The Wings Of The Pentagon

[Music] thank you hello and welcome to Monday's edition of cracking the cryptic where today we've got a puzzle called the wings of Pentagon for you by navario and this is just a normal killer Sudoku today we don't get to do normal killer Sudoku very often on the channel and when we do do them they tend to be absolutely exceptional and the various puzzles are always exceptional but this one I just had a look at it on logic Masters Germany and there is a rather well it's an amazing compliment from fistemophel about this puzzle where he describes this puzzle as sensationally beautiful um now that's sort of I think that would be one of my ambitions in life to to create a Sudoku that fistema bell calls sensationally beautiful so navario I think you've achieved an ambition there at least an ambition of mine and I'm looking forward to trying this the only thing I'm slightly perplexed by is why it's called the wings of Pentagon for some reason my brain wants to read this as the wings of Pegasus but it clearly isn't that it might I suppose that's a pentagon the given digits are a pentagon and the cages are very symmetrical I don't know whether it's meant to look like the building the Pentagon um in America maybe I don't I don't quite know that anyway novario may watch the video and make comments so um any any Enlightenment would be most welcome um now I've got a few things to mention before I read you the rules of of the puzzle let's start off with the fact that today is World mental health day um and when Mark and I started the Channel all those years ago and even when the channel became popular we had absolutely no idea that the channel and the videos that we we make do seem to have a positive impact on people's mental health and it's completely humbling when we find out about this and we do actually now regularly get a couple of emails every day um that talk about how cracking the cryptic is is helping people uh mentally I thought I might share with you a couple of recent emails um on an anonymized basis um I just just you know just because I think it's rather rather special so I'll start with this one I have to say thank you for these puzzles I am an engineer and a mathematician and logic and numbers have always been my forte all my life but when I got covered a few months ago I experienced Panic that I wasn't able to calculate the area of a regular hexagon not even with a calculator seriously impacted my brain's ability for several weeks and it undermined my own sense of self if this makes sense not being able to trust myself when dividing 12x4 was absolutely terrifying a few weeks ago I stumbled on CTC and at first I just watched the videos and then I started trying to do some puzzles and I was still making a ton of pedestrian logic mistakes but it was great to be able to rely on the videos to help me figure out my mistakes and slowly and surely I've got better at it and at the same time the effects of covid seem to have gone away have this person completed all 14 of the puzzles in our Duality hunt which is a tremendous thing um and they say that I'm pleased to say with logic and not deep bifurcations it's restored my self-confidence in my brain working again um and they go on to say I've almost done all the puzzles in the 500 000 subscribers special pack with only the last couple to do and I feel so proud of myself now and of course they should feel proud of themselves what an incredible thing um and we get quite a lot of emails about people who have experienced brain fog with covid so if you do know anyone who's in that position show them one of our videos see if it helps them um and um then I'll read you this one as well which said as cliched as it sounds I want to thank you both from the bottom of my heart for saving my life pandemic has been so hard as a single parent whose partner lives in another country it adds an extra level of loneliness and it was at a particularly low and depressed moment that my partner showed me the miracle Sudoku it was just so wholesome and at a time when it felt like the entire world was burning down around me it helped the pandemic is still hard especially for us disabled folk and it still gets lonely but watching your videos each night has become a bit of a touchstone for us and whenever I need an extra pick-me-up I go back to the miracle um you know it's just it is heartwarming for us to hear these sorts of stories um and for all of you out there anybody who's feeling anxious or lonely or I don't know stressed or suffering from insomnia um we we hope that we help a little bit these videos weren't designed for that but they do seem to make a difference so if you know anybody who might be suffering especially on today World mental health day maybe let them know about CTC and maybe you can help them um anyway right let's move on to um less serious matters oh yes well that will start with last night's stream uh where Mark and I um uh well we we attempted to do the last two puzzles from our own app now I will start by talking about jovial's puzzle which I attempted that is one of the greatest sudoku's full stop I have ever done in my life it is an unbelievable puzzle what jovial has created is quite extraordinary um it is a killer Sudoku like like today's puzzle and if you have any love of killer Sudoku if you watch this video and enjoy killer Sudoku and think oh I'd like to do more of those check out uh that puzzle which is number 23 it's the very final puzzle in our free app you can get the app completely free just go to the App Store type in cracking the cryptic you'll find it there and work your way through to the last puzzle it's called Miser and it is Sublime it is a work of Genius um thank you jovial for making me literally lose my mind um in in the Stream last night and then the other thing that some of you asked to see more often is when we can't solve a puzzle and believe it or not Mark did get stuck yesterday quite badly on udacris's puzzle um so if you want if you if you have a bit of Chardon Freud in you or a certain amount of sadism um watch watch the stream for that reason and you'll you'll see Mark's struggle um now next lots of you lots of you are asking when when our Kickstarter is launching for our new book that we think is going to be Wednesday night at 8 30 UK time um as soon as I have that finally confirmed I will let you know um but yeah that's when it looks like it's going to happen next I've got to read out the names of loads of you who've managed to solve Duality which is um the 14 puzzles Sudoku hunt over on patreon at the moment the number of entries have from that has been absolutely extraordinary I am so proud of so many of you who have written and said you can't believe you've managed to achieve getting through it you didn't expect to several of you I think worked your way through to the first four puzzles and solved that and then thought well I've done four maybe I could do a few more and the amount of hours that have been devoted to this I mean it's just incredible the response is incredible um anyway very well done to Thomas Sylvester Brendan Roberts Jacob Hannah Steve Williams Simon HUD and joy Muirfield I'm very jealous Simon um yuha mati heikenen Rob Driscoll over there in Oklahoma City who who let us know how much it would cost um in terms of how much he would bill for the hours he spent on the pack it was a very large number of thousands um so Rob I'm sorry about that um sampath Kumar uh John Alistair warika slightly simple assignment John Bruns or it could be Bruins I'm not sure Andrew Pippin Alex Plunkett anakiara Bellini and iron Kramer all of you fantastic work and happy birthday today to James from your wife Amy um James she says you're a wonderful husband so good job there and I hope you have of course lots and lots of cake and with all that said and done long intro today but I hope you don't mind sometimes we like to get a bit serious um let's have a look at the wings of Pentagon by navario the rules are as follows normal Sudoku rules apply in cages digits must sum to the small clue in the top left corner of the cage and digits cannot repeat within a cage so that tells us those three cells come to 16 but we couldn't do it like this because although those three digits do add up to 16 you have repeated the five nautily you mustn't be naughty if you want to solve the puzzle correctly do have a go at the puzzle the way to play is to click the link in the video description under the video but now I get to play Let's get cracking and the first thing I'm seeing here is that there's some there's something going on with geometry isn't there looks like there's well there's clearly a relationship to me at least between this cell and this cell in terms of their quantum and we can work out that relationship because of a secret and that's something I only tell my very favorite people I feel a bit croaky today actually I hope I'm not losing my voice that would be a disaster um but anyway the secret is uh it's related to the sum of all of the digits in a box of a Sudoku or indeed a row or a column of a Sudoku because of the rules of Sudoku we know this box contains the numbers one to nine once each if you add up the digits one to nine you get the number 45. so we know that those cells some to 45 but we also know don't we that those cells sum up to something else they sum up to 28 51 is the number I'm getting there I hope that's correct so if we sort of remove those which are common to both sets of digits or both both sets that we just highlighted we know that this digit here has to be six more than this digit I think in order for those that the maths to work so let's let's test that out and see whether I've just made an absolute Ricket so if it's got to be six more it can't actually be six so it's going to have to be at least seven so if that's seven we could then see these would add up to 16. 16 plus 15 plus 13 is I think 44 which would make this a one yeah so we have got that right so this has got to be seven eight or nine and this has got to be one two or three um now I don't know if we can improve upon that I don't know the other the other the other thought that occurs to me here is if we if I get rid of the coloring of the orange digit now the blue digit has to live in live somewhere in in box one and it can't repeat in its own cage and it can't repeat in its own row so this digit here is in one of those cells which is perhaps not important um okay but let's do we can do exactly the same thing look with this box can't we because again we know the sum uh of these digits it is 27 38 I believe uh it's just I'm just double checking that because of course if if you if you get the sum wrong here you could go down a lot of wrong paths in the puzzle so these add up to 38 but these add up to 45. so that and these are common to both both of those sums so this has obviously got to be very large compared to this it's got to be seven greater so there aren't there aren't actually many um many options then again are there so if this was one it could be actually let's give it a big one to celebrate it to one it's one fullness um this would be eleven 22 37 this would be eights yes so there is a relationship of seven between those which is what we were expecting so this Square here has to be one or two and this has to be eight or nine and unfortunately both of those seem to be possible and we don't well it looks like it's trying to develop a sort of one two eight nine quadruple in the top row which would require us to be able to get rid of seven from this cell although seven oh no that doesn't work does X7 was associated with one if I remember rightly so if that's seven that's one that's two and that's uh nine and that's all possible okay but I'm going to carry on doing this because it looks very much like navario has set all of these Corner boxes these Corner three by threes up in the same way so here we know that those cells sum up to let's use a different color again they sum up to 40. but we know these sum up to 45. let's remove the common digits from those thing so so this one's got to be greater than this one by five I think um and therefore this can't be six though so I think that's got to be seven eight or nine and this has got to be two three or four I want to say so let's double check our maths make sure it works if this is two this is 18 and uh 20. is 38 which means this would have to be a seven so they are five apart indeed so it's all it's all sensible but it's not not really resolving itself is it I can't see the relationship yet maybe this one will provide everything we need to know um and again we've got the same sort of thing going on let's make that red this time we've got 20 oh we've got 50 this time so this is going to be the other way around we've got 50 there and those only add up to um 45 so let's remove the common digits we know that this for this for that to be true this is going to have to be 5 greater than this one and again this one can't be a one so that's going to have to be a two oh and it cut ah okay that one can't be a four either so this is two or three and this is five greater seven or eight let's double check the math is working this is eight this is 22. uh that 22 plus 20 is 42 the Box adds to 45 so that would be a three so the eight and the three are paired off and that does make sense so we arrive at this little colorful Arrangement which actually probably we don't need the colors anymore it's a Pity to make the the puzzle chromatically boring but we're going to do it and we've got something going on there and haven't we so these are six apart so I want to say you know I want to say have we got the opportunity you know can we force the same digits in here or something that is the question that I'm asking myself unfortunately I don't know if I've got a good answer to this so if this is seven no I don't want to choose seven because that's going to put one here I want to put something that affects this if this is eight this is two aha right okay well that's not eight yes okay there's a simple the simple way of seeing this isn't is it is just to well it's not actually it's not simple to see this any other way but because these have a relationship of six between them and these have a relationship of five between them you can see that by making this eight this two that becomes three and that becomes eight again so there is a sort of cycle that you can appreciate which is rather cute but that means that's not eight and it means that's not two now the problem here is that now if I make this nine this will be three that will be two and that will be seven and that's that's fine okay so that's not actually going to butter our parsnips is it and what was the relationship here we had a seven relationship between those two digits didn't we and what was the relationship 5 is only five down there so that suggests that it says trying to work out what it might suggest um okay so if that's eight that's one now I don't want to do uh no it's a bit more it's a bit stickier actually in the bottom row I think thank you I think it's a bit stickier because I'm not sure how to or whether I can actually get rid of anything here I suppose I've got to get rid of something down here because I've got to force this digit so let me as I was trying up here but maybe I try down here to do it so if this is two and seven so let's try three and eight no that's just not going to cause a problem that makes this nine and this two four nine makes this eight and this one now there's nothing going on okay so that's a concern isn't it two now and in the bottom row I haven't quite I haven't got it going on either so what is going on ah oh wow wow okay I know what's going on bent triples are going on oh that's really that's really beautiful I love that that is very unusual right okay so bent triples what are bent triples well they have a technical term which is y-wing but I find that very uh unilluminating so the way I think about bent triples look at those digits and imagine those digits were all in the same row or column of a Sudoku or we'd instantly be able to say oh that's a one two three triple that's useful we could eliminate ones twos and threes from the rest of the column if these were in a column together but the when they're remote like this you can still do little tricks because this digit if this is a one that becomes a two and if it's a three which is the only other thing it could be that becomes a two and that means in this puzzle there is a two in one of those cells there could be a two in both of them but there must be a two and at least one of them and therefore that cell can't be a two anymore because it sees both of these so whichever one of these is two is going to knock two out of that one and two goes with seven so now I've got an eight nine pair foreign that is so beautiful right now I'm going to do it again with those because it's the same actually I've not used blue I'm gonna use purple because I want to um this is a bent triple as well on seven eight and nine so if that's seven that's eight if that's nine that's eight and that knocks eight out of this and makes that a nine which makes this an eight and now we can use the actual relationships between these digits we know that I can't remember what the one one up there was it was a seven relationship wasn't it so that must be a one which makes this a three these two were it must be taking the bigger digit they were six apart that makes this a two which means that's a seven and that's a nine so that's a four and all of a sudden out of absolutely nowhere we've got all of these top all of these digits sorted out uh well it's highly highly original as well so it's it's a lovely trick so what nevario's done is to basically I can sort of imagine how how he's created this he still ah why wings are interesting how do I set them up in a killer Sudoku and then he's had this beautiful idea of just using sticky out cages to force relationships between certain digits and then the geometry is sort of fallen out into into a lovely pattern oh I must have been so happy when he came up with this that is quality but having said its quality um I've got to figure out how to solve the puzzle now one second will I try and do that six is a bit restricted up here now because six go in the 11 cage um yes it's the short answer to that four can't repeat in the 20 cage down there so four lives in one of those cells where ah okay that that is useful because once there's four in the 14 cage the other two digits in the cage add up to ten and they can't be four or six because you'd repeat well they'd have two sixes and two fours in the box there can't be one nine and they can't be two eight because neither of these cells can be two eight and you can't make that a schroding a cell it can't be simultaneously two and eight so that's uh three four and seven which means these cells are now known one two five and eight which means that cell at the bottom is five or eight in fact I have got six digits in the bottom row three five and ah bobbins three five and eight to place no joy there I don't think um what do we do next maybe we say seven can't repeat in the thirty cage so that goes in the twelve cage along with two more digits that add up to twelve therefore which are not going to be five seven but could be four eight good day um maybe or three nine if it was three nine the three would go here does that break this that would have to be five eight it would do a lot of damage actually if this was three seven nine hmm I don't know I don't know if I can tell this is not four nine oh right okay so it's this nine I think it's probably oh this is good yes where does nine go in this box is the question I should have asked it doesn't go in there because it would repeat within its cage and it doesn't go in the 13 cage because it would need a four with it so it goes in the 15 cage in one of those two cells where it has to be accompanied by two digits to add to six that are not one and five so that's two four nine which means that we've got a two in one of those two cells by Sudoku and a four in one of those cells now does that can't remember what we were looking for in here surely I think that is useful isn't it because the 19 was looking we were looking for 12 more and we can't put 4 8 in there now yes and it come up at five seven so we know what this is this is three seven nine and the three goes here so three goes in seven and nine look up at the 13 cage which must be five eight now because it can't be six seven or four nine these digits are now known that's not nine I've Just Seen um these digits are wired that one's not one uh one six seven let's just double check the maths on this box yes that does add up to 23 so that's good if this is one six seven we can put six into here by Sudoku in box seven three comes out of here look this is four five and eight to make the box work and if this is four five and eight those cells are known to be two three and nine why have I pencil Mark threes into this I think I was intending to pencil Mark twos looking at the two I've got over there so that was a bit of a Ricket oh yeah I should have mentioned actually and I will mention it now because I've just remembered it um in yesterday's video right at the end I made a mistake I I said ah this cage needs to add up to 12 and it was a three Cell cage and then I highlighted two of the cells in the cage and made them add up to 12. neglecting the fact there was a one in the cage with it now unfortunately that because it was so late in the solve it didn't change any of the logic going forward but it did work in terms of the software so I didn't pick up that I made the error I did put because I noticed it while I was editing the video yesterday um I did put something in the video description to say oops there's a boo boo right at the end but many of you didn't read the video description so the comments yesterday were all about how I'd made a mistake at the end which I did make I'm really sorry um I didn't um I didn't think that the video shouldn't go out because there was an error in it because it was um it was so late on and it was clearly just a tiny arithmetic error and just switched a couple of digits in the final grid um so I'm sorry if that confused anyone and um yeah I did try and draw attention to it but failed to do it perhaps and I probably should have put a pinned comment but I I normally like to use the pinned comments in the videos for the constructors if they have any comments on the videos then if Jam did comment on the video yesterday um so I used it for that instead so anyway that's all a long-winded way of telling you the story of yesterday's puzzle while my brain was buying time to work out what I've got to do in this puzzle um now what's going on in this oh okay well there's got to be a nine in here now because two plus three is only five and that would require this to be a ten so that's not nine so we can say therefore that oh well this is lovely okay because this is not nine double three because that will repeat the three in the cage so it's two nine and four and that's become a three and there's a two in one of these cells now and then nine nine can't go in the eight cage uh three here is putting a three in my 14 cage by Sudoku which is placing my seven and my nine in box seven which is knocking four out of that cell seems to require it to go there this is so smooth Now isn't it I shouldn't have said that that was completely and utterly mad for me to say that that's a three in the bottom row because now when it all goes wrong I will feel like a prize Charlie now this eight cage is now not two six and it's not three five so it must be one seven it's a seven there so that's seven that's one that's one by Sudoku um what's the missing digit nine I've not put nine in row seven so that goes there this is two five or eight nine it goes here in the middle box by Sudoku outrageous navario making me do Sudoku in your Sudoku puzzle um and for our next trick we will argue about the nature of I don't know what to I don't know what we need to do here come on brain have an idea [Music] um no brain is being recalcitrant seven tea brain come on have a sensible thought look there's a seven up there I don't think I know in which position it lives so how do we do this then oh I see ah yeah I oh that's very pretty as well good grief right look at this box where does nine go in this box well it's obviously not in these cells because we have a nine here and it can't go in an 11 cage because it would have to be accompanied with double one which would break break the rules of sudoku for all sorts of reasons so it goes on the 15 cage but we can actually do better than that because look this is a 15 cage which is 249 so this can't be 249 or this digit would be broken so this must be one five nine which means that's not a one which means the one in box one goes here this is now an eight this is a five that's a five by Sudoku now can I do that I probably can that must be four seven I think it can't be two nine can't be three eight can't be five six so that is four seven which gives me a four seven pair in column eight that's now a six that's a seven that's a two this is a four that's a nine so those two digits are now known there are two three pair and the Seven gets placed and can I do the two and I can't do the two and the three um but I can do the four four and the eight go in this is no longer eight what about this column now I need to put eight in it and I need to put two in it ah well that's useful because I haven't put two in it yet I've suddenly realized so that's two that's eight that's not eight that's not seven that's possibly anything at all this two gives me a five here which means I've got a five here I've got a 2 8 pair here it's not resolved um these two squares ah I can put the eights in here that's got to be six so that's got to be eight that's got to be five and stuff stuff's getting done in the bottom of the grid but we have not Ah that's a nine because it can't be a one or a five and we now know the contents of this oh this is it this is two three six in the 11 cage and that can't be a two or a three so that's six that's six oh no there's a six in one of those can we put six in the 16 cage it would then need uh it would then need two more digits that added up which think it can do looks like it could be a seven here and a three I'm not sure whether it can be 2 8 I think the eight would have to go there if that case that would be no okay interesting it can't be two eight can it be four six well no it can't be four six because I'm already putting the six in it to make it to make me need ten so hang on if it is can it be one nine no that is interesting so if this is if this has got six in it it must go with three seven that would be seven that would be six that would be three that almost looks likely to me because that would resolve the three two two this would be a one hmm I don't know I can't disprove that um which makes me think it might be correct in fact look these are from one two and three and that's not three and that's not two so how do we how do we finish this off can I ouch maybe I can do it a different way can this be nine oh no it can't be nine because there's a nine in the column I forgot this sake Simon that's not actually going to resolve my 16 but it would have been a quicker way of getting another digit in the grid right this column needs one four five seven so this cell is a one or a five and if that's a one or a five that's a one five pair so this is a four or a seven which doesn't I think tell me about this digit might do if obviously if that's a seven it would but it doesn't have to be a seven okay so it is it's being a bit difficult now it's all going to be about this 16 cage and thinking about this 16 cage in the correct way which I'm failing to do there's no R there's no one in my 16 cage I've just noticed and there's no There's No 9 in it can have eight in it though still right maybe maybe the way to approach this is to look at this row where we need oh there's a three in it is there ah that I hadn't appreciated okay so there is a there is a if you look at this row we have to put three into the 16 cage so we know we need two more digits that add up to 13. now we can't put 9 in here at all so there's now now we actually know there is no 4 in there which removes 4 from this position which places 4 in this row I know it doesn't we have already got four in this row we don't we already knew that wasn't a four in this box so I was announcing things of total non-consequence okay so four is in one of these two cells I'm seeing that's really unhelpful okay so this is if this is eight five eight goes here the three goes here the five go that's that fixes it right so all so the way to do this with some sort of a plum which I failed to do utterly is to notice that three has to be in it then realize you've got to make 13 for the other digits then realize it doesn't have nine in it then consider whether eight goes in it if it does it goes there that forces this to be the three and forces this to be a five which it can't be so we've now learned the nature of this box it is three six and seven and look there's a lovely seven there which is going to help us so that becomes seven this becomes three and six we can do all sorts of seven inch in certain positions look um that gives me the four here long last this is three six so that's become a one that's become a six that's become a five that's become a five that's become a one has become an eight that's become a five that's because seven um have we got more that we can say about the world now probably let's look at this row where we need one three and six that cell is a three or a six apparently which is quite interesting because that gives me a three six pair and sorts all this out so that's one that's two that's three that's two that Square's got to be a five which at least is working this has got to be a one eight pair which is resolved that gets me the eight the two the two the three finally I get the six and the three sorted out that's probably been available in a different way for a while and that gives me a three as the final digit what a beautiful puzzle loved it the wings of Pentagon by navario I don't quite understand the title but what I can tell you is that that business with the um with this this this this this this this this this and this these cells here was just Sublime it is completely beautiful to build in bent triples to resolve this pattern um and after that it was still still a lovely puzzle but that that break-in is uh it is Sublime nevario loved it I hope you guys had a go hope you enjoyed it too let me know in the comments I do enjoy the comments especially when they're kind and we'll be back later with another Edition I'm cracking the cryptic [Music]

Channel: Cracking The Cryptic

Views: 38,789

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Id: oLaXCAeinzA

Length: 39min 37sec (2377 seconds)

Published: Mon Oct 10 2022