Phistomefel Blows Our Minds

[Music] hello and welcome to Monday's edition of cracking the cryptic where loads and loads of you have been asking me to have a go at the brand new fistel puzzle called border Square diagonals I'm going to try it for you um I've just read the rules before I turned on the webcam and I am astonished this has a unique solution um I mean let me just basically explain to you I mean you can see there's not much going on there's not much grid Furniture in this grid and the idea is that if you can construct 2 by two regions that cross a box border so like that would be one of them and what what the instructions say is that the two diagonals on this in this 2x two add to the same number so the two diagonals on that one add to the same number the two diagonals on that one add to the same number the two diagonals on that one add to the same number they don't have to be the same number between so doesn't have to be this one doesn't have have to add to the same one as that one but that's all the rules the only other rule is that the gray ones don't add to the same number and there's two tiny arrows and that is all the rules it it is it's absolutely perplexing um but fistel is a complete genius always makes me feel utterly inadequate um but I don't mind being made to feel inadequate if I manage to solve a fistel puzzle I feel slightly adequate at that point it's just the process that going from sort of Unsolved to solved that makes me feel inadequate um but anyway this is what I'm hoping to try for you in well I'm going to try it in today's video I hope I will be able to solve it we shall see um and I'll read the rules properly in a moment or two's time but Maverick that's taking you 1 minute 43 seconds Maverick's about to buzz the window I'm so sorry um anyway what else have I got to tell you on Wednesday night at 10 p.m. Mark and I are streaming the game braid this is Jonathan Blow of the witness um uh his his first game although they've just released this anniversary edition which I think has updated Graphics or something so this is what we we plan to try apparently it's good um I'm hoping it doesn't require awesome levels of coordination or we could be in trouble um but we'd love to have your company for that if you're free um other news where we are closing in slowly on 600,000 subscribers on YouTube we're we're under 5,000 subscribers away if we get there we're going to release a brand brand new free puzzle pack to the world um filled with puzzles to celebrate reaching such an incredible milestone for us um and some of the constructors of the puzzles in that pack are people like codec um P traie Peter Venus James Sinclair and also fistell so if you do this puzzle and you think you like more Fist and Mel that's one way to get more fist Mel and then the only other thing I wanted to mention in fact speaking of fist Mel is what's going on over on Patron we have my solve of a different fist ml puzzle that one is called sky skyscrapers it's Jolly hard and and Brilliant but Jolly hard um so that's over there now and also this is the big news on the first of June we have the Lord of the Rings sodoku hunt coming this is blo blob's magnum opus incredible incredible stuff um filled with the artwork of Ted Nate Smith one of the world's leading tolken artists and this this is a special one uh have I got I might have another picture of yeah here we go there's another oh that might be too big but hopefully you get the idea I mean it's just just gorgeous um and yeah 400 p.m. UK time on the 1st of June that is when that competition launches so look out for that um and then I've got some birthdays to talk about so let's start by wishing Louie a very happy birthday from your girlfriend Lucy um Louie apparently watches every day and therefore so does Lucy that's what Lucy wrote in the email um so Lucy thank you for writing and Louie many happy returns I hope you get chocolate cake uh today um next to long down there in Australia from your partner Mo um who described you as one of the most well no the most incredible person she's ever met um and you make her heart sing um you wild thing you um and um uh yeah and and she wanted to wish you many happy returns so long happy birthday down there in Australia and to the two of you good luck with the arrival of your little boy in July um next next Natasha and Maxwell twins turning 18 today over there in Wallingford Vermont and I know this because your mom Molly wrote to us and said you might like a shout out and I got sent by Molly a picture of the chocolate cake you're getting and this this looks Splendid to me I can't quite tell how much icing there is but I'm going to trust Molly that there's a good deal of icing so that looks absolutely brilliant and Natasha and Maxwell I think you're going to have a good day um many happy returns then to Dom from your sister Alexandra down there in Melbourne Australia um a city I visited on a few occasions I have relatives in Melbourne or just outside Melbourne Mount Eliza um and um Dom I hope you have a great birthday today um and then finally roit roit your friend Trisha wrote um and said that you watched and apparently we've become part of your bedtime routine and you once described the joy of watching a cracking the cryptic video and a solve as like watching your favorite football team score a goal what a that's a that's incredible analogy um I I hope it really does make people think like that um and roit anyway many happy returns uh Trisha wrote wrote a lot of very nice things about you I can tell you that and I hope you have a great birthday today now let's do the rules properly system's puzzle let's see if I can do this border Square diagonals these are the rules normal Sudoku rules apply so we have to put the digits one to nine once each in every Row in every column and in every 3x3 box digits along an arrow must sum to the digit in that arrows Circle so these two digits add up to that so let's do some example if that's a four and that's a three that would be a seven that's how it works um and then what else so we got now well now we've got the Border Square rule a border square is a 2x2 square that crosses at least one box border so that is a border Square for example in fact let's do an example of the rule as I understand it so we'll highlight this one and it then says for all border squares except for the four marked in Gray it's two diagonals sum to the same number the diagonals of different border squares May sum to different numbers so let's use the pen tool so what that's saying is that we sum those two digits so let's make that six and that nine and that's so that's 15 so these two would have to add up to 15 so they could be 8 and seven now have I got that wrong or is that correct I think that's correct that's how I understand the rule for all border squares except for the four Mark in Gray it's two diagonal sum to the same number yeah and they do so I think it's that and we have to apply that throughout the grid and then the world will be a happy place do have a go the way to play is to click the link under the video as usual but now I get to play Let's get cracking I have done um fist ofel did another puzzle that had a similar rule set to this but it was slightly less mad in the sense that I think the Border like the 2x twoos in that puzzle had to it was something like sum to a multiple of eight or something and you could do that you could sort of use that I remember to get some relationships with Domino's on the edge of the Grid or it something like that so I suppose what we have to do here is to use the secrets do we um well maybe I don't know so what I'm thinking is I know a secret about sidoku um I share it with my very favorite people if you're watching this video you're definitely one of my favorite people so I'll definitely tell you the secret the secret is that a whole column of a sidoku indeed a whole row of a sodoku or a whole box of a sodoku because of the rules of sidoku contains the digits one to nine once each if you sum those digits you get 45 now that's the secret but in this puzzle I think it might be two whole columns or two whole rows that's more interesting so two whole Columns of a sodoku sum to 90 now oh bird just that wasn't Maverick that was a bird now how can I use that so if I know those yeah okay so that that that Congregation of digits there is an even Congregation of digits what do I mean by that well what I mean by that is that because uh let me draw it in um because that diagonal and that diagonal add up to the same number um and let's say that number was X then those four cells must sum to 2X and 2x is even so the same if I if I do that one that's another even 2x two I'll do that one that's another even 2x two I'll do that one that's another even 2x two so all all of the colored cells I've just highlighted are even in total the whole column or two whole columns sum to 90 which is even so these two squares add up to even um right is that helpful is it helpful if you know I think in the other puzzle you got we were much better off than that we we knew that we knew they added up to 10 or something need we do it a different way ah oh yes okay so those two are also even by that logic all right hang on let me just I'm going to notate that one these two cells add up to an even number oh is it parity then hang on I've just had another thought is it parity because those must have the same parity if they add up to an even number they're either both odd or both even aren't they they can't be even and odd because even and odd would sum to odd I don't know uh but the other thing I was I was going to think think about was this if I start my 2 by tws in a different place that 2x two that must sum to even that must sum to even that must sum to even uh let's use orange now if I pinch that one that one sums to even cuz it Doesn't overlap fully with the gray so this Domino because the whole column again sums to 90 and all the colored cells add to even that is also a um an even Domino which okay let's just think about that a bit more because doesn't that mean that's even or is that wrong that in that 2x two the overall yeah of course it does yeah the overall sum of that 2x two I know is even but I know th those two add up to even so these two add up to even so those have also got the same parity and that's that's going to go up the column isn't it CU that's going to that has the same property then that has the same property then that has the same property then that has the same property and then you end up there so actually in this column there are an awful lot of um dominoes that contain digits of the same parity so each I don't know what these are but so I don't know if this is two odds or two evens and then I don't know if this is two odds or two evens but that's uh and then this one is going to break this up somehow is it but I doesn't I don't really understand this so if that's four and that's six so I've just made made those the same parity then what are these that the these are tot well no all all you know is a very tiny bit of information about these which is that these digits are selected such that the diagonals don't add to the same number oh golly that's horrible that's so probably well probably what we're meant to do is to try and overlap these common like you know double even or double odd dominoes with rows somehow aren't we so let's just see what that would look like if we if we do that and that and that and that that would work then we get another parity Domino there and let's just see if we can pull the trick that we pulled over here now how do I how do I do that if cuz I can't start there because that's going to overlap the gray one um oh Poppins that's ridiculous that's totally an uly oh it's much less useful because here I can't propagate it because I can't this is in exactly the wrong place which means that's going to be in the wrong place as well isn't it yeah because look how this is going to work in column sixes and seven we're going to get that Domino that Domino this Domino and then that Domino that's fine let's make that red so this is a parity Domino because each colored 2 by two adds to an even number but if I want to split this column up in some other way which is what I was able to do here because of the position of this gray thingy I could sort of overlap it from the other direction which I can't do here because it's too close to the edge so it'll probably work better with this one then [Music] um how's that going to look so if we go there there sorry I'll I'll do it in let's do it in uh colors there and there yeah that gets me another one that's a parity Domino now yeah well actually that one's useful because if I can get one in the middle of the grid I can propagate it because this one I can't propagate it left because the left 2x two overlaps the whole gray thing but I can propagate it right because that 2x two must add to an even number overall so if those are even that's even as well so that's even that's even that's even and that's even now can we go the other way though can I so I have no it's weird actually that's weird it can't I kind don't think it works how could this possibly have a unique solution it's it's absolutely ludicrous I know these all have similar parities it must be this column this column is by far the most restricted well and when I say restricted I mean I've got more dominoes in it that that that have common parity I don't understand this I don't understand this at all I'm missing something about the actual numbers here let's let's let's do some examples and try and work out how this works so what do we have before we were we made 15 dominoes didn't we let's do that so we made that six that nine that seven that that 8 now is that in any way wrong no that clearly works and then this one this one that number is going to be providing that number is one less than this number the yellow the yellow 2x two will work won't it so let's put three and four there that's quite interesting so what that's showing that is interesting actually sorry I realized I stop speaking then I'm just I'm just trying to mull that over for a moment the thing I'm noticing is is that you always have a common differ ah is it you always have a diff a common difference that makes that actually does make sense now I think about it not only do you have a common difference between the do in in these cells here but you always have this side is always higher than this side by one so you yes that's all ah ah ah all right right okay this is really okay I hopefully everybody can see that this example is actually very helpful at least to me because what I'm seeing is that in any Domino one of the numbers will be bigger than the other and then that effect sort of has to be [Music] um the effect of one number being greater than the other has to be reversed out if you like by the the cell above it but because we're looking at diagonals the effect of that because because 9 is one greater than 8 we need we need the eight to get one more than than than the nine gets in this row but because we're looking at diagonals the higher number is always on the same side as the higher number below it and that's obviously propagating up the row now now why is that interesting well what I'm thinking now now this might not be right what I'm thinking is that one side of this either that side or that side is full of higher numbers and one side is going to have more low numbers because obviously if we extend this up the grid we're going to have loads of high numbers on the right and loads of low numbers on the left so that's going to be the same here right okay ah so okay let's think about no I'm going to think about this slightly differently what is the common difference what is okay what is the differ let's look at this Domino what is the difference between one side of this and the other and the answer is I have not got a Scooby-Doo except I sort of have got a little bit of a clue because these numbers have the same parity whether they're odd or even the difference between those two numbers is even imagine this was I don't know 8 and four the difference between 8 and four is even if this was N9 and seven the difference is even isn't it because these have the same parity the difference is even so down this column or down these two columns the diff there's going to be a high side and a low side and the high side is going to be an even difference so a difference of 2 4 six or eight to the low side but that's interesting I think that means the difference is two doesn't it because if the difference was four how could you yeah if the difference is four between the high side and the low side here let's say this is the high side which means these digits are four lower than these digits well where am I going to put the three in this column that would be my question that would be my first question uh the three can't go in any of these positions because that the three this this side on this side of the line we'd need a digit four lower than three and there are no such sodoku digits so the three would have to go down there but then I'm going to say okay if my three goes down there where am I putting the two in this column where am I putting the one in this column there's nowhere they' they'd all have to go down down here so what that means is that in this in this Arrangement the difference between the low and the high side of these is two and then right so I know what these are these are 1 2 8 and N because because you can't you can't put uh this is this very hard to explain it's very to explain because I don't know which way round this goes but let's think about let's imagine this is high let's make high numbers hot they can be sunny numbers and these cold it might not be this way round um but let's just assume this is the case now where could I put the nine and the eight in the cold numbers bearing in mind the hot numbers have to be too greater you can't put the eight and the nine here can you so these would have to be an 8 n pair and where in in the hot numbered column where can you put the one and the two because the the cold side of that line would have to be two different and two different than two is zero two different than one is minus one that's no use so these have to contain the numbers 1 28 n that is not well okay good G it's so simple now ah this is beautiful the logic here is beautiful because now this is the high well no it no hang on hang on hang on well that's high so we know we know this is also High don't we because it's the high numbers that have not been able to be put in here but does that mean that's actually ah no so these colors are are the wrong way around I think yes they are yeah because because I can put seven into these cells and have a nine on this side because these are higher so yeah I've got I've got the order well I mean it's actually a good thing in a way the blue and they're going to be high and then these are going to be ones and twos and I can put a nine on the hot side cuz I can then Shield that with a seven on the cold side um but I couldn't have put a one or two on the hot side because then I'd have had to put a zero or a minus one on the cold side oh this is gorgeous so now well now what so now come on we're nearly there I think um well when I say nearly there I I mean I almost understand it now which is much better than I was doing before so [Music] oh so I just I've just totally missed the point here haven't I sorry yeah I think I might have done I'm what I'm now thinking of is that if we look at if we look at row six and row seven combined the only the only 2x two that is that disobeys the rule that dis disobeys the common difference rule is that one so all along here we get overlapping 2 by tws that all have to obey this rule before finally so on one yeah okay so on one side sorry I'm just going to get rid of this oh no I don't know if I want to get rid of that I want to sort of remember it I'm going to get rid of it momentarily um because I want to just I want just want to focus on this now one side here is going to be high again and one side is all going to be lower and what that makes me want to say is that who what was that noise sorry I think that was a big noise oh I think something fell out of my pocket uh that doesn't matter um what I want to say is that isn't this a 1 nine pair then because on the yeah that must be right this is a one n pair so that means that's going to be a one nine pair as well because because in this row let's say that this was let's say this was the high digits and this was the low digits again it's the same point isn't it in the we can't put a one in the high digits because this would have to be a lower number than a one to maintain maintain this relationship between the numbers so and and then vice versa on the cold side you can't put a nine in because this would have to be a 10 or higher but does that mean [Music] is does that mean the difference is one definitely in all these dominoes yeah yeah it does it does it does mean that that was my instinct and I think it's correct because in in the high in the high row which might be this one might be this one but in in that row there is going to be a two isn't there and what are we going to partner the two with here it must be the one and that establishes the difference of one which must propagate along the line this is so brilliant this is absolutely brilliant so so this right I'm going to get rid of the colors again now cuz they might be wrong although they weren't we do actually know them here so I must remember that um I'm going to get rid of this cuz we don't need that anymore I think I'm starting to understand it so what we're now saying is that in these two rows there is a difference of one between vertical dominoes but I don't know whether it's I don't know which is the high side and which is the low side in this that must be exactly the same logic here all of these 2x2s must have a common difference one side will be high all of One side and then another side will be all lower digits so one and N are going to be the problem digits don't know the order and there's a difference of one between all of those squares now this one this one I'm not really sure what I'm being told here I'm being told that these digits so okay these digits all have these do have the same parity so we're in this world again aren't we the difference between all of these digits is an even number so all of those on one side or another right right okay I might be about what I'm about to say might be silly but I'm just let me overall yeah ah got it I think overall the differences have to sort of the differences have to match out or or even out because because both both rows and columns have the same numbers in overall so if for example all of those were bigger than all of these then these will all have to be a bit bigger than these to even out the difference such that overall net net the difference between the two rows is zero now that's interesting isn't it because what you've got here is five Lots of an even difference and what you've got here yeah yeah watch watch watch all of those have the same difference and then the then then then this breaks it up and all of these have the same difference but with the additional bonus that we know the blue ones have an even difference but yeah but but there are five so five times some difference here has to equal four times some difference there so right so 5 * 4 is 20 there is no there is no common multiple I mean we it must be it must be 20 mustn't it because what what I mean what I mean is I think what that's saying is that the difference here on the blue ones is four because if I do four * 5 I get 20 and then the difference here is going to be five because 5 * 4 is 20 and that's going to even out the differences overall so say this was this was these were all Heavy digits High digits these would all be high digits in the other direction and overall net net the the row would balance and that also well that's sort of conf confirmed by the fact I know I know for sure these have an even difference from the work we did earlier so so it's something to do with this I don't don't understand it immediately but it's going to be something to do with this Arrow isn't it because now I know that either this is uh yeah I don't quite I don't quite know how to to show this uh let me go to the pen tool again uh go yellow so I know that the difference between this digit and this digit is four but I don't know which is higher and then I know the difference between this digit say and this digit is one because of the the work we did earlier on understanding how one and nine stick out so does that mean the difference between this and this is five it might do and well more more to the point is it telling me is it telling me that this is the higher digit in this row CU if yeah that that must be right mustn't it let me just I'm going to have to play with some numbers here to to really convince myself this is true but I'm what I'm going to try and do is is prove this that this is not higher than this so if this was higher than this let's make this seven then we know because we know that the blue differences are four we know this is a three and now th well this it doesn't matter if this is higher I mean it doesn't matter we know the difference in the yellows the yellow plane of is one and the arrow doesn't work does it that's great that's absolutely great because that's telling us that these are high and it's telling us these are low and the difference on the blue arrows or the blue struts is four so I cannot put a digit I cannot put there cannot be four in these top digits 4 3 2 or 1 because these would become zero or negative so these are a Quin Tuple these are 5 6 7 8 9 and these are 1 2 3 4 5 it's a lot of pencil marking and I hope you'll forgive me but that is what's happening right but right but this but which way around does this one go now I know it looks like first blush not sure actually I this one I feel like that wants to be a massive digit um but so you know I want to make that nine but maybe that could be high I'm not I'm not sure I'm genuinely not sure if that's eight then we know that this would be four different so that would be a four and then this has to go in the same direction and these are one different so why couldn't it be that they add up to 11 there might be a reason I don't uh so my I'm just trying to prove to myself why cuz my my instinct was this would be the higher side of this column that might not be right I can't a sorry and I realize I stop stop talking I'm just trying to I'm just trying to understand it is there a reason why then by maths this would be three but I mean these numbers don't mean anything I could have picked other numbers three that would be two so at the top of the column this column couldn't have a nine in it so that would be a nine and that would be a one no I don't know I'm not sure wow okay but let's let's keep thinking because if we know these are all the high numbers in row three these are all the low numbers in Row three and we know these are therefore all the high numbers in row four and we know the difference on this line in order to make sure that overall we're net net in the same position these have to have a difference of five so one of these is going to be a one six one of them is going to be a 27 one of them is going to be a 38 one of them is going to be a 49 ah okay right maybe I should have started here that is not one or two that is not eight or nine and what did we say the difference was so four so this is not 6 or seven and this is not three or four now okay and we yeah and we we'd already worked out hadn't we that this was the high side of col of these two columns so the these are higher than these oh they're higher by by two aren't they that's what we worked out in this column so if this is three this is one if this is four this is two and we can probably do something with that can we oh I've got something else in oh this is lovely right in these two rows we worked out that the difference between all these dominoes is one well if the difference between those digits is one this is odd this must add up to an odd number so that's a ner I've got a digit 98 I've got to make the diagonals add up to the same number so let's reverse that out there oh that's gorgeous so so this is a four five pair um I probably know the order somehow I don't I don't actually know if I do know the order I can't see how I know the order good grief that's just oh that's not a four uh which means that's not a nine because we have to we have to pref preserve differences of five on this string it's quite hard to keep track of this actually it really is okay and let's check that the difference rule Works according to my understanding of it because I've got seven differences of two here which is 14 of difference yeah and these two numbers both differ by seven in the other direction so I've got 14 of difference throwing throwing the sort of weight back onto the left side from these being higher so this this is this is It's All About balance we have to balance the force um okay well let's try this one then so that's not one and that's not n now what are the differences here the difference is four on this side so taking one out of here knocks five out of there taking nine out of there takes five out of there right disaster um I there has been an enormous Interruption just now um I have still been sat sat here um but I got a phone call that's meant I've had to make lots of other phone calls to try and arrange lifts for people and that has been an enormous Interruption um I have not I've not been able to do anything on the puzzle it has been in front of me having said that but I haven't been concentrating on it um and yeah I'm I'm sorry um and now I will have to I'm going to have to re reinvent the wheel and that is not a good thing um but let's see what on Earth were we doing here let's go back a bit we were oh okay I put four and five in there why did I do that that was because we worked out that there was a yeah because there was a diff yes because there was a difference of one in these two rows I remember that um and then we did something here okay that's just sodoku isn't it what with the yeah the we worked out some differ didn't we these all had differences of these all had differences of some sort or another four and those yeah they all had differences of five right okay so and had a thought about this Arrow let's think about the arrow again um what what on on Earth had we concluded about this um can I use this one n pair to do something what one is over there actually uh so okay maybe sodoku maybe I'll do some sodoku ver there's a nine over here by sodoku by using this nine and the fact there's a nine up there no okay sorry that's probably not it [Music] um he says I'm trying to do soku now this is how desperate I've become um no okay let's go back to this Arrow let's have a look at this so what were we saying here we were saying that uh yeah there's there's some weirdies going on isn't there if this digit this digit is definitely four bigger than this digit but then this digit I know it's one different because of this but I don't know whether it goes up or down to get there so let's just make that seven for a moment and just let me think about that so that's going to be a three this is going to be a two or a four two or four so this digit is a three or a five depending on how this plays out and that should be consistent should if I make that six that's going to be two and then depending on which way round this goes whether this is higher than this all down the column or whether this is lower than this all down the column 62 this will be 62 this will be one or three yeah okay and that this is three or five I mean admitted it couldn't be double three in that situation but there's no reason that this would necessarily have to be a six it could be when when it was seven that that would work um right okay so that digit is restricted I think because because that this digit must be one differ from this digit in a particular direction which we now going to have to rework out again let's make that seven again make that three I'm sorry about this I was probably on the verge of basically doing this in some sort of sensible way before but it's been it's been a long long Gap [Music] um so if this is seven this is three this is two or four so if this is two what we're saying is that this is this is the high side of the equation so if that's two that's five this is higher than five so that's six whereas if this is seven this is three and this is four then this side's higher so that being three means that's two and this is two or six and that is absolutely useless that's rotten okay so that's okay that's not how to do it and depending on okay and then depending if that was 32 then this side's higher so we couldn't put one in here so this would be one so if this is 32 this is one if this is 5 six that's nine presumably yeah that's right okay [Music] um oh dear uh I'm really discombobulated now let's try and I don't really know I don't I don't know whether I meant to where do I think it would be they are they restricted because they have got to be they've got they've got to they've got to obey the rules for columns three and four yeah there was a two difference wasn't there there was a two difference in columns three and four we are and we do know the order these are higher than these according to that anyway so this is the high side this is the low side but also we've got these going on so in the vertical dominoes here let's put some vertical dominoes in in those vertical dominoes these are differences of one now what does that mean and well that's not nine is that a valuable deduction it's not nine because that would be eight and that would break that square because these differ by one oh by the well by the same token that's not three because that would be four okay so that's not it's not very extreme so hang on let's just let's just write the options in four five 6 7 or eight that's a that's pathetic Simon hang on if that's four that's five that's four oh I see no that still doesn't work does it this might be absolute rubbish I'm just going to I'm just going to check this logic though if that's four that's five and that's four that's clear but now the direction of travel along these two rows is that the bottom row is bigger than the top top row so this is a three to preserve the the the relationship and that cell still broken so that doesn't work so that's not four all right let's try that uh or maybe it doesn't work with five either if that's five this is four this is five now this has oh that's has to be higher that's going to work isn't it because now now now it's not under pressure it's not under the pressure of that digit anyway okay but now if that's 5 six 7 or8 this digit is to lower than 5 6 7 or 8 so that digit is three four five or six I don't think this is the way to do this um uh sorry sorry sorry um maybe if maybe I can stop this being eight because if that's eight I know it can't this can't be nine so we have we have to be going so so again the bottom row is higher which means I I would know that that would be six that would be five now is anything broken there may don't think so um no this is this is absolute bobbing sorry sorry this is um this is tricky isn't it okay let's try something else let's try I can't this can't be 67 so if that is six that's five I'm just going to check that as well sorry 6 five so now this has to be in that order these have to be greater so they have to be seven8 oh this I just reinvented what I just looked at I fear I fear so I think I've just re reinvented literally what I just looked at from a different perspective okay sorry [Music] um ah okay okay where where is yeah look at this Row one and two are in those squares somewhere which means one of these two digits uh let's make that what color yellow uh one of those two digits is a very low digit and it can't go in there anymore so one of these digits is in one of those squares and is very low so it will have quite a low digit here which might be important one of these digits is six or seven as well that's interesting isn't it if if if the seven wasn't here the seven would go up there and that would be a nine I have to go there that would have to be s n seven there nine there that would be eight that would be six um if that's 32 they have to go there look that's quite interesting actually um if that's 32 by sodoku they go in those squares and then my yellow digit couldn't go here actually okay um let me just have a look at that if that's 32 I can't put a low digit here anymore can I when I say a low digit I mean a one or the one or the two that must exist in yellow if that's a one that's a three and if that's a two it just breaks so in fact the yellow digit would have to go there there and that would be a one or a two well ah ah well it couldn't be a one because that would be have I got this the right yeah that would be the three so it would have to be a two there that would would have to be a four two four would have to go in those squares that would be a five that would be a four two four hang on that feels wrong that feels the wrong way around hang on 2 454 means ah right I can prove that they're right I can do something this is not 32 although This is complicated right um so let me try and explain this slowly okay so yellow yellow which is a one or a two and I don't know which has to go some somewhere in this column now I'm going to claim it's in one of those squares I think that is true isn't it so there's a one or a two in one of these now if this is 32 I think it's legitimate to say this can neither be one nor two and that's right because this is always the high side so this is one this is three this is two it just breaks so that's not yellow anymore so this is definitely yellow and it's definitely not one because if it's one that is definitely three so it's definitely two here now I think this breaks for a rather weird reason to do with that if that's two we know this is now four we know this is now five we know this is now four and look that the this Top Line is the high side so these digits need to be lower than two and four that needs to be one and that needs to be three and that's most certainly broken yeah you can for any number of reasons oh that's very lovely that is very oh well I'm not saying well it's very lovely because it means I can at least progress um so that's a five and that's a six that meant something didn't it about the order of those but let's not worry about that for the moment let's try and do some sodoku if we take five out of these we take nine out of those because we need we know that on the blue lines we've got differences a four that is now not a six so this is not now a two that is not a five so that is not a one yeah but now oh no easier still six is higher than five there is a knowledge bomb for you so six is higher than five this is all the high digits and this is all the low digits so this has got to be the one in this column this is the nine that's not a one anymore which means that's not a five anymore um yeah okay but we also know don't we that the these digits are now in this column these digits are one higher than these digits so does that help us to know things about the world so if that's seven that's three that's six that's two and now the world Works yes okay okay um well um nine nine in this string of digits is definitely in those two squares which means these two squares definitely include a five or we already know that we can already see that so there is a five in one of those cells there's definitely a six up here and there's a six here now so there's definitely a six in one of these squares oh that's this is peculiar isn't it because it I thought it would just this this would be sort of very powerful but actually it's not really it's not really open the puzzle up to us has it [Music] um no miss the answer to that one of these is a five that's a five this is one greater all of this is one greater than all of this so presumably oh what am I meant to do what am I meant to do with this you naughty puzzle is there's now no problem with this being a low digit because this digit is under much less pressure although no and also this can still be a one no it can't be a one can it oh is this is there a more General point is there a more General point which is that the yellow digit can never go here I wonder if that is that the whole point of this sorry okay I'm going to come back and think about this again so what I'm wondering is if if the yellow digit did go here let's just examine that for a moment we know it's we know we're now claiming this is a one or a two but we know that the orange stripes represent a difference of one don't we so this would in fact be a two again and that would definitely be a four and this would definitely break again because this is now five this is now four and this needs to go downwards and this can't go down this is this is really big this is really big I'm so sorry I didn't see that but I'm going to blame everything on the fact that I I got into interrupted but now this can't be yellow at all so in fact that is always yellow that is always one or two there's a one two pair in the column this square is a three or a four um and that must do something probably there's a three four pair in this column uh uh I wonder if it's saying something more generic about the order of this as well it may maybe that is also an interesting thing I ought to understand if what was that caused by it was caused by this being a two4 pair but I'm not sure actually I'm not sure that that is right that there is some more General point that we can determine that digit there is definitely fully yellowed and the other digit is going to be a three or a four but that could go there so we can't assume that goes there otherwise we probably would be in luck so okay so what do we do now I don't know I really don't know um is there going to be I'm sorry if you can all see this I can well believe it actually oh here's a tiny point nine is in one of those three oh in fact in one of those two squares so n is either here or here yeah that's oh that's really easy yeah okay so I'm going to claim this can't be nine because the the the orange line is going to make this be an eight and that's going to break that square so that is in fact a nine which means and that's on the green lines which have a difference of five so that is a four and that is no longer a nine and if that's no longer a nine that is no longer a four which we've the coroller which we've already sort of worked out haven't we okay so does this nine now do something I would love to know the order of this because that feels like it would really matter doesn't it because it's going to determine every the direction of the orange lines in that box this four oh yeah that's big so sorry so that's got to be a two that's a one and that's a three I'm just pausing because I want to see what that's doing well that's two that's got to be a seven doesn't it it's got to be five different so this is a 68 pair this is a 1 three pair which I suppose we sort of already knew well we didn't know but we sort of right so what does that mean has that has that done dramatic things these now don't include three so three is definitely in one of these squares three we know lives with seven on the blue line so there is a seven in one of those squares so these don't include seven and if this is two or four this is no longer eight look so that's come right down that's seven or nine which means this is no longer four and it means the oh that's fine isn't it it's CL well we're getting closer I think slowly slowly being the operative expression um okay so it would be nice as well if any of these digits I was putting into these columns were affecting these two digits somehow I suspect I do think there's likely to be something going on there that I'm just not seeing can I make better use of I mean that can't be no that can't be nine nine is in one of those cells if nine was here that would be nine that would tell us these were lower than these I think that's my best guess as to what's going on maybe three and four here so if this is five now this is six and this would be a 3 four pair well actually that looks quite like that looks quite plausible doesn't it three in the column three is definitely oh yeah that's interesting I will make use of that three in this column is definitely in this Domino here I don't really want to pencil mark it across the box but it is definitely one of those two squares by soku now we know therefore that five oh that's it so five is in one of these two squares and it can't be there look so that can't be the three because that would make that 35 and break this Square yeah okay so that's three so that's five and this can't be two so it must be four I really hope this this goes the right way around now because that's five and that's four by sodoku and it is going the right way around in the sense that all of these are going in the same direction which gives us confidence that we understand what's going on so this is one this is nine now that what that's given me a one by sidoku there that's on a blue line so this is five oh please please work now I've I've tried hard that's a one um by again by sidoku come on come on we must be close right we know what these digits are 1 2 3 4 they are five and six so these are seven and eight that's good that means that's known that's six is that going to tell me how this arrow thing works uh I know this is the higher end and these are one differences yeah that's fine so that's seven this is two and that's three and everything is increasing by one that's got to be a two because that should increase by one that is a 2 by two to which the rules apply fantastic right so now that's an eight by sidoku that is a four that should be a nine which means that's a five oh my goodness there is a there is now a semblance of a chance I will finish the puzzle and that's that frankly is just relief because I was very very worried that I would completely lose track of everything but actually it's going okay it's I don't know how long it's taken me extra but it's taken 239 into the that's a three by soku that's a three that's a one and now we know the differences here were what they were massive weren't they they were the massive differences so that's eight that's six this these two squares are two and nine so in this row we've not put in seven and eight and we can do it by using an old friend called sidoku these are two these are two and nine that's nine that's two um now what were the differences ones and the top digits were higher so 18 is how that must look what a puzzle this is by the way I mean how do you set how do you come up with these patterns fist ml again just demonstrating awesome awesome oh no I've broken it no okay that's because that's not 67 I've already got a six here oh that was horrible okay so this is 78 I don't like that so this is 67 okay so 6 7 87 please don't have broken it these squares here are three and four and that should be a an eight so these squares are two and three which we can do these squares are 3 4 5 six oh that's not resolved uh okay let's try something else let's try where should we go there's a bottom of this column four five okay so these squares are 2 3 6 7 so there's a two in the corner 367 triple left over which I don't think I can resolve so this column needs three five and six that's five or six could get a three in the corner up there five six pair in this row that's again a slightly desperate thing to spot 47 8 9 so this is four or seven it's not seven is it that's a naked single sorry I didn't see that so that's four uh this is three five or six and it's three or six then so there's now a 356 triple in row one so I need four seven and eight that's a naked single seven so that should be a four if all of that logic was correct oh I could have got that probably from sodoku if I'd done it in a different order uh these two squares are an eight eight and a nine so that's a nine and that's a two now in this column I need a one six pair which I can do and is that going to do things over there well not quite um oh I could use the rule use the rule Simon it will help you maybe two goes there five and seven here oh I don't like this oh it's going to be the rule here isn't it um so which side was greater this side was greater over that works oh no have I reached to some sort of deadly weird pattern in this puzzle it's possible oh no here these these these were two differences weren't they so that gets me a 635 that gets me a 3 34 four five it is resolving I don't know how uh but it is oh I think I've done it let's see oh thank goodness for that that is absolutely startlingly brilliant what an extraordinary puzzle what an extraordinary conception to it's beautiful it's so beautiful this is this is like I don't know this is what I imagine pure mathematicians relish when they see Fat's Last Theorem or something they can just understand it at some level that's profound and I think that's what fistel does with numbers in sidoku grids he understands them at a level that is profound I mean it's so weird that diagonal 2x two boxes always cause a number it always cause a big number to be on one side of the of the line you know and then small numbers on the other side of the line the way it's been used in this puzzle it's quite magnificent it is quite magnificent I look forward to the comments on this I enjoy the comments especially when they're kind and especially when they give Fist and fell the most immense amount of praise and we'll be back later with another addition of cracking the cryptic [Music]

Channel: Cracking The Cryptic

Views: 56,688

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Id: REUywhgfkRk

Length: 79min 25sec (4765 seconds)

Published: Mon May 27 2024