The Most Incredible Sudoku Rules EVER

[Music] thank you hello and welcome to Sunday's edition of cracking the cryptic where I'm I must confess straight away I'm feeling slightly delicate today um at a dinner party last night shout out to the cornishes and the beaumonts I I rather over indulged it was entirely their fault I have to say um and I've been feeling very sorry for myself this morning and I don't really know why but I think that today is the day where I'm going to be well I'm going where when I when hopefully if I can get the words out I'm going to attempt knt's Infamous and apparently Majestic puzzle Pathfinder um now this was a puzzle that we put up for a vote a couple of weeks ago we said you guys vote for the puzzle we do the following day and although this didn't win the vote it attracted some absolutely extraordinary praise from some of the greatest solvers and Setters in the world apparently this is a truly unique puzzle um and it is supposed to be brutally hard um so I do this with some trepidation I have got a supposedly easier puzzle in reserve so if I can't do this and this video never sees the light of day you won't even hear me saying this but I will um I well I will I should be okay because there is another puzzle that's gone past our testers um which is apparently very suitable as a backup so I might I might I might do that later we shall see um but let me let me just talk about knt because I just snipped um I just snipped this which is knt sort of recent record of puzzles and I think it's just worthy of attention there are very very few Setters in the whole world on logic Masters Germany that can achieve this sort of consistency almost every puzzle is rated a hundred percent um and almost every puzzle has five stars out of five for difficulty kmt is clearly a phenomenal brain it really is it's startlingly uh or starting how clever knt is I've read this rule set now twice as well and it is baffling it is baffling um I have no clue really how to approach this one but I'll read the rules and share them with you in a moment or two's time I do have some birthdays to do today though Horner it's uh it's your birthday I know this is your boyfriend Jeff wrote to us I hope I'm saying your name correctly Jeff did provide me with some guidance but I I'm I'm not sure if I got it right but I I hope I did and I hope obviously you have a brilliant day with lots of cake um Jenny it's your birthday today I think you're in Stockholm your boyfriend Magnus wrote to us um and he thought he well he asked me to say to you that he thinks you're the funniest and smartest person which is rather lovely and Jenny I hope you have a brilliant day and also to the Constructor spell daddy spell Daddy it's your birthday today I know this and I hope that you have a great day too um and the only other thing to mention is what's going on a patreon where you've got the opportunity if you can solve this month's monthly reward um which is by glum hippo it's the fossil hunt to win the glum hippo blushy so look out for that that is going to be a prize worth winning and then um some of you of course managed to complete the whole of Jay Dyer's hunt last month and I want to congratulate lepi r64 Zorro Parker Bond Beyond book Ori Pitts Chase pajani pajani Chase pajani I think jarco Purdue Niemi but you need me yeah I think it's that petunia me um VJ Toco I think shyra Golda Jackson Keaton Hancock Dr G Andrew montillioni Mark dumore Eloise and Jenny Cook Robert dalstrom Micah turvey Oleg Isa and Anders Sorensen well done one and all now now let me get my head in the game and let's see if we can even start the puzzle Pathfinder by knt I have got an example puzzle let me get that I snipped that just before I turned on the camera um so we will oh what have I done there didn't mean to do that oh it's just that okay so let's get this on our screens while I read the rules so our job is to divide the grid into regions each consisting of nine orthogonally connected cells so the example is just using the numbers one to six each row column and region must contain the digits one to nine once each now this is where it gets mad the digit in the top left cell of a region it's left most cell in its highest row is its region number All Region numbers are different Okay so we've got the digits one to nine acting as region numbers in the example these cells are circled I see so yes if we if we study the circle digits here you can see they're a set of the digits one to six and they all appear in the top left most cell of their regions now you must find an orthogonally connected path so it visits every region exactly once and the path must visit each region in ascending order of the region numbers hang on sorry I've just got to scroll down that I'll restore that there right you must find an orthogonally connected path that visits each region exactly once and the path must visit each region in ascending order of the region number so if we come across here and look at this again okay so the path starts in yellow on a four and then it goes into a region two and then it goes into Region Three and then it goes into region four but it goes into region four in with the digit three and then it goes into region five then it finishes in region six okay fine um within each region digits strictly increase along the path that's interesting so that means that we can view the path that is pursued it within a region so like a therm a thermometer um now that doesn't really work when we just snip one cell from a region but you can see in red for example four five six in beige two five six in green 245. so we have to sort of build little thermometers along the path within a region [Music] um a digit in a cell with arrow brackets arrows a digit in a cell with an arrow indicates the total number of cells in the same region as that cell that are part of the path in the indicated directions combined hang on a digit in a cell with an arrow indicates the total number of cells in the same region as that cell that are part of the path in the indicated directions combined right let's look at this three then what is that saying I see so that's saying that within the beige region I'm looking at this digit you can see there's an arrow pointing left and then arrow pointing diagonally downwards and if we count how many path cells there are in beige in those two directions combined we get one two three so that's why I think this digit is allowed to be a three let's try another one um yeah okay let's look at this two clue here let's look at this so again looking in the red region which is what the region that the two is in there are two there's a path cell here which is the four cell and a pass cell here which is the sixth sixth cell so there are two cells in those directions on the path okay that makes sense sort of um if a cell has multiple o if a cell has multiple arrows there must be at least one cell on the path in each of the clue directions I see so what you can't have is a frivolous Arrow so if we come to this two clue it wouldn't have been allowed for there to say be two cells in red on the path in a North Westerly Direction and no cells in red on the path in a southwesterly direction that would have just been that would have meant one of the arrows wasn't really counting anything and what we're being told is that all all of the arrow Clues have to point at at least one One path cell okay so that's the rules um this is the puzzle do have a go the way to play is to click the link under the video as usual now I get to play Let's get cracking and I'm going to start I always start these puzzles the same way I look for cells that are pointing it's a bit trickier here I was going to look for well that sells okay isn't it that's got one arrow pointing down there so that can't be greater than two I don't think that's one or two that's one two or three that one is one two three or four um yeah but I was thinking for example this one is not very helpful because that could be one two three four five six seven eight that see that can be basically anything this one points in four directions one two three four oh it can obviously it can be massive down there this one can be massive again I think that could be as much as eight that one ah that one can only be four because it's only looking to the West therefore that one can only be four for the same reason that one's looking East and could be massive this one is no that's a one two three four five or six oh dear oh dear we're already in trouble we're already in trouble here foreign I have a horrible feeling that there is some Meta Meta deduction that might one might have to make to even start this puzzle because unless I've missed unless I've missed an arrow here nothing is very I mean none of this is helpful is it is this one helpful right let's try and understand what this is saying this is saying that there are either one or two path cells in yellow in this direction Earth is that helpful I don't even know that this one is yellow it's possible that's yellow although how I see this is pointing at something to the east so whatever color that is there's got to be some similar color in that direction so maybe it would have to go like that if it was just this one and what I'm thinking is if that's out I don't see how to do this at all I don't even think I can I don't think I can conclude anything here um sorry uh I'm totally Bamboozled that one this one is looking at one or two do I know that I don't know the region number of this do I of course I don't because we don't know where this region goes I mean if it's top left cell was there it could be any number I know that there is at least one path cell down here and if there were two path cells down here oh and I've got the thermo thing to think about haven't I so okay yeah but that doesn't doesn't do anything is this somehow meant to interact with this clue so if that if that was yellow it's quite hard for that knot to be yellow then I don't know that it's impossible but if that's yellow and we try and make that red then that would have to be red because this Arrow clue to the West must see some cell that's on the path in its region and there must have to be some cell up there you know no this is okay isn't it I could do that and that one two three four five six seven eight nine in fact that only oh that one no that might break there um but anyway this is the problem is this is a hypothesis on a hypothesis because what I'm doing is I'm saying if this is yellow which it doesn't need to be is it possible for this not to be yellow and I'm still not sure I'm absolutely convinced I know the answer to that but I can say that it's quite difficult but of course this doesn't need to be yellow this could be yellow and that could be not yellow or they could both be yellow ah this is nonsense absolute nonsense right okay there's something cleverer that we've got to appreciate here what about if arrows look at each other um no that doesn't tell me anything it might tell me something if I knew they were the same color but I don't know the same color I don't know they're in the same region uh wow okay um I don't understand this one does it matter if I if I know oh okay maybe this one is more interesting if I know that that one has a loop or not it's not a loop is it's a path it's a path not a loop it's got a path in each of these directions let's actually just list or have a look at those now obviously the simplest thing would be if it was those four but what's to prevent it from say not being that one but being that one instead or one well I suppose it's quite difficult for there to be one miles away if we sort of had that shape six no then you've only got three more cells to play with so so if you try and do this so what we're saying here is that let me um think about this how am I going to show path cells should we use circles so we're saying that those four green cells are on a path and I'm not oh I tell you something that I'm now thinking is that I'm not allowed to leave the region am I before I if yes it visits every region exactly once so in order to visit all of these cells I've got to do it once Ah that's another thought just had I don't know how that's a horrible thought I've just had a horrible thought which is I was going to say whenever the um whenever the path comes into green it has to then pick up all of the Green Path cells before it leaves screen again but that's on the presumption that green is not region one or region nine because if green was region one then you could start anywhere in green admittedly you'd still have to pick up all the path cells and if green is region nine then you don't have to get out of green having picked up all the path cells it is quite challenging to do this I think because I've got to make sure this is all orthogonally connected so if I did that to connect these three together then then seven now then I can't do it okay all right so maybe this is impossible maybe this is impossible no no it's not impossible rather annoyingly I've seen one way I can do it I can make that green and now now I've got four five six I've got three more greens to connect everything together orthogonally so why can't I do that that does it one two three four five six seven eight nine bobbins although um although that's hard no okay that still doesn't work that doesn't work for a different reason I've managed to connect them all up but I haven't managed to connect them all up in a way where I could visit all of the circled cells without in one go I'd have to dip in and out of green to do that because Well we'd have to decide which was the starting selling green but if it was this one say we could go along and get that one or we could go and get that one but then we'd have to go back on ourselves we're not allowed to go back on ourselves are we no because we can't then increase along a thermometer oh you must find another and the past must visit each region in ascending order of the region numbers yes within each it's quite a clever rule that within each region digits strictly increase along the path is basically saying you can't backtrack because imagine you went along a one two three Thermo one two three and then you try to go backwards the next cell would be a two and two is not higher than three so so I don't think well let me look at this again how can we how can we connect this is the minimum extension of green that's possible over and over so this is the minimum so if we have this pattern as the base pattern this is clearly I think possible well that must be possible because it's the simplest way of or it's the closest way of putting path cells that meet this criteria so that that the minimum extension we could do would be to hear I'm just what I want to do is just prove to myself I don't think this works one of these must be green at least in this Paradigm mustn't it because if neither of these were green to achieve an orthogonal collection I think would be too taxing on this this would have to come round here and it would cut off a region yes yes it would cut off one of these regions so I either have both of these as green now if I have both of these as green it's clearly impossible because I've got seven cells there and I can't connect this up to this lump of green in two cells so you have to do you have to take one of these as green and leave one of them as not green um now does it matter which way around you do it properly doesn't actually because I think it's symmetrical so one of these gets in and now we've got six cells and this is still very unconnected I've got three cells to do it in and I can achieve it I can achieve it in a few yeah I can achieve it in a few ways but nothing there's never going to be a way where I don't end up with too many circles that are that have to be start or end points for the path in green that's the problem is yeah maybe that's the way of proving it so whichever one of these is purple forces it's going to for I mean let's say this is purple obviously this is now an end point within green or a start Point within green I.E you can't visit this cell once we connect this up you can't visit this cell in the middle of the path within green it's clearly an end point that's clearly going to have to be an end point because it's so stranded so the two end points become these two cells which means this has to be a midpoint and this has to be a midpoint but that's also going to be an end point because it to connect this up we can't we can't take anything down here so there's too many end points this just doesn't work I'm cut I'm I'm satisfied that's true so that means right so what does that mean that means that this is the arrangement of cells around this this Arrow and that means well I think that means I've got a digit believe it or not because if this was any other number than four we would just be exacerbating our problem with greenliness if I make this green I've got all the problems I had when I when before but an additional problem that this also has to be on the path so that doesn't work so this is a four so this is a four I bet you this is a three by three region now um because I can see oh no maybe I can maybe it's not a actually maybe it's not a three by three region I've just had a thought that's oh no uh no I don't think it is I don't think it is a three by three region for a weird reason which is if it was a three by three region let me just think about this because this is a lovely thought well I mean it's a lovely thought in my hungover State um if this was green and I have to connect all four of those together I don't know of course it can be that I was suddenly thinking this four was going to be in the wrong place on the path because I was thinking I had to I had to do a thermometer that was something like that and then this should be a five but that's of course total and that's a nonsense because I don't need to include this cell on my thermometer I could do that that could be a path yeah so that's absolutely gibberish what I was about to what I was about to think about there right okay so what on Earth do we do now we now say that we've got a ditch it this is not a four by the power of falliness well it gets it gets a little interesting doesn't it if that isn't isn't green let me just look at that that's not green there's got to be a purple cell over here and a purple cell down here one two three four five six seven eight that doesn't work you can't do it but the path is too long so because I have to have a purple to the West in one of these and a purple to the South even if I go in the most efficient way which I think is that way I think I've used up all my nine cells I can never reach this point so that's beautiful because that means this cell is green and if this cell is green we must know this number do we um well it's probably not a big number I think I'm not actually I'm not sure I know that number I don't know I don't think I know where green goes wow okay is this green if that's green let's look at that if that's green I then got seven of my green cells and I've got to connect but I can connect these these two to Green just with this one that would give me although although no I can't because then then I've got four end points within Green ooh okay let's just make that green for a moment that is eight but then I could do that and that's nine and then I could Loop like that and that would work right okay so I don't know whether this is green or not I think it do I think it is I certainly think it could be I mean what on Earth am I meant to even look at now how many how many greens do I need to connect these up and not have too many end points how many of these is what I'm thinking of I could obviously have all three of them can I only have one of them if I only have one of them which one would it be I don't know let's say it's this one now that doesn't work but it definitely doesn't work that it's only this one because that gives me the the problem of how do I connect this to Green again and I'm going to have to Loop and enclose a region of nine cells and I think it's fairly clear I mean I didn't do this before but we've done this a lot on the channel before if you try and put a nine cell sized region and then loop around a nine cell size region like this this screen length with jaw we've drawn here is going to be greater than nine cells large so that's clearly just not going to work so actually this one doesn't work what about if you did that one only well that one doesn't work yeah now I have achieved connection I've got cheap connectivity but I've got four end points so if these two are both now not green it doesn't matter where I build green out to be there's no way to connect these up within a single visit to Green I would have to come through here I'd have to yeah I mean that's the way to look at it you have to come through there now how do I visit all of all four of these end points with one visit where I've got I've got two more greens I can add so I could do something like I mean it's just impossible it's so impossible it's almost not worth worth attention I mean I you just can't you cannot get anywhere near it you could visit this and you can visit that and I've got two more green cells to use and I have to get to this and this it's just it's just absolute absolutely bogus isn't it so in fact now we either have a three but we either have a three by three of green which is what we're going to have to be a three by three of green um or or we have two of these three cells because this one's symmetrical with this one in terms of the logic if we if we just have that as green this is isolated and there's no way to connect it back if these two are not green so eight I've now proved I think that eight of the nine green cells live in this three by three and possibly all nine of them so there is very little extra leeway for where green is going to go so if right and if this was green then this would be the ninth green cell along with two of these three which I don't know is that am I supposed to be appreciating is there a problem with that I don't know what the problem is I'm afraid right let's get rid of the color here and instead of that let's so okay I can now say for certain this isn't green which is a marginal thing to say but I'm very happy to do it actually now my Logic for saying this isn't green is that I know two of these three cells are green so I know Green can extend at most in One Direction so it could one of those could be green one of these could be green one of these could be green or one of these could be green that's it that's my ninth green cell and this has arrows pointing North and East and I can't put a green here and a green here and simultaneously put two greens into those three cells because that would be ten cells so this is not green here is a thought do I now know for sure that this cell is on the path I think I think I do because wherever the purple is in this row and wherever the purple is in this column that are on the path and in this region where wherever the purple is in this column the only way of getting purple to connect is going to be up this column so imagine that was purple then how would you connect this to this well you can't go around there that's going to be way too many more than that's way more than nine cells so you're going to have to go down there so if this was on the path and something in this row is on the path and you can't Loop Round you're going to have to go through this cell so the mid yeah okay the minimum the minimum you could do would be those two cells so imagine this was a two and it was just those two cells that it was referencing how could this not be on the path then it must be on the path because otherwise because these are both on the path and you can't leave purple and go back into it you'd have to go in a big loop layer that's too long so I'm going to allege I'm going to allege that this cell is a circle I suspect although I'm less confident that this cell is a circle and purple as well let's think about that what if that was Green or another color that's not purple but let's say green because it's easy easy for it to be green if this was Green purple would have a cell up here that was in this region well that doesn't work that's too long if this was yellow or some other color that's even worse you you know purple's going to be well yellow's gonna have to get out and then purple could be here but it's even further away from his friends right this cell is purple and this cell is on the path which is quite cool so now that cell might be interesting is that cell well this cell let me think about this cell for a moment that cell is either I know one of these at least is green or possibly both so if if both of these were green this would either be purple or green because it's got a South West Arrow um sorry pregnant pause 37 minutes no no no how could that be oh um right I'm totally discombobulated by that right let me think this is either well it's either purple green or some other color that comes into these cells oh but whatever it is has to be the same color as this so can we prove that this this if this was green yeah okay let's think about that if that was Green then because we know two of these two of these three cells are green oh hang on this is pointing West here is Ah that's not green that's the simple that's that's really simple I just didn't see it that's not green if that was Green we know two of these three cells are green so we've only got one spare green to play with which is this cell this arrow that the West Arrow is telling us there's a green in there and that would be a tenth green cell so that's not green so this is either purple let's see if it's purple or it's some other color that lives in these two cells in way and in exactly one of those two cells so if this is purple purple must do that well it doesn't have to do that well it could it could do a more circuitous route but the most efficient way it could join up would be like that and that's eight of its cells and there's a nut on the right and that's what it would do in fact that is exactly what it would do and the reason I say that is that this has an Eastward Arrow so there has to be a purple in this Direction that's on the loop or on the path so that would have to be there so in fact if this is purple oh it's broke no it's broken all right I've seen why it's broken This is complicated if this is purple this is the fourth most efficient path to connect this purple cell to this cell but that's nine cells already and what color would I make that that has to be purple because you can't see any other colors in its row that's really really complicated so right and weird as well because that means that this color I'll make it yellow is it's not green and it's not purple so that has ah right so this is cool actually right that's green right I think this is green because I I've been working on the logic that we did earlier that said that two of these three cells have to be green but I've now proved that one of these two cells has to be yellow so that must be green and one of these is green and one of these is yellow so if that's yellow means where it means a little thing if that's yellow it's more potent isn't it then we've got one two three four five six seven yeah uh eight yellows because we're gonna have that problem again as well we're gonna have eight yellows doing that but I'm afraid foreign then I don't know I can't quite I can't quite decide which of these I think I want this to be yellow because if this is yellow I think I think this becomes quite forced doesn't it yellow would have to get out this screen needs to connect to its friends so it has to take that cell nothing else these two cells now well one of them could be green I suppose because green hasn't reached its core core 8 number yet that cell would have to be well that's how it would have to be yellow or oh no okay neither of these could be green because what color is this this cell is yellow or green because it only sees yellow and green in this direction it can't be yellow because surely that's more than nine cells that is more than nine cells so that's green right so if this is yellow the the ninth green goes here that's on the loop I think it gets very hard to make this work actually I don't I'm not sure I can join the loop together in this box but let me just think about this up here so these these two are now yellow they can't be a third color because that third color would get out and cut this yellow off right so we get this that's then yellow because it only sees yellow we get five six seven eight we get eight yellows we get complete greens we get the start of purple also oh this is the this is where it's going to get impossible though how do you how do this juncture how do you work out how the loop moves through green if you've got to have all four of these on the loop what's that what is that digit is perhaps the best question what what is that digit that is a two isn't it because it only sees two cells it must it must see a loop cell here but that cell would be on the loop I've just realized because if there's a a Westward pointing Arrow so that would be a two counting this cell and this cell now this can't be a two now so that has to be a one and that's that's absolutely impossible that's absolutely impossible because this cell is not on the loop now because of this one clue and which is counting this four clue and you can see you can't or you've created a little bridge in the middle of this green region that's a loop end that's a loop end but you can never get to the other cells as again it's very very complicated to see that um let me just think about if if there's a different way of visualizing that I think maybe what I've got to do which might be simpler is to say what is this number I know one of these is yellow one of these is green so this number could be seeing green there so one two three four it's one two three or four it's not four because it sees four right it's one two or three it's not one because it's meant to see a loop segment in this direction and this direction so it's two or three so this can that be higher oh depends if it's green or if it's something else I'll probably um okay wow I don't think that's cleared it up has it oh I tell you something foreign do I know whether this is on the loop this cell here if that's not let me think about that if that's not on the loop let's just put an X in it to say not on the loop I just foreign well I I I'm really skeptical that that's possible the problem is it's you're sort of trying to envisage a lot of things in the future one of these is green one of these is yellow I don't you know that's two different situations if we make that green there's one more green to come which is also not helpful in terms of the arbitrary or trying to work out what's going on here but it just feels to me if this is if I'm not allowed to use this these are two sort of loot pens aren't they that's become a loop end that's become a loop end I could I could make that green to create the three by three that I'm very suspicious we've got but even if I do that how would I make this work oh no I could now I'm totally wrong I'm totally wrong why couldn't I do that this wouldn't be green then that would have to be something else so those two cells would be the same color one two three four five six uh that works I don't believe it yeah that's interesting so if you join up these two cells together they'd have to be yellow in that instance or I think it's the same it's the same count if you go downwards that would be purple you do get a nine cell region dear oh dear right okay so I really have not progress this very very far at all I think I might have to go back to what I've what what I think I was able to do but 4 although it was complicated was I think I managed to prove that wasn't yellow but it was it was complicated to do that let me just think about that so in this example we worked out that couldn't be yellow so it had to be green so that was that was the ninth green so we reached this situation and we're left with the question how do we connect everything up within green so once the loop or the path comes into green how does it collect all of these things and here there is a problem I think because I can totally see how I can build a loop that passes through these four points but that I think has to look like that I do not see another way of doing it and this cell is on the loop but it's not thermometer but it's not thermometerable because it's a two or a three and it's in the fourth position along the thermo now the only problem with that analysis is if I have missed I've somehow missed a way that I can draw a path through this exact green area so if this is not on the if this is not available then that's clearly not on the path it's impossible I've got four Loop ends it just it just is nonsense I I'm I don't believe I can do that so I think all that being said and done I think we can say this is not able to be yellow so if that's not able to be yellow but this Arrow this South West Arrow has to be fulfilled that has to be yellow we know this has to be green now to connect green out we don't know where the ninth Green Arrow is but surely this now has to be yellow it does because yellow hasn't reached nine cells by this point so these three are all yellow foreign so now I'm sure this is some of you this is obvious to me I have to confess it is so not obvious um I want this to be green now oh do I maybe I don't want it to be green because then it's actually interestingly now if that is not green it's seeing that cell and it can't be yellow because yellow if it goes up and does that that's not nine cells anymore it's ten so that if that is not green it is purple and purple would be a sort of an expanded you pentomino are you non non-nomino or something uh now do I have to still be well let's let's look at this cell in green that's on the path so how is that not on the path but that's a fair question how is that cell not on the path in green if it's not on the path in green this has to get to here and it would have to do that and that's going to make green too large so that is on the path aha aha ah come back I want to put you on the path you are on the path and you are a very low thermometer number whoa whoa so well I have to go directly from this cell to this cell now there's no way there's nowhere I can go I can't go there and then somehow get over there this I think I think I'm not very good at here right so if I is is being able to really prove to myself if I think if I was solving this off camera I would fiddle around with this and be able to do it quite quickly but actually proving all of these options feels quite quite difficult um but now this cell is lower than this cell because I have to I have to visit this so early in the piece this is an early thermometer piece within green so that cell is a one or a two now from there how could I possibly go here or here there's only one more cell of green in white that we've got to identify like so I can't wherever that is I'm actually thinking it's not going to be visited unless it's after that on the end of the the end of the path I can't come here on the path I come there I can come back and get that but I can't come and get this without leaving green so I've got to go there again if even if I extend green I can't go into that extension because then I would have to leave green before I come back so I think I've got to do this but this is where it gets even more tricky is what what there is still I think at least at least three possible well there are at least three possible extensions of the path within green which would be here here and here although maybe not that one and now I see it because that's got a if that was Green Oh that's not green in fact ah so what I should do there is I should do that because if this was green it needs to see another green cell over there and it couldn't because it would be the ninth green cell so um okay but also it'd be perfectly possible I think for this to be green and if this was Green then you know it just wouldn't be on the path within green right so what I should do now is to good lift my Thermo surely this square is higher than two but not 4 so one two three five six seven that's at least an eight I think I think so there aren't many degrees of freedom if that's right that's got to be three it can't be four or five six seven eight nine so this is five or six six or seven seven or eight eight or nine ah right so what number is this that is counting the number of cells on the path in this direction well that's one and this direction which is another one so it's two and if we were to try and extend green here or here we know that those green extensions would not be on the path so this is a two and that's beautiful so now we know that's a one and now oh no I was about to say something that's not true I was about to say we now know this isn't green but we don't know that at all that could be green and just not on the path and the path goes into yellow this is so hard this is so hard right that Square's not a two anymore uh Ah that's that's not green oh that's that's huge that is absolutely huge that is not green because if it's green it's seeing two Loop path segments and it can't be a two because that's a two you can't see another loop segment here it's impossible because we can't get that cell to there without leaving green so that cell is something different we know it's not yellow because it has to then because because basically they were saying these two cells are the same color now so they've either got to be yellow and that's a nine cell except that's a tenth or they've got to be purple so those two are both purple purple forms its little U shape here and that's massive now we've actually we've actually suddenly made a jump forward this Square well that's now Loop and this square is a one because it can only see one cell in this direction so I I now think it's necessary for this cell to be because this is looking East it's saying that there is an easterly path cell in this direction well what you couldn't have is this being path and this not being because then to connect this all up you'd have to leave purple so that doesn't work so that cell has got to simply be passed but maybe more of them as well and what's more we don't know oh I tell you something we know well we do know it but we don't know the import of it do now know that this cell is the region number of purple because it is the top leftmost cell now do we know that that is the region number of green no because that could be uh that can't be green can it so yes so where is Green's region number you know well it's got very few options it could be here no we go nope no if that was green it's not its region number though so that would still be the region number right so the region number in green is either here or here it's one of those two cells but if it was this one well I'm wrong I'm wrong I was wondering if well if if the loop if this is green and on the loop it is a nine by thermologic and that would mean green was the ninth region but that would mean this purple would be the first region it's not a loop is it it's a path you must find an orthogly connected path the path must visit each region yeah I don't think it's a loop I was suddenly thinking if that was Green and it was on the path which it could be then because this has to increase this has to be higher than eight so this would be nine and it would it would also be its region number so this would be the ninth region which means this is where the loop ends in this cell but then what's how do you get to this cell at all so this cell would have to be the first region and this would have to come down here but this can't be the first region so I think that I think all I'm actually proving here is that this cell is not on the path and green so it's not both of those things but it could still be green and specify Green's region number foreign but then the path well then the path would have to go that way because if this isn't the ninth region it can't be the the ending or the beginning of the path oh this is tricky as this is um oh okay all right I know what I'm going to do now that cell is on the path because of this Arrow this southwest Arrow oh I see I see I've got something here that arrow is now much smaller than it's ever been able to be before because it can't be one or two it's only counting one in this direction so it's a maximum of four that is a three or a four that's all it can be counts this for one and then it's there's at least two more Loop segments in these three squares that are yellow so there is a yellow over here so ah no it's about to say something it was no that's not right I was about to say if that's yellow that's yellow but that's not true because this could be green oh good grief what about uh come on Simon oh that's not a one by Sudoku this one is useful so that's a two three or a four what if that was but yeah all right here's here's a simple deduction that is yellow because if that was not yellow that would be saying there's a blue over there somewhere and to connect the blues together you'd have to do that and then there wouldn't be enough room for nine cells of yellowness so that cell is yellow which means that so right oh no I was about to say that means it's one different from this but I'm not even sure that's true now if that was a three and it counted those two cells well it actually yes okay it is one less and that's because it can't be the same because it would be possible for this to be loop as well so if this did something like that that way this one would count this digit and these two digits but then it would have the same count as this one because this is also counting this one and it can't have the same count so it must have exactly a one small account now does that mean that cell is not Loop oh that's weird right let me think about that that felt correct when I just said it but now it seems if this right so my question is is this Loop now if this is loop I know that this three or four has to see two at least yellow Loop segments let's just say it's those two in this direction I'm saying both of these are yellow so now this is a three but this because this is a loop segment it's seeing exactly the same count that doesn't work that's really weird so this cell is not loop it's demonstrably not Loop and maybe I maybe I do it small like that now foreign I was wondering whether it could be some weird Loop but it just cannot be Loop if it's on the loop that would have the same count that that is right that is right and I can't have the two two numbers the same within a region so that so these do differ by each other by one which means this can't be a four so this if this is three this is two if this is four this is three this is never on the loop but this is on the loop so does that mean that's on the loop yes that that is on the loop and that's because I know there's some Loop there's some yellow Loop over there so I've got to connect this cell up with the other yellow Loop segments aha right so that goes up there so is this yellow now or is this nuke a new color now this could be this could be a new color no no it can't no it can't no Simon it can't silly man how could this not be yellow if this is another color we know it's not green so let's make it blue now blue hasn't got enough room to live just in the top left so Blue's gonna have to come across the top somehow to get out but this three clue is telling us that it's a yellow there's two yellows in this row over here so we'd have to make that yellow but we couldn't then connect yellow with the rest of yellow so that doesn't work so this square is yellow foreign now do we know if that's it it's quite difficult for this to be on the loop now because you're going to have to sort of scurry across the top and you're going to have to keep all of this as yellow oh without the hang on a minute hang on a minute hang on a minute one two three four yeah okay how is that how is it that a specific cell yellow I don't think it can be I might be wrong about this but I don't think it can be and that's because what color is all of this white space on the left now one of these cells can absolutely be green and connect to this if this was green but the other four would then have to be yellow and that makes yellow 10 cells so this cell is not yellow uh I'll make it blue then now blue hasn't got enough space in the top left so blue blue comes across the top of the grid to hear at least so so now this cell cannot be on the loop because to connect if this was on the loop given this is on the loop you'd have to leave and go into blue to get back into yellow and that won't work so that's not on the loop in fact nothing over here in yellow is now on the loop so that square is only seeing that digit and that's a one I see but that doesn't actually I'm now wondering if this is the this is the start of the loop if this is the start of the loop as as in is this region one of the loop not Loop pass if this was if this was the top left no no it can't be the top left side I know it can be it can be the top left cell of yellow because of this three clue if that's Loop and that's Loop and that's Loop we would go up from the one along the thermo like this say one two three or something then we would go into green now green needs to oh green can't be reached two that doesn't work sorry sorry that's nonsense so this is not region one um and the the reason just to be very clear if this is region one this well actually and I've just changed my mind again well I tell you what if this is region one that's not on the loop because then this is on the oh because then this is on the loop and the loop can't stop and has to go into green which cannot be region two because the two in it is not in its top left most cell but what I've just figured out I've figured out something else that might be possible this is the one but then then then this this is the start of the loop in yellow so this would be a low digit going up here and we would be going away from Green but then that wouldn't be on the loop oh so then we go oh that's lovely yeah that could be right so then we go up here and into purple so that would mean purple and purple car no that doesn't work either purple can't be region two good grief okay I'm starting to lose my my hunch here my hunch was that this one was making yellow the first region in the puzzle because it looks like it's sort of a high top Lefty cell but I don't think it can quite work because if this is not on the loop in order to allow this to be the start of the loop rather than something that has to go into green you'd have to go up here you'd have to go up here you'd have to go across here you'd have to go down here oh this no this doesn't work at all anyway because not only can this not be a one or a two but this cell would have to be on the loop and yellow and that would be have to be yellow and on the loop and now this would be the region number of yellow which wouldn't be a one okay good I'm just talking apps I was I was I was trying to demonstrate something that just clearly cannot be true right so the the thing we've got to do now is to work out is it where the final piece of green goes because the final piece of green is quite restricted now or or maybe we determine how green moves from here that seems a good idea is green going in there or is green going in here and if it does go in here what color is that which is not purple but could be green no or can it be green is that the question is if this is sorry I'm getting very confused myself here if this is what I'm trying to think about is whether or not we can tell at this point weather Green is partially along the sequence of regions so imagine the greens in region I don't know five if Green's in region five then we know that this which is the first cell of green must connect to something else on the path which is which is probably that could be something from here and we also know that Green's final cell which at the moment is this one but might be this one although I don't think it can be this one because if that's green I think it has to be nine and it would be the region number as well um then bye then this has to go somewhere but that could go there as well so at the moment it feels like this this Row three column three cell is sort of it quite wants to be joined to the start and the end of the green line which is really not going to work so I'm not quite sure how to attack this at the moment I want I think it might be possible to prove that this is not yeah well if that was green and it was how green extended this would be the ninth this would be region nine yeah okay that I've already proved that haven't I this is not green and loop because if it is it's a nine which means this is the this is the end of the loop that's the final cell of the loop that would then have to be the start of the loop and it can't be because this cannot be region one so this if it's green this is not Loop so so let's try and make it green now but say it's not Loop if it's not Loop can this be the ninth region no because this is defining its region number okay the loop just stop now it's still got the same problem it's this if this if this is green and its region number is nine this has to be region one whether this stops here or goes to here and it can't be region one so if this is green it's not nine and it's not one or two so it's a middling number which means that this is not the end of the loop so the loop has to extend there we go now that so that so if this is green the loop extends it goes into yellow this is not one or two so let's say it's three so this is Region Three it must be going into region four but this right okay but now we have to increase as we as we've gone into yellow this is a low number this is a higher number and therefore we can't ever go in the one and the puzzle breaks aha this does not work because because remember this three clue is telling us that there is there are two Loop segments in yellow in this direction here two of these strip cells at least are Loop now if the loop does go into yellow it cannot visit the one as a loop segment because we have to increase from a thermometer perspective and this is the only bulb Row three column three is the only bulb in yellow so that has to be yellow and loop and the loop is just going to close unless this can be region nine and this can be region eight ah good grief no that still doesn't work oh wow this is so complicated uh so then then I had this thought is okay I can get to this Square in yellow but only like this but I make by making yellow Loop over the top of the one to get to this yellow cell here and trying to argue this was the end of the loop so I didn't have to go back into green again but the only way that could be is if yellow is in region nine the only way that could be is if this is a nine the top left cell in the yellow region but if that's a nine how could you ever end it I suppose you wouldn't have to go to here I know you do because of the three or the four clue so we could this would have to be a 10. it doesn't work it also doesn't work because then this would be the start of the uh the loop and it would be in region one which it cannot be ah this is really complicated okay but now now we have got somewhere very a very small wear but we have got somewhere I don't believe this Square can be green therefore well therefore I was I see what I was about to do is this nonsense I was about to draw that line and say the loop can't go into this Square well that's total and utter nonsense of course the loop can go into this Square it's just not going into a green square here foreign I don't know I'm so sorry I've I think I'm not understanding this quite at the moment right let's I'm going to check this square one two three four five six that is a maximum of six and it cannot be less than three so this is three four five or six it's in the middle of a thermo run but I don't know is in which direction this Thermo run goes but this is not green so this is yellow or blue probably yellow I think no I don't think it can be yellow this is mad it's maddening this I don't think this can be yellow and let me explain that if this is yellow we've then got the problem of deciding is this problem again is this is this on on the path within yellow now if it's on the path within yellow you can see it's the start of the parts within yellow which means that yellow must go unless this is the ninth region again now oh no now I'm getting really confused this is the start of the path within yellow then yellow has to go into green but then green would have to go into yellow unless unless yellow yellow went here and then ended in row three column three now okay that doesn't work for a different reason if I try and argue that yellow is in the ninth region that means green is not in the ninth region which means this has to extend into yellow oh I suppose the yellow could be eight yes that might work no that doesn't work either because then purple has to be the first region again I can't go around in circles this is absolutely fascinating um but I might be about to prove that this this cell is blue I think let's just think about this again so if if yellow if if yellow includes this cell on its path it's obviously the bulb of the thermo so we're going to have to somehow end up in this cell maybe not directly um but we get into this cell where the only way that we don't go into green is if yellow is is region nine but if yellow is in region nine green has to extend from this position into yellow which is going to make this the first region which it cannot be so that just doesn't work what that tells us is that yellow is not region 9 which means yellow must extend into green if yellow extends into green we know that green can't then extend into yellow so green has to be the ninth region which means purple ah that might work purple's the seventh region oh wow okay this might work this might work I think I found a Lacuna in the logic that allows us to poke through and find an answer so now my new hypothesis is that yellow is region eight now if yellow is region eight foreign then I can extend into green and I don't have to extend green back into yellow again because green will be region 9. but then the question is oh no so that means blue is region seven no that doesn't work again it doesn't work again because now I've got the same problem that purple needs to be region one I thought what I was going to be able to do was to connect purple as region seven to Yellow as Region 8 and put this in as a region but I can't do that because that this then obviously the bulb of the thermo is the start of the of the loop within yellow and that couldn't be the case so you'd have to go up here into blue but that makes this the start of the loop again this this one is doing absolute Mighty work so now all right so now what we've proved is that that this this cell if well we've proved if this is yellow if Row three column one is yellow this is not on the loop foreign purple being region one oh I see okay yes so I can do that so this works as well I think now because now I could loop around here and join purple here we go right what's wrong with that and that allows green yes no no no no no no no no this doesn't work either this doesn't work because where's the ninth green cell and the answer to that maybe this was easier to see before if the ninth green cell is here it can't be a half or something like that it's it so it cannot be on the loop this is the bulb of the thermo but if this is the bulb of the thermal we've got to go from yellow into green and this this is region one which it cannot be so we have to go from yellow into green into yellow again oh oh and unless this is region nine and maybe maybe that works actually maybe that works so this is region nine which means this is region eight are all these yellow oh now I've got too many yellows now oh no I've got 10 yellows that doesn't work I've got 10 yellows because to connect this to this I know this has got to be a loop segment to satisfy the three clue to connect this and this together I have to go across the top so I can't go through the one and if I go if I do that then all I've got 10 yellows this is just nonsense absolute nonsense so so now so now if this is if this is not this is not on the loop this is not on the loop let's do this slide if that's not on the loop that is on the loop to satisfy the three these have to join it just simply breaks there and then doesn't it because I've got to connect those up and that's creating a 10 cell region right wow okay that's great then that's great because now I think we know the color of this cell this these two cells are not yellow this cell is now reproved it's not purple it's not green it's not yellow so it is blue and it must connect up there and now blue is nearly finished yellow is ah green is finished like that which means yellow is finished not finished but it comes out which means blue three four five six seven eight blue comes here as the ninth cell and then all we've got to do is work out how this all connects up oh oh here we go we've done it we've done it yellow is region one this is the topmost leftmost cell of yellow so yeah yeah this works I think so so yellow goes so because of the three clue we need two clues that are in yellow this way so that has to be those two so we know that the bulb is the one so we have to do that now this is region one so we have to do that this is three uh this can't be region oh no no no no no no this can't be region two oh no no no no no no no no no no no no what was wrong with that there was nothing wrong with that that was absolutely forced hang on hang on hang on let me just think about this again so this is three or four it is three or four it would be so easy to miss one of these tiny little options this is very very complicated I had an hour and 30 minutes and that's something it's flown past but I I don't I mean look I'm hardly in the puzzle at all at this point foreign blue has to get out yellow has to have that has to be yellow I have to go in oh no I've got it right okay sorry sorry I said that if this is one it was the region number it doesn't have to be the region number because I can get that to be yellow right okay that is absolutely that is absolutely brutal but I think that's right right so let's come back to this again let's think this through again so if this was the region number for Yellow I think we are broken because it's on the loop I mean it is on the loop it is it doesn't matter where yellows region number is it is on the loop because we need to satisfy this clue in fact we can fill in these Clues that's probably the sensible thing to do that has to be three that has to be two this has to be on the loop so we are forcing this pattern within the yellow within the yellow region that's forced now the weird question then well I then said I then said this had to be the first region which you can see is wrong because if this is region one we have to go out of it and we have to go into green which cannot be region two because the two is in the wrong place but I'd forgotten that you can get an extra I could get a higher sell in yellow that cell I think it has to be that cell which is going to mean that I've now got nine cells in yellow but this is the region number of yellow now the only issue with this is that I don't think still don't think this is that straightforward to figure out what's going on I'm desperate to avoid I'm desperate to avoid purple being region one this is this is demonstrably not region one now is it region nine if it's region nine this ends you know that would be a nine then I don't have to go into green okay but hang on Green is green is Region 8 or region nine now because this is an eight or nine and it is its top leftmost cell so if I think I think it's still broken I think I've still made a mess of this I don't know quite how I've managed to do this but I can't see how to do it at all sorry and I know they must be very frustrating if you can understand all this really quickly I concluded at some point that this couldn't go up here can't remember why I concluded that I concluded that green couldn't go into yellow but if the yellow was why did I conclude green couldn't go into yellow up there into this cell this would be an eight then that would be a nine this would be the end of the loop so then this is what's this then hang on this is this is nine what's this region then that has to be region one doesn't it because if this is oh hang on I'm now getting confused again this is eight this is nine this is this is eight so eight can join to seven eight oh oh hang on no hang on how does this how does this really can get out is it oh hang on okay maybe maybe foreign I'm still baffled about how this works if this is I don't think this can be eight going into nine and the reason is that this Loop segment has to go somewhere into regions seven and it can't go anywhere because it's only able to join up with yellow so in fact what we can actually see there is that because this is not region one and because this is green and cannot be on the loop within green has to join there so now seven and we have to be really careful here because if if blue is now region nine I.E if this comes in here like this so this is region eight and then blue is region nine then that makes purple region one which it cannot be so I think that's forced now now that means that this has to be a nine I don't know what it means for this cell actually but I think this is nine which means that yellow is region eight now you can see that blue therefore this this digit here is the first cell within yellow which is region eight so this must be region 7 which puts a 7 in the top left of the grid now the interesting thing about that is that this has relieved the pressure on purple so it's probably right I think this because now purple can be region six and we can join up like this into into region seven set this see this I don't think anyone would disagree with me if I said this is the most complicated Sudoku we've ever featured on the channel it is I've had what I've I mean it's almost the longest video we've ever had already and I've gone I've done nothing in the puzzle done absolutely nothing it's flown by but it's so complicated I cannot tell you there are so many little Wiggles and ideas that you have to balance in your brain and let alone setting this I mean what is going on now region 6 joins to region seven now region 7 has to join to region eight so I have to extend the loop again to at least here where I could shimmy across or I could go up here and then shimmy oh no interesting right I don't think I shimmy up here into the corner and then go that way to join up with yellow and the reason is what digit would I make that is has got to be higher than seven on the blue Thermo and it can't be eight or nine and that doesn't work there are no options for it so actually I think we do that which is per taking all the pressure off these digits but I'm quite thrilled I have to say I'm quite thrilled that I've even managed to you know get to an arrangement in this top left that even works now this square is not six or six it's not six or five anymore because it's got to be sufficiently it's got to be two less at least on the thermo so if that was five this would have to be four so this digit is four or five it's almost doing something over here but not um this digit which is again on the path and therefore thermoable is less than four so it's it's not one because there's a one here so that's two or three uh um what do we do now I don't know oh I've broken the puzzle or maybe not actually okay I suddenly realized by the law of leftovers these two digits here can't repeat in blue so they have to appear in those two squares in in the top row and one of them is therefore an eight me actually that one can quite easily be eight if that's eight that has to be nine even that might be possible even that might be possible right what about this digit then that digit is not is higher than one because it's higher on the thermo it's not two three or four so it's at least five so that's five six seven or eight and it's not eight because it's an eight in its box already or it's region so it's five six or seven this square is six 7 or 8. which is marginally interesting isn't it it's not eight again because Eight's there sorry it's not 80k so that can't be seven now so this is down to five or six which makes a pair here which means this square is a seven now if that square is a seven presumably in some way important yeah I know how that's important where does seven go in row two of the grid can't repeat in yellow can't go in blue there that's a seven wow wow this do I know what that digit is that digit is a region number actually that's an interesting thought because it will because it's not blue and it's not yellow and it will be the highest cell in whatever region it lives in so let's make so this cell is a region number and by the law of leftovers this cell goes in one of those two squares so the region number this is by the fact we've already got a seven we've already got seven six seven eight and nine so this digit is one two three four or five don't really have a view on what I think is likely to be if I'm honest um I'd love to know what that digit is the spare green digit is there a way we can we can know the answer to that at this juncture um I don't know there might be or what else would it be nice to know at this point there has to be a seven in green somewhere and that seven is in one of those two cells there that's a useless deduction I mean even now when we've done so much work foreign I can't see could work it's possible one thing I'm suddenly thinking here is I've got so much notation in the grid it might be I might be missing um arrows that are hidden behind all of the notation like this one I can I can just about see it foreign three here that's that's become a five by Sudoku so that's a six oh I see that's seven that's eight that's five by Sudoku that five means that squares of four which means that's a three that's a two do I know more about these cells now I'm almost attempted to get rid of the circles because they CL they they're so overpowering in the cells and I'm really struggling to see um also do I need the circles over here now do we know where the purple the purple ah ah huge huge where does the purple Thermo leave purple and the answer is there because purple cannot if it continued here it would have to be a one and it can't be a one we've already got a one in purple so that is is where where we find the beginning of region five although it might not be a five depends but this this is a new region down here let's make that gray so now actually I'm going to just check this route one two three four six five five where does five go in purple by Sudoku goes there whoops that's a five so these squares are sevens eights and nines that squares the only place seven can go these squares are eights and nines I don't think I can do that this is an eight nine pair though that digit must be knowable B8 or no it's not eight or nine um that is going to be a three apparently uh because I've not got three in green so do we now have a view on that digit let's check that digit by Sudoku that is not one two three four five six or seven that is eight or nine which is transposing we know in this row to either this digit or this digit so if it was this digit that would be a nine but that's not a nine because that's a region number and we know we've already got region nine so that is not nine that is eight which means this square is a region number and I mean when I say region number it's that region number so this Square by Sudoku is not one so it's two five six seven it's two two or five so this is region number two or five up here but that's region number five yeah okay so we know this is region number six and it goes into region number five so this is region number five so this is part of region five this cell well that can't also be part of region number five without that being a gigantically large region and that is not going to work so that is region two this is a two by Sudoku these digits we now know are four six and nine [Music] that's going to be helpful he says not really understanding how um um come on these squares ones fives and nines at the bottom of column one [Music] um do we know that is this the same color as this or can it be a different color I don't know what color is this this cut oh those two are the same color that's the simple point isn't it yes there we go right this has a Northerly Arrow so it has to be part of the same region as well it can't be part of purple green yellow or blue because we finish those regions so it must be part of this region so those are in the same region I don't know whether this is the same region as this it might be it might not be [Music] um that digit though it doesn't matter I don't think it's going to matter that digit it's definitely counting this cell in up to two more so it's a maximum of three and it's a minimum of two so this is a a two or a three right here's a little thing that's quite beautiful here is a little beautiful thing that cell is not Orange but that's because if this cell was orange all of these would be orange because obviously this this area is now hypothecated off and can only be the nature of oranginess and where would you put seven in that region nowhere so that's not orange that is something new let's make that could I if I got color I've not used yet that I like using oh not really I'll make this blue I think on the basis it's far away from this blue so that's blue so if blue took all the cells in there blue is not orange we've just learned so if all of those were blue that would still be blue it's that square able to be to be or must it be blue if that square was orange you'd still have the seven problem yeah you'd still have the seventh problem yeah okay if this Square was orange those squares those are the eight orange squares Now by force so the ninth orange square is in one of these two squares and there's still nowhere for a seven in Orange so that Square's blue as well that can't be nine can it there aren't nine one two three four I'm even questioning that um but no that is not a nine that is not a nine because there are not nine cells to the right of it that could be part of this group so this is one or five and all these okay or I think it is fair to say that oh I should change the color of this because this color now is is either orange or blue I don't know which but it's one of them because you can't get a third color into this this bottom left region um foreign okay that's got to be blue doesn't it if that's Orange then I've got to run Orange let's go well the point is there has to be another orange in the bottom row and there's going to be a blue region in the middle of it the orange has to go all the way around and we know that's not possible so that square is going to be blue and it's one or five it's almost certain to be oh I was about to say it's almost certain to be five but that might be wrong because don't I have to put whatever this is this is in the fifth region I want to say that that might makes this a five is that wrong or is that right is this the re well this is a region number isn't no it's not necessarily a region number actually that's totally utterly wrong what about if that region went like that and that was the region number that's so totally wrong to think of that as having to be a region number what about uh uh ah that's a one it must it's not because this is not not orange that that must be orange in order to make this clue work so this Square uh we don't know depends still if if this oh I tell you something I know I know that's on it oh that's on a loop this is a loop cell because this is pointing at a loop cell and that means that this is within the orange this is the first time that the loop visits orange isn't it and we know that there's some orange cells over here so Orange has to so orange can't go there if yes I think that's right so if orange just went directly past go and collected 200 like this then we would never we'd never visit the orange shells on the loop on the path that must exist in row eight so orange doesn't do that so orange must dip down there except could orange do this no no it couldn't because remember orange is not the f I was about to say orange is not the first region do I actually know that or not I'm not sure well I don't think it can I don't think orange can go there anyway because if orange went there we know it's got to get here in the end and that means it's got to go through this cell which would be the fourth cell on its Thermo so orange doesn't wiggle to get to to get to get over here and because it can't go directly here it must go directly down and it must go directly across now I think we're on the cusp of proving that orange is in the fifth region but we might not I mean ah to do it what is okay what does the loop do I yeah maybe that's the way to approach the question do I know that this square is orange or could that be blue I don't know I'm gonna check that if that's blue we know there's a blue loop segment down here so we know that the loop oh this doesn't work the loop has to do that and one of those cells is a one and it's not the start or end of the loop within blue so that's wrong so that is a very very elegant way knt has ensured that this cell is orange now this Square we know is at least equal to three so it's three four five or six but it's not six because then this when we X it's going to be a seven eight or a nine and that's not going to work so this is now three four or five now if we did a wiggle here if we don't go directly into this cell we can't do it can we because if if we continue here and then go there and then go there then I've I've either left orange and come back into it which is not allowed or I've got to continually increase along my Thermo and there's going to be a 9 here which is going to make this a 10 which doesn't work and that is very cute so that it does go like this the problem we've got here believe it or not is that unfortunately I still don't know I now well I know that this is read right I tell you what I do know I know this is region five now for sure because it joins to region six therefore I know it's top left most cell is a five which therefore that cannot be a five because it's not the top leftmost cell this square is higher than three so it's at least four five is four five or six and that could be five couldn't it now now what does that mean so now okay so now we know this is a new region don't we because we know that the Loop's gonna dude over here it's going to come in here go there there there in region five so it's got so this has got to join to region four in this cell so that is a region 4 cell now that might be this I don't know it could be this joints to here and this is region four almost feels quite likely actually but I suppose what we can do is extend the loop there which is a rather cute thing to do now ah now Orange has to get out look even if orange took those cells 6 7 8 it's got to come out quite a bit further Gray's got to come out blue even if it took those cells would have six seven eight so it's got to come out a bit further orange needs one more blue I think needs this one as well even if it took all of these so that's got to be blue that could orange could be finished here this is gray this cell is gray and it's gray because it can't be orange because you'd have to Loop Round gray to make this orange and gray it's only you only got three cells at the moment it clearly can't be blue because that's even worse so that's got to be gray that's a loop segment now because this one is looking at a loop segment therefore that's a loop segment and that's a loop segment So within region 4 which is what this is part of the loop we actually know what the Loop's doing although the loop could go into the one as well of course because we're sort of going we're building backwards thermos because we're working our way back along the path oh good grief um right so blue if that's blue that completes blue so this would be the region number of blue which would have to be not five because we know this is region five and not nine because we know that's Regional so if if this is blue blue is region one which is rather cool oh no hang on it can't be oh no hang on I might have broken the puzzle uh that can't be a one I've just seen right if this is if this is blue blue is finished that can't be nine because it is the region number so it can't be five because I know orange is region five ah so that right so this is orange and that's perfect if that's Orange is it possible to get to a higher cell in this in Orange no it's not no that is the top leftmost cell of orange so that is five so this is not five this is a one in the corner which is a surprising number that's a nine one two three four five six seven so if that's blue again we couldn't get to a higher cell in row eight or row seven because we if even if we took this cell that's completing a nine cell region and this would still be the region number and it can't be the region number of its region because it's a nine and that's already got the region nine so that's orange and orange is now replete and quarate um foreign so okay so this is the end of Orange two three three four five six sevens seven oh nearly seven and eight in Orange are in these cells by the power of Sudoku that's not seven it's not impossible with another couple of hours that I'll be able to finish this this is going to be the longest Sudoku Soul we've ever had on the channel um and that is exciting because I mean I will be just delighted if I can finish this to be honest this is completely crazy [Music] um now what on Earth am I meant to see now I've got region two haven't I I've got region four winding its way here so that can't be the highest sell in this gray region because we need to put a 4 into it I've got region okay let me just think about this I've got region nine I've got eight I've got seven I've got six I've just found five this is the starting point of four so I need three two in one I know two lives over here so I need one and three region one and Region Three good probably this is region one although that can't be a one because one two ah no okay that doesn't work wow wow what an idea that is okay I think do I know that's in a new region actually that's an interesting question is it actually oh maybe it is possible five six seven no maybe it is possible actually bobbins I thought I was going to be able to work out which way round the regions go but I'd overlooked the possibility that this Square could belong to Gray in fact no it definitely doesn't belong to Blue does it it definitely doesn't belong to blue because blue blue would reach 9 by getting to this square and look this is pointing in different directions so that would take it to 10 and 11. one two three four five six seven eight nine that wouldn't leave enough of that so this is not red it's not blue it's not Orange can it be Gray what about that as a possibility if this is gray then I've got to have a gray here I've got to have a gray here at least I could have more grays so now I'm up to seven Grays but the problem is I can connect them all with this and then when I where am I gonna put my extra region I've got two here I've got I think this might be region one that's what I was thinking if this couldn't be Gray looks like there could be a three by three region there actually maybe that's what's hidden in the grid that would be what color would we make that if that was true um oh I've somehow managed to mess this up so that maybe it would have to be another blue region in order to not touch any of its friends so that would be its region number foreign actually that's an interesting oh it's easy oh that's lovely oh my goodness me right right here is the way to think about the puzzle at this point what what is the nature the precise nature of this digit and the answer is that it's a region number because you couldn't because whatever this is could you put it in a region that had an upper either a higher or a left most more cell than it no the only way you could do that is if it was in red but if it's in red oh am I wrong about this no I might be wrong about this now oh Simon um I'm not sure now what my thought thinking was if this is not red then it has to be a region number but it can't be one two or three so it would have to be a region it would have to be region four which would join it to Gray wow that's so beautiful but how could I how can I assume or presume or prove that this square is not red the answer is I don't know in fact it could probably very well be red if it was red it would be part of region two which region two needs to connect to region 1 and region 3. hang on hang on hang on maybe that's it this is so complicated I mean this is so complicated again I'm going to change these from being great because I don't know what color these are but if this was red let's join it up because we would have to we can't fit another nine Red Cell region in here how do we join this region which I believe is region 1 or region 3. has to join to red orthogonally well we've got six cells there so we could get we could get red down as far as this and I can get blue up as far as that but I can't connect them there's no way so actually I think it is legitimate to say that that's not red because this whether this is region one or Region 3 it must connect to red and it couldn't in fact how does it connect maybe that's the point how do you connect red and blue together because you need to that's a weird question maybe they have to connect down here anyway I could have come back to that thought in a minute but this is not red I've just proved so I believe this is a region number but it can't be region one two or three so it must be region four and if it's four it's gray and because you can't sneak any other regions in here all of those turn gray Bingo now I've got a great big dollop of gray and I might be able to prove this isn't gray one two three four five six seven 8 9 10 that's not gray okay I'm going to make that green is that legitimate it's definitely not blue I don't think it can be read one two three four five six seven eight no it can't be red so this is the other region we know uh but we don't know where its region number is so that means that this is either region one or Region Three but if this was region one let's just sketch that in for a moment if this was region one we go into region two this would be Region 3 at the bottom how would we then connect to region four over here we'd have to connect Region Three to region four we can't do it the connections too remote so this is seven cells of blue I could get there would be about as good as I could get this cell here with blue but then I can't I still I can't connect gray to this cell so this right I Now understand right so this is region one by force and if it's region one it's region number is one the which means that the one in it which is there must be the uppermost leftmost cell in blue and therefore we are doing this we are connecting this down here somewhere because this is not there are many degrees of freedom in terms of how we're going to connect this in fact what it what color is that cell if that color was green which is the only other color it could be then in connecting greens up I would isolate one region one from region two which I cannot do so that's got to be region two which means the whole column is region two because we can't adulterate this string with anything else that we have to skip around the edge of that gives me eight cells of region two this square has now got to be green because there's an arrow pointing at it that's got to be green because there's an arrow pointing at it this digit is now actually equal to two and the connection the connection of region one two region two now can only happen there this is so clever so now we don't know how long and we could probably I bet we're gonna have oh no I thought we were gonna have one two three four five six seven eight nine across the bottom that would have been comedy if if we'd had a complete Thermo um okay so we go from region one to region two then at some point we go into the green region then at some point we go into the four region and the four region turns into the five region and that becomes all of the stuff we've already done so we are two hours 16 minutes God imagine if my graphics card fails or something now I will weep I will weep weep weep um right five six eight into these squares by Sudoku five six eight that's not eight um that screen it can't be any other color orange is finished and it can't be blue because Blue's finished what about what about that cell that cell and I do have one red to play with don't I so oh hang on but that's path oh right this is going to be important yeah look not only is this a 2 counting the cells it can see but of course these are two path cells it can see now well that's an interesting point how how do we not turn directly into here so if we sort of did this this the only way of getting out of this corner is going to be to Loop and take the two but you're going to take the two two left too far along the thermo you're going to try and build in green so in fact in fact what you're going to have to do here is much more profound you're going to have to take this corner cell as quickly as you can and you still can't go in here because if you go this way it's going to be the third cell on the thermo and it's a two so you've got to go up there which means rather beautifully this cells become green oh no better than that it's much simpler than that well not simpler but look now think about the four clue or the four region because we can't now go directly from the four into the two cell because there's too many other Thermo cells here so we never go into that cell which means we must go into the one on on on the in the four region and then we must leave the one directly because there are no halves in the fourth region the only way to leave it is to go here which must be a green cell because it can't be any other color all right so either this closes or it does a little wiggle [Music] um [Music] I don't know how am I going to tell how far this comes along the bottom I suppose if this was a nine or something then I would know yeah that would that's going to be it this will be a nine to lock this in the corner I think um I've only taken one cell in the two region okay let's have a look perhaps this Thermo because there's a little Thermo we're growing in this in the in the gray region isn't that this square is not it's it's three or five because it can't be four or perhaps six or perhaps seven three five six or seven I think one seven eight nine I think it's possible one seven eight nine yeah okay right this square is not four so this is it and it's not five so that's at least six seven or eight so this is at least seven and it can't be seven so that's eight or nine let's just pause there and see whether we can get rid of another digit from this position we're going to put two in Gray yet actually how many twos have we got oh a few hmm That's mildly interesting perhaps let me think about that too how many twos have we got one two three four five six I've got three twos left to place I've not put two in Gray I've not put two in blue and I've not put two in orange either which is almost forced but not quite oh I know what I can do that is an arrow cell that I've not filled it in that is a two I think one two it's a two all right I get my two in Orange that was not that sure I would much rather that have been a three that would have filled my Thermo in right what do we need in this column then we need three eight and nine that square is three or nine and that square is three eight or nine now so now I've still got to put my two into Gray and I've still got to put my 2 into blue which is almost fascinating actually what's the what color is this Square that that square cannot be red Red's only got one more Square to get and it cannot be green because then those would be green and gray wouldn't be nine cells so that cell is gray and it's five six or eight that doesn't tell us anything um I was thinking about that cell though in the context of twos because where does the gray get its two now and I think it's fair to say I think that it can't get it from this column because we've now got eight cells in Gray so this would have been the only opportunity this cell here to get a 2 into gray that was in column eight so the two in oh no I've broken the puzzle now I haven't broken it I thought I'd broken it I haven't broken it oh dear dear dear that was that was incredibly awful scary moment so yeah so the point is you can't get a gray two in column 8. so what color two do you put in column eight you can't put green too Green's already got to do you can't put a red two we've already got a two here these can't be two these can only be well these can't be gray they can't they could be green or red but they couldn't have two in them so the two two goes down there which is very very weird because now I don't see how this Thermo is going to be deter I suppose the thermo can only be starting here now in the first region oh no maybe no it can only start here in the first region of course oh no no no it's my oh Simon just use the clues no okay so when we got the one this one has an arrow so there's only one cell so this is the start of the loop we've we've done it this is the start of the loop that's the end of the loop and well when I say we've done it we've done about half of it um but at least I Now understand how I could do the bottom row I'm so sorry for not spotting that more quickly um okay but but let's come back to what do I wanted where where is the easy win here I don't think this puzzle has any easy wins in it it well where's the two right where's the two in gray that is an easy win because it has to be here that was the thing I thought I'd broken so that's all the twos in the puzzle done now where is three five six seven eight nine I don't know I'm sorry I'm not quite seeing how to is it this little Thermo I very much doubt it oh maybe actually maybe I can prove how this closes because if it does a wiggle it's gonna this is gonna be quite a big digit isn't it let's have a think about that right problem is I think this Thermo can start with a one which obviously takes all pressure off it all right let's say it does start with a one then this is at least a three because it can't be a two this is at least a four this is just not doing anything is it five that can't be a six actually that would have to be an eight and that would have to be a nine so if we wiggle this is nine which would be helpful but if we don't wiggle for this has to be six it can't be seven it's six eight or nine if we don't wiggle so this is six eight or nine Which is far from being good enough isn't it what about one two three four five six seven eight it could be there could be some Sudoku to do what a terrifying thought um have I used up all of the all of the arrow Clues because I have found a couple of those that I've missed don't know this Square can't be an eight I'm going to argue because where is the green eight and if we look at green green can only go in these two columns so if Green's eight can't be in this column it must be somewhere in there and therefore that square is going to not be able to be an 8 which places a look in red which is a little tiny deduction which is I'm welcoming um we we know this corner digit is going to be the digit that appears in this column is in red don't we by the law of leftovers thank you maybe it's something like Whoa actually yeah I've got a lot of ones there are six ones there one two three four five six okay where where's oh yeah where does one go in the top blue region not here not here not here not here it goes exactly there that's come out of nowhere hasn't it so is that four five six seven so I've not put a one in row eight and I've not put a one in row row six there's a one in one of these two cells and there must be an equivalent in row eight one of these two cells oh no hang on that can't be right I was going to say I've got this up here no one of those two cells okay it's going to be this one isn't it it's going to be the bottom cell of the thermo I think I don't know um hmm if that was red that would be gray otherwise this is Green Oh I know what I know something I haven't thought about ah of course green what what number region is green it's Region Three so that's not three ah aha oh that could be massive where oh no it's about to where's the three going row seven don't know uh can this be four now this is at least four no so this is at least it's not five it's at least six so that's not six anymore so that's done that's done some business um so this is at least four now how high can that be could it be five if that's five [Music] this would still be I'd still be able to be six wouldn't it if this is higher than that if this is six this would have to be eight That Couldn't that couldn't work because if this was six this would be an eight nine pair at best um so that's not six so this is four or five so this is one two three or four it's not two it's one three or four it's not three because it's the region number so can that be four then that's quite if this was four this would be five this would be sit and that oh that breaks this Square is that right four five that would have to be six because if it wasn't six it would have to be eight and the only way of that that would break this Square wow okay so this is one which means that's one I think that's not actually going to do very much I mean it finishes our ones but it's put so now if this is if this is five now do we know this is six yes we do because it can't be an eight nine so that can't be five it has to be four which means that's become a six which takes six out of here and six out of here that can't be five look this five is looking at it so we've got threes sevens eights and nines that square is three or nine by Sudoku one for this can't be five this is at least maybe we can prove this doesn't wiggle now if this Wiggles six no that has to be eight nine broken so it doesn't wiggle we know the path goes directly like this we know that this square is a six I believe if it's not six it's got to be eight or nine and that's going to break this square that is exactly equal to 6 which means that's six that's five which means that that's six here we go come on yes this is four this is nine okay so now I need three and seven surely yes seven three oh now that three is weird that cannot be green oh that's it cannot be green because if it's green it can't be the region number for Green which means it's red because it can't be gray it wouldn't reach which means that greens coming up here to finish it's only got six cells seven eight so where does it get its region number it must be there that's got to be its highest cell that's got to be its final cell and this has got to be the final grade cell so five and six now it didn't doesn't work well it does work but it doesn't finish um oh this is so exciting come on come on Simon this square is eight or nine so that's an eight nine pair here which means this is a five tell me what about this Square that's a seven what about the three there so that's a nine we know that's a three by the law of leftovers it's got to appear somewhere in red so we need uh four five and six that's a five by Sudoku this is a four or six don't believe it four or six oh no six there I couldn't see it for some reason that's four that's six okay uh this one two so so may it must be this digit 9 by Sudoku yes eight seven three all go into the grid that's not eight anymore so the Eight's moving over into these two squares which seem yes these have to be a seven eight pair in Orange and that's a seven so that becomes seven that becomes eight that becomes nine that becomes eight nope still not done uh that becomes eight that becomes nine what about this column we need five and eight yes fireplace at the top eight goes at the bottom this where does the three go three goes there four goes here what about this column six and nine um what about this column four and six no oh no no no no no please please imagine if I've got some sort of weird deadly pattern what about this column 23 foreign six again this doesn't know four and five oh and the five here so that's four that's five so that's six that's four that's nine that's six that's three that's nine oh my goodness um right three goes to six goes to one four six nine in Region Three goes to in region four one three seven eight in Region 5 goes to one two three six which is increasing which in region six goes two three four six which in region seven goes two eight in region eight goes one five seven which in region I goes one two five six seven eight nine that's a path set obviously I should put paths around circles around everything what a puzzle that is that is simply one of the most extraordinary things I have ever seen in life itself let alone Sudoku that's the longest Soul we've ever had on cracking the cryptic um if you are still with me thank you I'm lost for words that is so unutterably brilliant of knt I shudder to even begin to think about how you constructed that it is mad you are quite frankly my friend as mad as a badger to think that rule set would be possible let alone to execute it with that sort of a plum it it blows my mind it's a it's a work of true genius and utterly staggering I am quite mildly staggered that I have managed to solve it in this astronomical astronomically long video I must go and have my lunch now at ten past four in the afternoon but let me know in the comments how you got on I enjoy the comments especially when they're kind I know for some of you this will be too long in addition um but for me I loved it I do not feel I've spent the last two two hours 37 minutes doing anything other than something I love and that was amazing for now foreign [Music]

Channel: Cracking The Cryptic

Views: 177,676

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Id: IR5J__kHgLk

Length: 157min 43sec (9463 seconds)

Published: Sun Feb 05 2023