A Sudoku That Teaches You A Discovery

[Music] hello and welcome to thursday's edition of cracking the cryptic on an absolutely beautiful spring day here in the uk i have my window open today so sorry there might be a little bit of bird noise coming in from outside and maybe maverick noise as well if he decides to buzz past my window but i hope you'll forgive me it's too nice today to have the windows shut um now what have we got for you sudoku wise today we have a puzzle called downward spiral which has been recommended to us a few times actually and it's by the sudoku skunk works of course it is now the sudoku skunk works i'm informed is actually a collaboration it's a team of setters many of which you will have heard of so we've got virtual sotek exion risk rift clown um bremster and eclectic hussier so apparently that group of setters have got together and made this puzzle and i am noticing as i stare at it that there is a spiral thing going on in the grid look if i sort of go around like that you can see it sort of spirals out which is rather rather pretty um anyway this puzzle is meant to be approachable so if you watched yesterday's video you will have seen i had to do battle with an extraordinary extraordinary sudoku one of the best sudoku's we've ever featured on the channel it was by emery kalotta glue and it was called german whisper cages it took me 100 minutes to solve and i don't think that was too terrible it was magnificent start to finish but apparently i've been given something slightly easier today and for that thank you um now i don't have much news what i do need to do today though is to say thank you to some people because many of you will know this but we released a book this is it it's very beautiful we're very proud of it but we couldn't have done this without the help of some very special people and i said thank you to some of those people the other day and i want to say thank you to more of them today so thank you very much to st johnny von pauliemath one of the great apes thank you saint johnny to richard barley to emmanuelli juliana i think emmanuelli is a very good solver i think uh i've seen emmanuel emanuelli's name on lots of emails to do with very hard puzzles um to brian drumgool um and his partner teresa hart and his children caitlin daniel michael andrew and anna to ken uh der gernel i hope i'm getting your surname right ken um to jack of andre to benjamin wood to brian heteroth to alex mussino to albert stanfield from the pacific northwest no less and from dominic oh i need to say thank you to dominic kazuski as well now dominic asked me to read a message which i'm happy to do and the message is intriguing it is the following alice may your exams be easy and your furry friends boopable whatever that means the mind boggles anyway there you go so thanks very much to all of you seriously we are very grateful uh for your all your help in getting that book done um now i i could tell you about other things as well there's a whole load of stuff going on on patreon but i've mentioned it in recent days um and i'll mention it more in the coming days so why don't we kick straight off with downward spiral and our regional rules they are as follows normal sudoku rules apply digits on a purple line must be a set of consecutive and non-repeating digits in any order now all of the purple lines today are very similar they are four cells long and in an l shape uh so imagine we worked out that this cell was a one then we would know that this purple line must contain the digits one two three and four because the digits on it have to be consecutive now unlike thermometer clues which we sometimes have on the channel um the two three and four that we put on this line can be in any order so we could do that for example that would be completely legitimate way of filling the remband line just make sure you don't repeat digits and you make sure the digits are consecutive cells separated by a black dot contain digits with a one to two ratio so some people get confused about this by the way it's very simple don't worry about the whole ratio aspect of this just think about a domino like this one of the digits must be double the other one that is all that rule is saying so if this was a two that could be a one and then we'd have two being double one or it could be a four and four would be double two they would both be legitimate ways of filling in the black dot um cells separated by white dot must contain consecutive digits so if this was a three that could be a two or a four and not all possible dots are given so all that's there to do is to say imagine you found out that this was a four and this was a five you might worry that there was no white dot between these these this between these two cells it's absolutely fine there's no white dot all we're being told is positive information about these dominoes here and these black dominoes as well we can absolutely have consecutive digits elsewhere and ratios of one to two elsewhere we just know that these specific ones definitely have the relationships mentioned now there's one other point about this puzzle which i should tell you apparently there is a discovery that we are going to make when we solve this i have no clue what that means um whether we'll find a black hole in the middle of the spiral or something i do not know but find a discovery and you'll have understood what's going on let us let us do this together let us try and discover what's going on and um do have a go at the puzzle the way to place click the link under the video as usual but now i get to play let's get cracking and we shall start with it does look a bit phystomothelian doesn't it except this this spiral piece here is not quite in the right place um so i suppose there's nothing really we can say about a four cell rem ban let's just think about that for a moment so the way i conceptualize ren ban is i imagine a string of nine digits lined up in order so one two three four five six seven eight nine all in a line now if we're going to cut a sequence of four somewhere along the line you can see there's no need for there necessarily for example to be a five within that cut whereas if it was a five cell rent ban you would you always know a five cell rent i must have a five in it because however you cut the five digits from the numbers one to five you'll always find the five is in the sequence now a four cell rem band doesn't have that property so i think we know basically nothing about these four cell rem bands um so the the dots are gonna have to be massively powerful so i'm guessing we either start here or here now i am going to prefer to start here because i can see something parity related so let's what is the property of a four-cell remband line well it must have two odd digits and two even digits on it because if you take four consecutive digits from anywhere along the entire number sequence in the universe even if we start with four hundred 10 seventy two and we go ten thousand four hundred and seventy three etcetera you will find two of the digits are odd two of the digits are even and i know something about a white dot this is telling me that these two digits are consecutive so that contains an odd and uneven digit so this black dot contains an odd and an even digit and that means that it's not a 4 8 pair which was one of its options before we realized this so this has to have an odd digit on it so it's either one two or it's three six uh yeah here comes maverick right now and now if it's one two we would know there was a one on the ren ban so this would have to be a three four pair and if it's three six this would have to be four five so there's always a four on this red man that's quite cute um ah okay and this four in one of these two cells is looking at this black dot so now this black dot can't be two four and can't be four eight and that means that this black dot also has an odd number on it because all of the other options for black dottage have an odd number on them there's only four ways of filling a black dot in the sudoku one two two four four eight three six things like five ten however we much like them to might like them to exist don't yet we haven't evolved to that point in the world of sudoku so again if this is one two that's got to be three four again oh in fact look there's a white dot here so we can we can be much more specific about this remban if this is one two what it cannot be is one two in that order because then this will have to be a two as well and that won't work so if this is one two we need to have the one on top of the two and then the two can be next to a three and then the four will be the final digit on the ren ban but if this is three six this will have to be 4 5 so we've got to reinstate the 4 here and put 5 in both of those cells so again there's always got to be a 4 in this domino here because it's either part of a one two three four sequence or it's part of a four or five pair to make the three six that we've got in there which means that this black dot cannot have a four on it so this black dot also has an odd number on it again so this is either one two or three six right okay and i can tell you something about this that is not a three-sixth pair because if it was a three-sixth pair what digit are we going to put in this cell because if this is 3 6 this has to be a 2 which means this is a 1 2 3 sequence and the 3 will clash with the 3 6 we've got in there so this is in fact a 1 2 pair which means that's not a two ah it means that's not a two which means that's not a one this is a three six pair which means this is a four five pair which means this is a three six pair and it means three six so this is a four or five pair and we've actually made a bit of progress we've got a one two four five quadruple in row eight and is that telling me something mark mark would pencil mark this cell i refuse to do it that's five different options and that means this has got a lot that's got more than five options um so that's weird actually that's weird i don't think this is i'm probably about to say something very stupid but what i'm going to say is i don't think this has helped us at all i'm now wondering whether what i'm meant to do is to do the spiral in that way maybe i should have no i couldn't i couldn't have known anything about this to start with but all i'm seeing is that at least i know something about this rem ban now whereas i don't think i know anything about any other remban in the puzzle ah ah not only do i know that yeah this is really this is really cute this is really cute let's look at this ren ban because we know it can't have three or six in any of those cells so ask the question is it possible there is no three and no six on this rembat and the answer to that is surely no because again if we imagine our list of digits one to nine in order and we take out the three and we take out the six how could we possibly make a sequence of four digits anymore we couldn't there's only two digits below three there's only two digits between three and six and there's only three digits after six which is seven eight and nine and that's not four digits so so that's a three or a six and that's on a black dot that's really beautiful there must be a three or a six on this rem and i'm actually wondering if that's the point of this so that's a three six here now oh look this is this is it this is that we've this is the discovery this is the discovery this is this is beautiful there's a three six here which puts a three six at the end of this rem ban now there's a three six here so where are we putting the three or the six or the three and the six that we know must exist on this rem man well they can't go in those cells so that's got to be a three or a six ah and that's much more restricted than if we approached this from the other direction and looked at this digit and then sort of put in all the options for this one so now this oh yeah this can't be three that can't be three anymore because this would have to be two or four and it sees those digits and that's beautiful so that's six that's six that's three oh this is this is lovely this is lovely this can't be five because five's in the row this is seven but look i'm more excited about the fact that i've got three and six looking at this now so this is three or the three or six that must exist on this four cell rem ban has to go here oh yeah yeah yeah three six in the column so there's got to be a three six on this rem ban which now can't be there so it must be here which is on a black dot i would oh this is this has been put together with such panache frankly panache is what this is because now there's a 3-6 pair that's emerged in row four looking at this rem ban which must have a three or a six in it that gives me a three six on its tip which gives me a three six on the black dot so now this rem ban has actually got a bl it's it's got a three or a six on it so it could have another one but i don't think we can can we propagate this logic again i'm not sure my brain is not telling me how to do it but but anyway that was beautiful so the whole idea i think of this is to sort of work your way around the spiral noticing that you've got to keep putting three sixes in the sort of in the foothills of italy each time um now ah that's a five because it's got to be consecutive with six so that's five that's four uh now what do we do the answer is i don't know we could maybe we've got to look at this row we need three eight and nine oh yeah that's actually not a bad idea oh in fact look this is simpler listen we've got to put three in column eight that's got to be a three we need to do sudoku of course we do now there's a three and one of those dots in the middle box right i understand this puzzle is slowly clicking with me yeah this is right that you can't this black dot is not three six and the reason for that is rather beautiful if this is a three six pair this cell is broken because it sees those two cells and the thing about these two cells is they are on a rembat so one of the characteristics of these is that they are different numbers and if they're different numbers this is a 3 6 pair and both of them see the central cell of the grid ruling it out from being 3 and 6. that is very cute so the 3 must be here which means the white dot relationship means this is two or four now that's on a black dot which means this square all right what you can't do look is go 2 1 because that's going to give this no option so if this is 2 that has to be four and if this is four this could be two or it could be eight um so ah that's got to be a three or a six oh no i was hoping that was going to get rid of eight but it doesn't actually six eight there would be a seven in this domino okay so ah three here's resolved more sudoku that's a six that's a three oh well that gets rid of eight because yeah you can't put eight and three on a four cell rem ban so this is a two or a four there's a two four pair in column five so this is a one this is a two there's got to be a two up there you can't put two on a four on a rim band with a six can you six five four no you can only get down as low as three in fact look at that you can't put three on this rem ban here because of the three six pair in row three so the minimum this rem ban could be would be four five six seven so there must be a seven on this remember not sure if that's useful or not that square cannot be a three because if it was a three what would the nature of its red band be it would have to have a four on it it's a four cell rem ban so even if you minimize the digits on it they're one two three and four and you can't put four on that rem ban so that can't be it's simply impossible for it to be a three that's six that's three so that's three and that's six oh that's a weird deadly pattern that we've just unwound there's no three on this ren band so this red band needs a seven on it there's a seven here so that's got to be a seven in one of those two cells there's got to be a seven on this red band because again it can't have a three on it so the seven in in this rem band's got oh look no no better there's got to be a seven on this rem ban that's right isn't it four five six seven yes it has to have a seven on it so that's got to be the seven there so that's no longer a seven we've got a seven in one of those two cells so this is seven in one of these two cells now this ren ban must be interesting now because it can't have a four on it so it could have a five on it it's either five seven eight or it's seven six it's either five seven eight here or seven eight nine here so it's definitely got seven and eight into those three cells which means that square is not a 7 which means this square is a 7 which means this square is not a 7 which means 7 7 that square is a 7 by the power of sudoku not the power of grey skull we don't need that yet um seven is in one of those i think it could be on here if this is a six five has to be right uh that fixes this rem ban we've got fives going into into this domino oh with wow this is interesting yeah yeah yeah because that because there's a five here we now know this remband is five seven eight but look yeah we've got five seven in those squares by pencil marks so that's a five seven pair and this is an eight and now there's no eight on this rem band which fixes its nature because we know it's got a seven on it and if you can't have an eight on it it must be the consecutive digits from seven six five and four so these digits are seven five four and that one is not seven so these squares have got to be ones twos and nines and oh i see the same is true in this column i think one two and nine into the gaps i might be wrong about that but that feels like by sudoku that's what we're looking at which hmm i can get rid of one here if this remband has a one on it it's got to be one two three four and the two will have to be in one of those two cells which will clash so that can't be one if this is two three you'd have to put four five here which would have to be this way round four five four five four five you get loads of things going on i'm not sure that those things that would be going on are not possible things to go on so seven um what about ah this has got to be an even digit because it's next to an odd digit on a consecutive square so that's got to be four six or eight and that's very annoying um [Music] it can't be eight because there must be an eight in one of those two cells so that square is not eight so it's four or six which is probably important in some way i can't see um now where do we look next uh three one four oh dear i think i'm getting stuck here what do we know if anything about um it must be a must be one of these rem bands i think that we we can probably learn more about oh no hang on what about sudoku i've got an eight nine pair in [Music] row eight so these digits have got to be from one two four and five ah so we can get rid of what you can't put one or two on this on this remband so that's a four or a five which means it has it has got a digit lower than six on it so it never so this is not seven eight nine so it's either six four and then a five seven pair or it's six five and then that could be four seven or it could be seven eight it's still got options then this one two ah okay this one can't be three two anymore because if it's three two we can't put one in this domino so it would have to be a four or five pair and that would break that cell so this is not three two so this is six oh six and nine because it can't be six and two they're too far apart so this is six nine and that's seven eight oh which does nothing oh no it does it gets me an eight here by sudoku rid of a 9 in this square gets rid of a 9 in this square so this has got to be a 1 or a 2. ah ok there's a small point there isn't there in row seven where do the ones and twos go in row seven well they can't go here so they have to go in those two cells so that square's got to not be four or five which means that square has got to be four or five and oh um okay has that done enough damage to get us this oh this six is getting me some digits at the top of the grid by the power of sudoku that's a six and three go in which ah that gets me a three here by the power of spoken so i've done all the threes in the grid however and how am i doing with sixes the answer is i'm not doing badly but i'm not doing brilliantly either there's a six in one of those two cells oh i can get six in the middle box it's got to go there so that's six and there all the sixes done so threes and sixes are done i feel like that must be five four three two yeah so now there must be a two on this ren ban i think because it can't have a six on it so five four three two or one two three four are the sort of options so it's definitely a two in one of those cells now it's still not cracking is it still giving me a little bit of recalcitrance so how do we finish the puzzle what is it that we're meant to realize oh six is looking at that square so that's got to be four now ah which resolves the five and the seven and the four and the two in the middle oh that's better right right yeah i've just worked out there was a two on that remband it can't be there anymore so that's a two this has got to either be one or five depending on whether this is one two three three four or two three four five this two is seeing this digit so that's a one which means that's a two and that's a one and that's a two ah one nine pair here so this is a two these squares here are two i see there's sort of a two four five triple in the box that's still not resolved come on we must i think we're cl we're getting slowly closer aren't we we still haven't cracked the puzzle but we're not as far away as we were do we know do we know enough about this rembant ah yeah there's something interesting this can't be a four or five pair because that will break this digit so that means the best the lowest you you could put five here it but not four so five six seven eight there must be an eight in this domino which means there must be an eight in this domino and oh two i can unwind pencil marks so that's got to be a two how many twos have we got lots yeah yeah we can keep going with two so that's got to be a two and that means this has got to be a two so all the twos are now done i've got a four five pair here four or five pair there if i knew what this rem ban was it might tell me whether this was an eight or not we still don't seem to be quite finished that square's got to be a one or a nine just to complete column two these squares have got to be one eight or nine ah okay once we do something with one oh look yes we can where does one go in box three it can't go on that rem band so that's a one it can't go on this rem ban so that's the one yeah ones might be profitable here nine nine one that gets us down to a one eight pair here which might be yes where does one go in box two it's got to go there now that means the one is placed and this did become a one two three four rem ban so that's one and eight now all the ones in the grid are now done and we can celebrate that fact by getting rid of four there and we can where else should we look i'm trying to do this efficiently and failing miserably aren't i um hmm have i used all my dots have we have we fully exploited the dottage i think we probably have three four five seven nine into these squares let's actually just fill those in and see if we can can't put nine on this rem banks it needs to have a four or five on it so that's just five or seven so does there need to be yeah there's now got to be a five on this ren ban but that could still be the nine in the column there are two places for nine in column nine oh i've got a four five pair in column seven so that's got to be an eight or an r blimey that's surprising so i've got an eight nine pair in column seven but this cell is seeing an eight on that rem band so that's got to be nine that tells me that this rem band's got to have five and eight to finish it you can never reach four which means that's the four good grief so now i've got a five seven pair in this box this is very clever and now this has got to be a four eight pair and the 5 in this row has got to move over onto the left hand side so now that square has become a 9 out of nowhere and that 4 is resolving the 8 and the 4 and i think that's huge isn't it because that's getting a seven and eight into those squares a seven and a five into these squares this four is quite useful that's fixing the whole of box eight this square needs to be an eight by sudoku this is a five seven nine triple so that's five and this is a seven nine pair and ah come on give up now i think i think you're beaten i think you are um right yes okay that digit is now obviously a writing that's got to be a four how many fours have we got several not all of them until we put that one in okay so this needs to be a seven or an eight and it can't be eight because there's a four and a six on the ren man so that's got to be seven which means that's five that's five that's eight this is nine that's nine that's seven and the last digit in the puzzle should be an eight into that cell and that is a very pretty puzzle indeed a downward spiral i reckon that some of you will get that done really really fast because i have a feeling if you approach it the correct way the spiral probably just unwinds itself very naturally and i was having to jump about a bit on the ren bands but what i think i do appreciate about that is this beautiful point that we found very close to the start which is that apparently a four cell remban line must have a three and or a six on it and that allowed us to place loads and loads of little digits around the spiral and sort of got us started on the logic the other bit of this that i really thought was beautiful was was the trick here where we could rule a three six pair out of that black dot that was lovely as well that's a quality puzzle a great you know i love puzzles like that where you sense that the collaboration has made that puzzle into what it is it's just you know it says combined brain power that's just been exerted upon it to give us something really really gorgeous to get our teeth into hope you enjoyed it let me know in the comments i do enjoy reading them especially when they're kind and we'll be back later with another edition of cracking the cryptic [Music]

Channel: Cracking The Cryptic

Views: 50,204

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Id: xtP1vwEHWLQ

Length: 35min 18sec (2118 seconds)

Published: Thu Mar 24 2022