidoku stuff now that's an eight I don't know I I think I think I could have there's eight here by sidoku this is three we can fill these in across the diagonal 8 three when we bump into a problem now there is going to be no rescuing it if this is wrong I am absolutely um somewhere without a paddle like these are one and five which means that the but we can copy those across the diagonal so these are one and five can't see how that's resolving itself maybe did I did I do the the four implications no I didn't that four is telling us that's in row five column 5 so that does it those are both five those are both one has that done the yeah that has where's the one in this box now it has to be there so that has to be one all the ones in the grid are now done let's fill those in all gray that's that loses its gray loses its gray threes threes and fours well we can make oh we haven't done all the threes let's make them purple for the time being um W can I put a yeah I was just thinking can I put a three into that region but I think I can there so that has to have a three yeah that's okay still works working um this is a no no that's a six by sidoku that should be useful because that means I can fill six across the diagonal in this has got to be five that's got to be five and hopefully these can be the same digit which looks to me like it's four wow what a puzzle that is so let's let's double click sixes have we have we filled in all the colors that we've sorted maybe I should give everything a color that feels Fair doesn't it sevens can be light green fives can be yellow and fours can be whatever I've got left it might have to be black and that that needs to lose its flash what a puzzle that is hard that is so clever oh oh right this is cuz no one's managed to do it right so I am the first person to solve it cuz the test just couldn't finish it so I don't know if this is even correct I don't even know how I'm going to know know whether it's correct um W I will I'll have to spend some time I think uh thinking about this because nobody has put the solution in um so I will try and work out whether there's any mistakes in this I don't I didn't find a mistake as I was solving it I think I did it logically the fact it's come out at all gives me quite some comfort that it's probably right I mean it's absolute genius this man is an absolute genius Setter because that well what I there's many things I actually admire about this two given digits and this funny rule is enough to solve it but you have to understand the cycling and even understanding then you have to understand the diagonal that that you can't have a repeated digit I haven't got a repeated no I haven't got a repeated digit on the diagonal that's good [Music] um but even then then it was still quite difficult there may have been a let away I don't know I mean this this stuff here was very pretty the way that that the stop digits appearing on the diagonal there I don't know how you set something like this it's just staggeringly brilliant as always OD Take a Bow Take a Bow let me know in the comments how you got on we're just about in time for you to switch over to the streaming I'm sorry it's a long video again um and we'll be back later with another addition of cracking the cryptic

Channel: Cracking The Cryptic

Views: 64,620

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Id: t48G-kT-zcs

Length: 73min 36sec (4416 seconds)

Published: Tue Mar 12 2024