The Great Zetamath Reef

[Music] thank you hello and welcome to Tuesday's edition of cracking the cryptic and the return of the great zetamath to the channel and a brand new Sudoku uh called a reef to have a Triumph now um we had an email yesterday from zetamath uh alerting us to the fact that this puzzle existed I will tell you that one of our testers had already sent it through zetamath and said that they had tried it in their spare time and that it was magnificent um so they recommended we tried as well um that their email came with a warning though it I mean I've got about I don't know I was going to say 20 but it's more than that um my to-do list of very hard puzzles is astronomically long and the tester said that this you know this basically falls into that category it's a very difficult puzzle but very brilliant and I checked it out on logic Masters Germany before I turned on the webcam it does indeed have a 100 approval rating and five stars out of five for difficulty so this is going to be testing and it seems to involve a coral logic um which uh I mean I have done Coral puzzles before but not for a very long time but anyway this is what we're going to have a go at today I think I think zetamath has been very busy actually uh he and Tristan have moved house recently I'm not sure where to um but Tristan of course is is one of our famous moderators when we occasionally stream games um and uh yeah they've obviously they've also had a lot of Life events recently I hope I hope Zeta math and Tristan all is going well in your new home um and uh yeah I mean space actually speaking of things going well and having good days I was tickled pink by something that got recommended to me on Twitter the other day that I thought you might be interested in um if you are well whether you're from the UK or not if you are a music fan you will be aware that Glastonbury happened this last weekend um the great music festival uh culminating on Sunday night with the pyramid stage performance I think maybe the final live performance of Elton John um and that the scenes from from from that that concert are unbelievable the number of people I mean it's astronomically large number of people it must have been I I don't know 250 000 people maybe at that concert but Twitter recommended this diary entry from Elton John in 1973 and So speaking of you know having a good time woke up watched grandstand wrote Candle in the Wind went to London bought Rolls-Royce Ringo Star came for dinner imagine if you could write that in your diary that wouldn't be bad for those of you who aren't from uh who aren't from the UK you may not know that grandstand is or used to be anyway a great sporting show on Saturday afternoons in the UK where you know they would sort of it was it's really in those days when we had no channels we only had three channels uh back in the day you know it was the only place you watched sport um and yeah so it was it was very popular but I'm guessing that this was a Saturday and uh yeah Elton had a good day that day um hopefully we're gonna have a good day solving say to math today uh do I have anything else to tell you about before we um we get cracking just one birthday to do today we had a lovely email from Mary um in New Jersey about her son Michael's birthday in Rutherford New Jersey uh Michael has turned 41 today and your mum Michael described you as an extraordinary son husband and father clearly an exceptionally bright man as well um and she's very grateful to you for introducing her to cracking the cryptic which I think happened during during lockdown as it did for so many people and Michael she wrote that you brought her along in terms of her cracking the cryptic experience uh like a frightened bird which I thought was a brother a rather lovely expression so you sort of you sort of tempted her in with uh some tasty souls and then then the gas puzzles before the full-blown the full-blown Monsters made their appearance um and she promises you some chocolate cake when she sees you at the weekend with the correct ratio of icing to cake one to one of course so Mary thank you very much for email um I was delighted by it and Michael we hope that you have an absolutely brilliant birthday today now let's turn our attention to reef and see what the great zetamath has in store for us these are the rules normal Sudoku rules apply Shades themselves in the grid oh that's a stress a strange sense it just ends Shades themselves in the grid those cells are part of the coral the rest of the cells are water okay so we have to divide the grid into coral and water cells all Coral cells are orthogonally connected okay what does orthogonally connected some of you may wonder about um these two cells are not orthogonally connected because although they do touch one another they touch one another just at a single point or thugly connected means shares an edge so to make these orange cells orthogonally connected we would we could add this one now these are orthogonally connected so all the coral cells need to be orthogonally connected all bodies of water connect to the edge of the grid right so there's going to be some water in the grid and say we discovered these cells were water we'd have to connect somehow the water to the edge somewhere um no 2x2 is entirely water or entirely Coral okay we see that rule sometimes or maybe in yin yang I think we see that rule so we're not allowed to have a two by two of water or a two by two of coral I might I might actually use um blue and orange today because I know that is the most colorblind friendly option that we have from our palette um okay digits do not repeat within cages I noticed none of these cages have any toe tools ah okay and the sum of the coral cells within each cage must equal the sum of the water cells within that cage okay so each cage what we're basically being told there is that each cage has to have some coral and some water because if it was entirely one color it's obviously impossible that cage to contain enough Coral cells to equal the value of the water cells in it the digit in a circle gives the number of cells within its cage that match its color coral or water the total includes itself so let's experiment with this one and see if we can understand what this one might be so this is a six Cell cage the number of cells of its color so let's assume this is water for a moment so I can see it well obviously it could be a three perhaps couldn't it could have three of this we could have three water cells and the sum of these three cells would equal the sum of the the coral cells but I think that might be able to be four I don't think it would be five it can be four I think if we were to do something like that then we'd be saying those four add up to those two and if those were maxed out at an eight and a nine that would be 17 and it looks very possible that these could add to 17 to me so this could be four I don't think it could be five because obviously the Triangular number for Five is fifteen and I can't write 15 into this square or any higher number indeed so this could be yeah okay and then the inverse must be true mustn't it so it must be possible because we worked out this could be a four it must also be able to be a two so actually what we could probably do to start this puzzle is write two three or four into that Circle but we'll do that in a moment do have a go at this the way to play is to click the link under the video as usual but now I get to play Let's get cracking there we go um now that must be true for any six Cell cage have we got any others uh yes I do that must be two three or four um yeah that's another that's another one that could be two three or four is that oh that one's five so we do the maths on five cells How's that gonna work then so that could be Well it can't be a one because obviously it can't be a five but if it was a a one or a four I don't think that works either does it because we'd be saying if it was if we're saying it's a one well one obviously wouldn't work but let's try four we'd be saying essentially there are four cells in this cage that add up to the other the other number and the Triangular number for four is ten one plus two plus three plus four so that's never going to work so that's got to be two or three I think yeah and two and three are sort of the inverse of each other aren't they because if we're saying this is two we're saying two cells and there would be three cells that would be the opposite color so two and three are sort of the same right yes okay you can never put one into a circle for obvious reasons because it's Counting the number of cells in the cage including itself so it would be if you do put one in a circle you're saying the other three cells which that's in a group all of its own these three squares have to add up to one that's clearly nonsense so the rest of these are four cell cages I want to say these have to be twos or threes it could be threes yeah they could be threes I think they are twos or threes the way I think they could be threes imagine that was a three then we'll be saying three digits add up to this number actually it's actually is it is interesting in this box because if that is three that's two and vice versa and that does put more pressure actually um yeah ignore ignore that Circle for a minute but if that's three then that could simply be a one two ignoring this that could be a one two three adding up to six couldn't it yeah if that's three you can't make the total the three cells add up to seven because seven would be one two four yeah hang on I'm actually I'm actually gonna think about this because one of these has to be three and sorry and the reason I am interested in that is that whichever one of these is three has a two in the other position which takes two out of the options for the three sum so that the sum of three in this case if it was this way round then this cage has three digits which are the same color and include a three in their sum but do not include a two so they would have to include a one because two three four isn't that two three four adding up to nine is no longer an option so if we were in this Paradigm there would be a one in one of these squares and the other digit would be a four or a five so the total for this would be an eight or a nine I don't think we can sorry I'm just mulling that over I'm just letting that percolate um through the the coffee filter that is my brain um one four one three four eight ah maybe okay so I think I'm going to delete this because I don't know which order these go in but there are several things that I think we can say here that are those are mildly interesting so I think I'm going to stay in this box uh in fact I know I'm not going to say I I might stay in this box I've got obsessed with this box because I was doing it as an example and I could see this 2-3 thing going on I'm just going to I'm just going to zoom out a bit and take another staritis because I haven't really thought about whether this low hanging fruit here that is more obvious given five in the grid that's very generous say to my thank you um all right now I'm going to come back to this box because I think we can do some some parity here can't we well there's two things I think are interesting firstly my my sense is that this digit has to be high and I do know this digit has to be odd and I know it has to be odd because of the secret now the secret is something I only tell my favorite people but if you're watching this video 14 minutes in you are definitely one of my favorite people there are very few people in real life who would spend this long in my company um and not be deeply offended um or bored or asleep um so thank you very much um for for spending 15 minutes with me the um the secret uh is is a course that any complete row any complete column and any complete three by three box of a Sudoku because of the rules of Sudoku contains the digits one to nine months each if you add up the digits one to nine you get 45 45 is an odd number so this adds up to an odd number but the nature of each of these cages is that they add up to even numbers don't they because they contain an equal equal total of coral and water cells in them so we could if the coral total was X the water total would be X which means the sum of the cage is always 2x which is even so if if this is even and this is even together these are even we need to get the whole box to add up to an odd number so that is odd um that is true so it's one five seven or nine it's not three which has to be in one of those squares but but when I've been thinking about the the way that these cages work it's quite difficult to make it's quite difficult to make these totals huge by which I mean um let's make this one the three what is the absolute maximum value of those four squares now well that would be the maximum value would be if the if the three digits were adding up to nine wouldn't it and that would make this this these four cells add up to 18 overall but that if if we were in that world two of the digits in this two by two have to add up you know have to add up to something and then the other two digits are going to add up to something so the maximum we could partner the two with the absolute maximum would be a nine so if we make this a nine these two squares add up to 11 and they can't add up to more than it well in fact and I've chosen nine here and I had nine in this one as well which I obviously can't do so the maximum values here are going to be to partner up to with nine or two with eight and three with eight or nine sorry not three with eight or nine but the total here to be eight or nine which means these cells or these two cages together now see now I've broken the world now I'm being now I'm being too I know because the two comes back in yes okay I was going how can this work with eight and nine but of course it doesn't work it doesn't need to work because the two is partnering the nine so it's not it's not right to think of this as eight and nine being the sum the sums we're going to I'm confusing I'm sure I'm confusing you all because I was confused in my brain what I was thinking about but but basically the absolute maximum that we can make the big the total digits that we're looking at in these would be to partner this two with eight or nine here and to make the three digits here add up to eight or nine and if we do that we can see that the total of the high digits is eight plus nine plus two which is 19 19 times 2 is 38 that is the absolute most we can go to so this has to be at least a seven now now can it be now if if this was nine on the other hand then I'm depriving I'm depriving these cages of having nine in them which would mean the maximum totals that we could go to would be seven plus eight plus two uh which is uh 17 times 2 which is 34. which is not enough because that cannot partner nine and get us to a higher and get us to 45 so it doesn't work it only works with seven that is weird that is absolutely weird and I still don't know which of these is 213 but I do now know weirdly I do know that whichever one is three I know it has a one in it and I know it adds up to eight or nine and whichever one is two the two will partner with an eight or a nine hmm I don't think I two will partner with eight or nine no it's not it's not gonna do it is I can't I don't think I can I don't think I know how to do this so I get a 7 here ah oh okay okay how could that be a three no no no no no that can't be a three I think we thought about this here um if this is a three I've got to pick up three digits in here that add up to the other digit so if this is a three are we going to include the seven in the total of the three digits well obviously not because then the single digit would have to add up to at least eleven three plus seven plus one and we can't put eleven in so the three has to sit in us in a in a total which would add up to seven but it can't do that because the only way of making seven in three digits is one two four this is very very interesting so that's got to be two and that does things that oh that's three in the corner that's three in the spotlight losing its religion um this is great we've actually got to start here um three is in one of these three cells by Sudoku two is in one of those cells by Sudoku ah ah okay I I overlooked a possibility didn't I when I when I put two yeah okay I didn't quite understand this when when I put two in these two circles and indeed this circle I was thinking of two and four as being this having the same quality because it's dividing the six Cell cage into a twos a two piece and a four piece and that's sort of true except that the two P if the two pieces circled it breaks because what on Earth do I partner the two with the most I could partner it with would be a nine and that would require the other four digits to add up to 11 at most without using a two or you can't do that uh one three four five adds to 13. um so I can't I can't keep it down to 11. so in fact well this is huge because that means this is a four I think it means neither of these squares can be a two can I put four oh no I can I absolutely can put four in here I was wondering suddenly whether I couldn't do that um I tell you I've not even thought about the coral logic yet okay hang on hang on hang on hang on this one has got two in it yes okay so this this cage is three one two three one two adding up to six isn't it and we can see that because we have to add three digits in this cage together and we're not allowed to use four so if we pick the minimum digits we could we could do three one and two but if we'd missed out the one if we decide okay we're not going to have a one then then we would have three two and five as the next lowest digit and three two and five add up to ten which is not a valid Sudoku digit so the only way of making this work is three one two and six and we know that the two is in this row and now am I going to go full good list I think I am going to go for good lift here because this puzzle is confusing me enough that it deserves it so that square is not seven so seven oh seven goes here by Sudoku because seven um seven in this box is in one of these three squares so seven can't go there so so seven well let's do this long way the Long Way Seven is in one of these three squares that's seven rules seven out of this one it would repeat in its cage this seven rule seven out of that one it would repeat in its cage so now seven is here and three is thrust into just one of two positions this one and this one's got loads of high digits in it oh and no two surely this one needs a one in it hmm is that true if there was no one in this cage and no two in it then the other digits the other six digits I want to say would add up to 30 3 is that wrong three four five three four five six seven eight three four five six seven eight twenty one and twelve is thirty three well Thirty ah [Music] they couldn't add up to 33 could they they must add up to an even number so they'd have to then add up to 34. so it would have to be an eight yeah but that might work oh hang on I'm confusing myself now so if we had eight nine and then what would we need along with that we'd have to have three four five and six but hang on there is a seven in the cat oh this is confusing me sorry three four three four five six is eighteen oh yeah oh no hang on that doesn't work I can't make this work I'm struggling why why am I struggling to understand this why am I being slow that's the question that's the question on my mind now why can't I see how that can work I feel this wants to have a one in it if it doesn't have one in it and it was three four five five six seven eight that would add up to 33 which is not allowed so I could take the eight out and put a 9 in oh and then but then that then that gets me to 34 which is not valid because I've taken the eight out and put the nine in and and once I halve 34 I need an eight and a nine uh this is why it's getting confusing okay so maybe you can't do it maybe you can't do that make it work without a one if you try and do it without a one you've got to be adding to 34. that's absolutely forced because you need an even total which means that the two cell total must be an eight and a nine which means the four cell total must include one odd number and that odd number is going to be seven so you've got to go seven four how can you do this you need no it's not it's just not going to work is it I'm trying I'm trying to think about it in terms of parity maybe that's not the sensible thing to do 34. you've used eight there aren't enough the parities just it just doesn't work it just doesn't work I know that's just an assertion it's not really um it's not really useful is it but you but let's do this slowly if if you don't have one in here you have to have eight and nine so eight and nine would come out of these squares and now three five seven I mean this is just far too many isn't it it just doesn't it just doesn't add up you can't make it add up when you can't put two in there either I'm I I'm just grappling with how to demonstrate this in a sort of in an elegant way and I'm failing miserably to do it um 17. you can't put so you could you could put three in it because you could have the three over here could have the three exactly there actually so you could so we could have three in it so we could have three four five seven is the minimum because we know there is a seven in it and three four five seven is nineteen um and so it just doesn't it you just can't make it work without a one I'm not even sure it is ludicrous amount of effort I put into proving there's a one in this cage is in any way valuable but I think there is a one in one of those which would be useful if it was here um ah all right well I I can't prove it's there but I can do I can do the next best thing because this three clue needed a one in it didn't it because if that three clue doesn't have a one in it then the three digits that we're adding together would be a minimum of three four five which is already 12. so there's a one in one of those squares and therefore the one therefore if you like if we think about row two and three together there has to be exactly two ones in row two and three well I know there's a one in this Domino and I know there's a one in that triomino so there are no more ones after that so these are not ones so this is a two six pair which means this is a one um no okay I thought that would be good isn't um what about six six up in I don't think I I think when I was thinking about the three options I thought it was either going to be one three four adding up to eight or one three five adding up to nine it never included a six so six goes here in this box now now what does the two partner with here there is a question two doesn't partner with the six does it because then if the two and the six were the same they would add up to eight which would mean the other Domino would have to add up to eight and it couldn't be three five one seven or two six so it couldn't so the two is not a partner of the six in fact we know that the two is the partner of an eight or a nine from the logic we did before so either oh I see so either either I partner the six with a four or a five I can't partner the six with a four so I have to partner the six with a five because I know the overall total the the two is going with an eight or a nine so if the two went with an eight the six would have to go with a four so the two goes with a nine uh and the six goes with a five and therefore right so therefore this is now one one three four adding up to eight this is mad uh this is not four come on I'm sure this is important um oh Bob in space what's this doing then so in the top row we need four four five eight nine I'm sorry but I'm finding it quite hard to juggle these options um do I know what this is now what does this partner with oh it's absolutely it could partner with the seven couldn't it the two and the seven and then these two would add up to nine would be a very natural way to go uh what about that oh actually what about both of these digits one yeah we've only got one three and eight left to put in there's no parity gig here is there let me just think about that um so if we think about the nature of one of these cages overall it adds up to an even number so it must have an you must have an even number of odd digits in it wasn't it that's absolutely forced so there must be an odd digit in one of these two squares yeah that's the world's most stupid deduction okay that's not clever um okay um what else can we do here and how are we ever gonna get down into the rest of this grid it seems like all the circles are crammed into the top of the grid oh oh oh no oh no okay I've missed something very obvious here oh bobbins yes okay right every cage in this puzzle sums to an even number but what do the first three rows sum to well they sum to an odd number they sum to three lots of 45 which is 135 which is odd now this little cell is the only cell sticking out of the top three rows so um so look hopefully this is fairly obvious but those those squares are all in cages complete cages completely contained within the top three rows so those green squares add up to an even number they're all in cages but we know the top three rows overall all all of these rows add up to an odd number 135 so those squares add up to an odd number but we know this cage adds up to an even number because it's a cage so how are we going to make that work that's going to be a three bother that's been I think probably available from the but litch in fact that has literally been available well you had to have realized it couldn't have been a two because of the logic I overlooked at the start but once you did that you could have done that right at the start it's probably the first digit we were meant to put in just didn't see it oh look and now it gets me a two here oh no so two is down here so what what is going on in this cage then K just got a lot of high numbers in it as again hasn't it I don't know I've Got a Feeling what we're meant to do hmm no I've changed my mind about what we're meant to do I'm going to look at this digit that can't be a one I don't think because if it's a one um what are we going to partner it with I don't think there's any good choice if we partner it with the seven these two squares would have to be a two and a six and that doesn't seem to be able to be a six and if we partner it with these two digits oh one eight does work when I add it up I didn't see it botheration one eight can add up to nine oh no all right that can be a one um oh it could be the corally it could be the corally logic what was the corally logic about we had to make everything connected oh currently logic what is that gonna do for us do we know oh okay here we know this one partners with the nine don't we which is either there or there can you oh you can't have checkerboard because the the the water has to get to the edge right okay another point that I I totally didn't really think about until I'm now starting to think about it is the structure of how we're going to divide this grid up so it's a little bit like Yin Yang in the sense that um let's let's divide this up let's have these let's have that pattern is this is this a permissible pattern in this puzzle can you have a checkerboard in a two by two I think the answer is no I think the answer is no let me explain why because it's not easy to understand this um remember that we have to connect orthogonally the land to each other so this is going to have to we're going to have to come along some path to connect these two together we don't know where they're going round the top bit or around the bottom bit but somehow or other these will have to connect now can you see it doesn't matter what route we take to achieve that the problem is for this water it can't get to the edge anymore because it will have been ringed and if we've gone the other way around in connecting the oranges up if we'd gone across the top to do it again it doesn't matter what what path we go on how long a route we take it's got a very long route this one can't get to the edge because it's encircled by land so actually we must avoid checkerboards now that means that this Square now the thing is I don't know whether this square is land or water but I do know because it's got to connect with one of these two squares it can't be that one because that would create an immediate checkerboard so I know that those two are the same and I know that these two are the same um and I tell you what if we did know this was land this would have to get out if this is if this is water it's already touched the edge so it doesn't have to also take this square but if this is land in order to connect to the land in the rest of the grid that would be land okay so we're going to have to think again aren't we how are we going to do this oh well what about that one that's got three three cells the same as this one that's got four cells that are the same okay um don't know um could we argue I don't know oh no I've got I've got nothing now uh my brain is not telling me anything about how to resolve all this if I knew those were the same color now then it still depends on what these are um um oh okay here's another little point this little pyramid this pyramid stage here has to um has to add to an even number but we know from the secret the overall box adds to an odd number so these three digits sum to an odd number but this cage overall sums to an even number so because the two won't change the parity of the odd numbers this must add up to that we're at odd once we add the two in so that has to be odd to make the parity work and it's not three so that's one five seven or nine which is unfortunately useless that's not five by the power of the given digit which is quite exciting okay three oh right three in this box we've only got two positions can we put three here and thought about that yes we can that's three that's got to be eight I think I think that's right yeah because we couldn't we can't partner that with six here so this is three it partners with the seven and this would be a two eight pair um I don't understand how I meant to do this I have to say maybe I can I get rid of four from that square then it might it might be just a case of whittling we might just have to whittle down options uh if this is four can't partner with the seven because we can't make these add up to 11. and we can't put five here that's just not four is it okay so that's a tiny deduction which tells us four is in this cage is that helpful I haven't got a Scooby-Doo um two three four that digit is not now it's not one because I believe there's a one in that cage it's not two or three it's not four which is up there now is it five possibly five six eight or nine I want to say golly it's really quite restricted then so do we have to be a bit careful no because it's because this is a three we're dividing this into a three and a three aren't we so it's not like where we have the four the one we have the two four division where there's a lot of a lot of play in that this being three I don't think it's going to it's going to be too important so the minimum we could put in here would be four five six and eight as the other digits four five six and eight so we'd have three four five and six seven eight which is which doesn't add up to the right number of oh it's it's not parity is it I've got to make sure this cage has an even number of odd digits at the moment it's got It's got a it's fine oh hang on if I put five oh if I put five in it would have to have nine in that's what we're learning but if it didn't have five or nine in all of these digits would have to be even and they can't all be even oh that's beautiful is that it that's real oh that look that's going to make this an eight oh that's beautiful if that's true that's absolutely beautiful so let let me I'm going to go through that logic again because I'm not sure I trust it what I'm thinking is in order to make any of these cages add up to an even number that cage must have an even number of odd digits in it this one has just three and seven in it so far so it has an even number of odd digits at this point now if none so the only options now are the two two of the other four cells are odd because they can't all fall Beyond there are not six odd digits in Sudoku so it could have two more odd digits which I think looking at the options there would have to be nine and five because one can't go in the cage so that's that's one possibility the other possibility is there's no more digits but then these four digits would have to include a two because they must be all the even digits two four six and eight and they definitely don't include a two so this tells us that there are a five and then there are five and nine in those four squares now that square C's all of this quadruple so that cannot be um a five or a nine so that's eight which gives me a one three pair which makes this eight which makes this a one four pair which makes this okay which makes this not oh that one oh yeah yeah yeah we we knew yeah this is great because I knew there was a one in this cage from all that nonsense I did earlier so that's one that's three how does this cage work then so this cage works by oh it's ten yeah if we if we add up the whole thing it adds up to twenty so we know that each each parcel of two is adding up to ten so these two are the same color and these two are the same color now this is tricky now because we're getting into a world of nonsense aren't we where we sort of I don't know how to relate purple and yellow to green and red I don't think I do anyway but right now we can take eight out of here so the total for this cage now well this this has got four five nine so that's got to be a six by Sudoku um the total for this cage is 13 and 80. now that doesn't add up no 16 and 18 that's better 16 and 18 does add up because that's 34 so each each slice of three here adds up to 17. so the nine has to go with two more digits yeah so the nine needs to go with two more digits that add up to eight and there's only one way of doing that uh with with the options available because one seven and two six don't exist as a package in this so the nine has to go with three and five so the six and the Seven are the same color and they go with a four in one of those two positions these are the same color I mean I'm go I'm going and getting into absolutely mad lands here I can't quite visualize it I I'm sure there's a way I mean we could do it by bifurcation but I'm not I won't go down that route I I imagine there's a way of working out which one of these is a four feels more difficult for that pattern to exist in the puzzle doesn't it that's what just just my sense these two would then be the same we have to avoid a checkerboard sure all right so what's going on then in this square is a five or a nine I think by Sudoku that Square's not a one anymore uh because of the one here oh in this one in this cage the 314 are all the same color I'm struggling to say I'm going to take out the coloring of this one I find it very difficult to to view on top of this one these are all these three are all the same color if it had been those four we would have been away because we could have avoided a two by two um now is there a problem with those being yellow if these are yellow that makes this water if these are purple we don't know I know these are the same um okay um stuck do we know what the sum is of this one I think we do know that don't we we've got 10 to 34 we've got 34 again oh right so this has got an eight nine pair in it that are the same same color so the four and the one are the same color oh golly this is getting very confusing yeah the four and the one are the same color from this cage the seven and the six the same color from this cage and which way around was this one the three and the Seven were the same color okay may actually maybe I can do this maybe I take out that coloring maybe that's better I'm going to take that coloring out and notes yeah there we go we have to avoid a checkerboard here that's great this is the way to do this it wasn't to start here it was to start here because I know the three and the Seven are a different color to the eight this can't be yellow can it so that's got to be purple but we know that within this cage these are all now all yellow oh this is beautiful now because now remember that the way the striping worked in the two by two if this um the six goes goes these two are the same color is what I'm trying to say oh in fact I actually know the order foreign I think I have yeah that's got to be like that because if if it we said that we had to avoid a checkerboard here which if this was a nine that would be automatically a checkerboard so so yeah I think that's been available for a while but the point here is now how could this be purple I would create a two by two so that's got to be yellow this has got to be purple now yeah now oh now now we're there because this has got cut off so purple is in fact blue it is water yellow is orange which is are going to be our land for maximum colorblind Effectiveness now that's got to get out because it can't be um it can't be thingy thingy right this is huge this is huge because remember we said the seven the six with the same color so if that's a four these these these all these three couldn't be orange because we know that there are three colors here that would add up to 17. so if that's four it's those three and they would be blue and this would be isolated so that is it's not possible for that to be four so this has to be before and if that's the four it goes with the seven and the six there we go Bingo boom we get a load of blue things in here we get a blue no blue blue blue blue doesn't have to connect with itself so we can't do total yin yang here but we do know that's orange because we know two and eight add up to ten aha aha oh I've got a five nine pair looking at that square so that's got to be a seven now well that's interesting as well I think because this too doesn't doesn't attach to this it doesn't take the seven as its same color because then then these three squares would have to add up to Nine without using a two so they could be two three four or one two six they'd have to be one three five and that looks like it's the reason for this given digit because that cannot be uh this cell by Sudoku sees one sees three sees five this feels deliberate doesn't it so these are different color these are a different color [Music] um sorry Maverick's just flying over no doubt here these are different different colors I'm trying to see what that means and I'm failing over the seven right hang on hang on a moment yes this is forced yeah this is ah oh my God it just takes a little bit for my brain to twist into gear so the seven here is part of a three cell sequence because it's not in the sequence with the two in this box but seven is quite a big number the minimum I could add to it would be a one and a three and that makes eleven and the maximum I could add to the two would be a nine so this is that's how it must work that's one three and nine into here the seven is partnering up with the one and the three and the two is partnering up with the nine foreign oh and there's a three here okay so we get we get some of this some of this is resolved so the seven Partners up with the three so these are the same um I would love to know what color they are don't oh that's a four Now by Sudoku so that's a four that's a one I'm gonna be a bit careful with having too many oranges along there look because that's going to create two by twos if we if we go a bit ham with the orange um can you go ham with the orange I'm not sure it doesn't sound like a very nice pop combination although a little bit a bit Hawaiian pizza-esque I suppose um all right what about I've got one here okay I'm just not doing my Sudoku now sorry I'm getting I think I'm getting discombobulated um now okay so those three are the same color I don't know what color that is I mean I can see how it's quite difficult for this to be if this is land this would be water and then then that would be water this would have to be land that would have to be water that would make this water lots of things would flow from that or maybe actually maybe it's better to think about it in terms of we know this cage is divided into an eight nine pair don't we that that are part of we know these two are the same color ah oh right that's vicious okay these are the same color they can't be blue they can't be blue because what's this now well this has to be land now what what would we like this to be in in its nature as land do we want to make it a six if we make it a six these three are all water and that's going to create a two by two of watridge if on the other hand we'd say oh no no this is a two then that three then then don't forget the one three and the two in this region are all going to be land then and that's land and that's land but that's water and that land is stranded because the six is always going to get in its way of getting out so this just doesn't work this doesn't work that's quite tricky to see but it doesn't work so those are both land therefore this is the right therefore that's to avoid a two by two this is water to avoid a checkerboard that is water which means these are land which means this is water this water hasn't got to the edge it might be coming down here uh oh we were we were we were on a good track there for a moment weren't we and that's all that's all gone it's all gone cold again um okay right so this is nine because remember we said that it's the nine and the eight that are partners um in this region so once we know that the one and the four the one and the four partner with the five and the Seven because five seven one and four add up to the Seventeen so we need to put nine here we need to put five here we need to put nine here now there is a nine in this cage at the bottom of column one these squares are no longer nine so these are five seven eight now I've still got two more two more oranges to find in this string so right so if this was the blue if this was blue I'd get a checkerboard wouldn't I because that would be I get this pattern and that's a checkerboard in those cells which doesn't work so this has to be uh right so this is huge that has to be land now avoid a checkerboard here makes this land foreign not running into problems now no I'm not running into the same problems I had before because I can make this six can't I in fact I can make it either because this isn't this isn't blue now okay that's fine that's fine right so what's going on this has to get to an edge somehow this square is not eight so the eight is in one of those two that's two these are both shaded and this is this is C and then C would have to get to the boundary so this would be a c if this is six all of those are C so this is always C is what I think I'm demonstrating here I don't know if that's right that feels a bit weird um let me think about that again so if this is a two it partners with these oh that just creates a checkerboard actually that's the simpler way to see that if this is a two both of those have to be unshaded and that has to be green now to be the six and that's a checkerboard so that doesn't work okay so so that is six which means all three of these must be blue that's got to be the two this has got to get out so that's got to come down this uh that's got to be eight because we haven't got the second blue digit in this this funny region so that's got to be blue this is now a five seven pair this hasn't got out it's got to come all the way down column one look I've not got any Circle in that in that region I wonder if that's oh we can do maths on this region because we've got 13 there so 45 minus 13 is 32 which means these ah foreign not only did these digits add to 32 but we know that each each section of of coral or water therefore ends up to 16. now you can't we can't divide this six cell region into two and four then because the two region would have to be a nine seven pair and it can't be so this region divides into a three-cell region and another three cell region right this is absolutely beautiful because knowing that I can I can extrapolate from that and say how does this segment here of land or Coral get to touch any other Coral in the world well one of these must therefore be land because if both of those were water we'd have strandage so whichever one of these is land is the final land piece in this region so those two are both water I mean I'm not saying that's amazing but it's interesting I know I know um four four is in that blue blue thingy thing four is there by Sudoku out of absolutely nowhere yeah okay I'm going to take that opportunity to do massive pencil marking five six seven and eight now that's not seven or eight that's not five or six so this one's got quite a lot of high digits in again hmm okay I was wondering if we could pull the trick of requiring it to have a one in it but actually this time this one is different to that one because in that one this one didn't have a 2 in it whereas this one could have a 2 in it oh we can get the parity of this digit yeah okay um because we know that's adding up to an even number we've got 16 we've got so we've got 16 there plus an even number so we're on even so this has got to be odd and it's not three or seven or our bobbins one five or nine not not terribly clever um right so there are definitely [Music] it's definitely two odd digits in here and two even so the two even digits in here are six and eight aren't they so they are if they were paired up they would add up to 14 and that would require five and nine to join them in in the in their little casket here wouldn't that wouldn't it but if the six and the eight were separated then whatever you partnered the eight whiz would have to be two less than what you partnered the six with but that doesn't work because we're picking digits from one five and nine and which whichever two you pick they're not two apart that's ridiculous I don't I don't know if that's the way you're meant to do it but that feels right doesn't it so that's got to be five nine six eight which means this Square here is a one out of absolutely nowhere one one oh we're getting to the point where it looks like the one wants to go into this cage here uh one is down oh no one is the right at the bottom it can't repeat within a cage that Square's not an eight these squares are not six that Square's not five or nine so this is six or eight um and we know don't we that okay so whatever that is Partners up with a six or an eight Somewhere In The Box um I don't know how to do that what about don't know I think I'm getting stuck again now do we know which of these is the method of Escape for column one and how can I have just looked at the clock one hour 11 minutes that has flown by it's a sign of a good puzzle three is down there look um five six nine what do we need down here five six seven and nine let's put that in we can take out um five six seven and nine we can take out five from the bottom row foreign desperately looking for some sort of parity trickage here what about three four six and eight down there ah that is that's interesting okay so so it wasn't here I could do parity it's here because there is a three at the bottom of this in this cage and it's combined with two even numbers but we know there's an even number of odd numbers in this cage so that is even it's not one three or five it's seven or it's not nine that's beautiful that is a ridiculous digit isn't it that is a seven that's not a seven now that is a ridiculous day those seven look look look look look seven here five here this is no longer seven so seven seven has found a home in this cage over here is slowly working our way towards I must know the parity of this digit as well I love I love puzzles like this parity is a complete um complete love of mine now this is even so at this point once we have the seven in we're on an odd number we need to retain that parity because it's 45 for the box so that's even and it's not three which Cuts me the three here this is even and it's not two or eight so it's four or six um don't know if we can tell which four right four six R that's four or six as well so the seven oh hang on why have I got four pencil marked here is that oh yeah this is a naked single I think yeah in this column I need four six and seven and there's four and seven looking at this Square so that's six that's four that's four that's seven that's really rather lovely okay so these These are five six and eight no they're not there's a six here that's total and utter rubbish that's not six these are two five and eight so these down here are one six and nine which means we know those digits they're two and eight is buzzing at me I'm going to ignore that um looks like this is going to be something like three combining with seven to add up to four and six doesn't it is there anything else that works there can we use the eight uh oh no you can four seven three eight would also work okay that doesn't that doesn't help me um [Music] I'd love to know which one of these is the way that this orange connects up oh can we work this out by maths now ah I haven't thought about that for a while I probably can um what was the total we were heading towards 13 yes yes we were looking for 16 weren't we and at the moment we've got 11 so I need to combine that with a five well that means this can't be five because it's not the right color so that's eight that's two that's got to be the five and eight two and six do indeed add up to the right number so we can do it it's surprising the way all of a sudden you can get look at look at this now eight comes over here this is now seven so this is a five six pair these digits are four five six seven which add up to 22. we've still got more adding to do to those totals see oh that's not sick oh this is good hang on I think we can do Sudoku on this box that's got to be a six so that's quite interesting we know the six Partners up with eight don't we but we don't know which one of these is the eight and we've achieved connectivity with our Coral so okay so we're in better shape than we were um that's five so that's not five so that's eight or nine two three eight and nine along here let's put that in to see if anything anything gets thrown out by Sudoku I don't believe it look this is a naked that's weird isn't it that's just a weirdity that is a naked single apparently two three eight nine yeah that's a naked single eight that's massive as well because that gets me a nine a five an eight we know these two are the same um so can we disprove yeah yeah yeah look if these if those are um a water those two have to be um coral and that's that's created a checkerboard so we've got to make these Coral these water don't make checkerboards all over the place here so both of those in our water ah this is great this is great now um now we need one and nine the nine can has only got one place to go and that's got to be a one nine comes out of these squares as does eight so this is a two three pair now but now we can get the parity of this we can get this digit can't we because we're on 22 we're on 23 we need it to add up to an odd number so that has to be three three and two go in now that should be 26 which means we need 13 is the divider let's just check that 13 and uh 26 19 that's right yes so so here we need we need to combine so we know this is combining with two digits that add up to nine oh so there must be three and six oh no hang on no hang on I might be wrong about that no no I'm totally wrong I'm totally wrong it's a four it's four digits ah what's going on if I messed this up then I know these add up to I know a 13 is the total so okay now I see so there are two digits in here that add up to 13 and they must be a six seven pair so that digit oh that's so clever that is so clever because look this digit is a color and it combines with a six as is as its color now imagine this was orange whichever one of these was the six would create a two by two that's so deliberate that's so deliberate and so brilliant so now these squares are all Are all uh Coral one of these is these are one of each I don't think we know the order um look we and we can do Sudoku I mean I know I resisted but let's just do some Sudoku 138 down here actually maybe not can we oh no that's not eight because it would repeat in the in the cage that's not three what about this one I don't know um can we actually we might be able to restrict this digit using the power of what's in there and what's in here let's just check this digit it can't be one two three four it can be five I think uh it can be six bother oh that'd still be interesting seven eight nine yes look there's a five six pair in this column so we need two and uh we need two and nine at the bottom there's a two here two here so there must be a two in one of those squares which means the two is going exactly there which means these two digits now when oh no hang on I was about to say something that wasn't right I've seen another way of doing that I was about to say these two digits have to be one apart but what if they were nine what if it was a nine equaling one two six ah oh that's festively annoying um all right well let's try maybe we try more Sudoku one five yeah where does five go in this column it's got to go here so that's a one okay so these squares don't include five oh we should be able to work this out now shouldn't we no no no no no not at all because it could be six two with seven one or it could be nine nine equally equaling one two six all right so this is not one in the corner um these are not six by the power of Sudoku oh okay can we get can we get the coloring of these done then the AES is eight and three isn't it going with seven and four eight and three going with seven and four I don't see how to do it um missing I'm missing something now missing something what is it I'm missing let's sync uh can I get the Pat I can do parity again parity keeps coming to my rescue um so I've got 19 there that's odd that's odd so we're on even so we need to stay on even so that's six that's beautiful six and five now that's going to tell us what's going on here we know yeah we know we needed 13 don't we so we've got to take that as the blue that's the land fine okay um so this uh this little Lake of blue in the middle of the grid needs to get to the edge so it's got to come down here somehow that little Lake of blue is already touched the edge and we've got full connective nearly got full full connectivity of the coral okay what about can we deduce anything about no uh that's not six it could be Sudoku now actually couldn't it it very well could be one three five eight nine yeah what fat let's disc that's fully pencil at the bottom of this column because we need four five and seven in there yeah naked single naked single I just didn't now what's going on this this must be done this must be done something's wrong in this row the six is doing this digit ah okay maybe it's not something that's wrong I could just sense that that we could do we should we should have it should be more resolved than it was one three eight aha right this is massive now so this is eight this is one it would be quite funny we might actually just finish off we might finish off the puzzle here you know when I say we might we have we've suddenly finished off the Sudoku but I've got absolutely no clue about how the um how the reef is is going to be constructed now okay let's start here because we can do the maths on this can't we've got 19 and 9 which is 28. so we need 14. so the nine is going to have to partner up with two cells that add up to five I believe is there any way we can do that so that is a strip of the same right so that's this is C because if this was land it would create a two by two so that is water these two are both land this land is not connected to anything so it's got to come down and now this has to be water but to make this one work we've got to have 12 and 12 adding together this land still has to get out so it's coming along here to me to meet up with its friends this doesn't have to extend uh let's um ah this oh this is big or is it don't know oh you know it is it's huge this one you can see the digits in it add up to 18 so we're looking for nine so this nine sits on its own and that's already been turned into water so those are water that's got to be land avoid a checkerboard that's got to be water this oh no it's all connected I was about to get excited and say that this had to come along here but it doesn't because this can come down here um what's the what's the situation for this cage we need we need to partner up the eight with the three don't we so those two are the same color these two are the same color well that's ABS that's it that is absolutely beautiful because what that means is that this is a sort of plug this stops this land coming down here and and connecting with anything saying box seven we know there are some land over here now or Coral I should say now can the coral here connect to this Coral the answer is no because this 4 7 pair is the same color now if it's Coral that's land sorry that's water and this is stopped from coming out and if this is water well it's obviously stopped from getting out that's going to be Coral but it still stopped getting out so that means that the way that this stuff here connects to the coral is along the bottom row so all of that has got to be Coral and that's coloring the three good grief as this has done it this is going to do it all now avoid a checkerboard boom I've not even thought about the maths down here have I let me just stare at this for a second or two uh well this has still got to connect this is because they've got there's got to be some Coral in here what is the total we've got 11 here so this is 34 so we're looking for 17's worth of coral and 17's worth of water but okay but but okay I haven't got 17's worth of coral yet so I've got to take that square now I've got Seven's worth of coral that's got to be Coral to avoid a two by two of water I mean the only way I'm seeing this work now oh no I'm wrong hang on hang on this is more so I've got seven I need ten more but I've got to make sure I achieve connection so is it just is it those or is there another way that looks right to me then that would be water I'd have a 9 8 pair which would be 17. and I'd have one three six five and two which would be 17. let me just I'm just gonna check this though this is this is classic zetamath trickery I mean if I made both of those Coral these would cut off that Coral from the world I don't think that can possibly be right and I can't see another way of doing it I don't think there is another way of doing it so I think what I've got to do to finish it is that and that now let's just take a stair is the blue always connected to an edge yes [Music] is the coral all orthogonally connected yes are there any two by twos in either sequence I don't think so I want to go with that is that right no it's not right what have I done wrong is it tell me why it's wrong no that's a bit disconcerting just as it's wrong uh oh did you miss some rules I don't know did I what have I got wrong okay we're gonna have to think about this so 10 17 that that one's right that one I'm just going through the cages now adding them up to see whether I've got the maths wrong I mean would it tell me it would tell me if the Sudoku was wrong wouldn't it I think no but why didn't it tell me that the Sudoku was wrong it just says it's wrong how does it know it's wrong and maybe it's trying to do cage logic or something I don't know I've got no idea normally when you get the puzzle rock it says it says why you've got it wrong foreign or maybe maybe the reason I've got it wrong is the Sudoku is right I.E I have put the numbers one to nine once each and every row column three by three box but the internal solution that the computer knows about has things in a different order that's very possible um 14 14 that looks right what's this one 1313 that looks right 11 11 that looks right eight that looks right 1414 that seems sense for all this one right no that's fine I didn't see the two for a moment that's elevenths and that's eleven so that's right that's 16. and that's 16. I don't know I don't know what I've got wrong I'm just not sure I don't even know how I'm going to tell whether I mean the problem is I don't have a logic Masters Germany account so I don't know whether you can put put your solution into logic Masters Germany as a guest or something and it will tell you whether it's right or wrong oh I'm so upset with myself I'm so sorry zetamath I think that you're not going to see this video my friend because I've got something wrong I've got I've got I don't even know where to look I don't know what I'm I don't know how to tell what I've got wrong it felt like it felt completely logical and very beautiful and full of lovely logic but somehow or other I've messed something up and I have no idea I have no idea where to begin looking normally you know if I got two sixes in a row or something I could I could investigate that but this is a very strange situation where I've actually I actually haven't got two sixes have I what have I done wrong here um I don't know I'm so sorry I'm going to turn off the video and do some more investigation and if I convince myself this is the correct solution maybe this video will see the light of day we shall see thank you very much for watching let me know in the comments um how you got on I enjoy the comments especially when they're kind we'll be back later with another edition of cracking the cryptic let me interrupt to say let me interrupt myself to say that I think this puzzle is correct now um I I checked with the tester who'd recommended the puzzle and have put it into our software he went back and had a look at his solution which is not the same as mine but I was able to spot an error in his so I think mine is right um and I'm very excited as you might be able to tell about that so I think the video hopefully uh stands on its own it can be released and um yeah and that's all I wanted to say [Music] thank you foreign foreign

Channel: Cracking The Cryptic

Views: 45,409

Keywords:

Id: keSNTPYnc8w

Length: 95min 35sec (5735 seconds)

Published: Tue Jun 27 2023