A Sudoku With Only 3 Given Digits?!

[Music] [Applause] [Music] hello and welcome to monday's edition of cracking the cryptic now ever since the dawn of codec has one of the very top tier constructors on the world sudoku scene we've been looking out for his puzzles and what we should have been doing i think is revisiting puzzles he'd already published at the time of his birth um and it seems that this puzzle here which appeared back in november 2020 on logic masters germany um has been attracting a lot of plaudits it's called embraced i think because these arrow clues seem to be sort of hugging each other and we've had two recent requests to have a look at this puzzle on grounds of difficulty so that's what i'm going to try and do today is to solve it for you um i think it's four stars out of five on logic masters germany so perhaps not as difficult as the star trek puzzle i did yesterday but no doubt tricky indeed um now codec um uh made this puzzle as a tribute to some of the world's great constructors as well this is a tribute to fistumafell glum hippo and reesa so goodness me um that is uh that's plaudits indeed and i'll read the rules in just a second um a couple of updates first obviously we've got the miracle sudoku app which we've just had a big update for 20 new puzzles so if you do own the app um definitely make sure it's up to date and you'll find all those puzzles there and it's the first of february today and that means it's groundhog day tomorrow but we've already released our groundhog day themed puzzles over on patreon so uh do get over there we've actually already had some correct solutions um to those puzzles um but they are proving very popular and we've we need to thank said hollasan um the brilliant constructor for the philip from the philippines for his help creating them um other than that oh we still not heard um from sting or selena gomez or um actually steve martin has aged rather badly in this photo but we haven't heard from steve martin or martin short either so we're still still trying to find out whether mark finished the cryptic crossword that sting is clutching in his arm here faster than sting did um so if anyone knows let us know we're still waiting now what are the rules for codex puzzle we have got normal sudoku rules apply we have got digits along an arrow must sum to the digit in its circle and digits may repeat along an arrow so let's look at an arrow that means those three squares whatever's in these three squares you add them up and that's what has to appear in this square but you can repeat a digit obviously you can't repeat those digits that's not gonna that's going to break the rules of sudoku but you could repeat those digits for example um and then we've got a nice move restriction so cells separated by a knight's move in chest cannot contain the same digit we've seen this a little bit recently so let's look at this square let's imagine that cell is a one now if this was a chess knight it could jump to a variety of different cells all of these cells in fact and in this puzzle none of these cells could be a one because that would if you did put a one there there'd be a chest knights move apart and that is not allowed so a little extra rule do have a go at the puzzle first the way to play is to click the link under the video now i get to play let's get cracking and as so often we have we're faced with just nonsense aren't we three given digits none of them the same so we can't use those even with the knights move constraint they are not going to help us so i i think we have to get straight into the arrows um right so actually as i was doing the example just now i was thinking um i was thinking i can't even write six seven eight and nine into this normally with a three cell arrow it's often the case that you can therefore conclude that this circle has to be at least equal to six because you could you have to put at least one two and three on the arrow but here because this arrow here pokes out of the box these two cells can be the same they can be tiny and that's a two that could be a four which is really rather upsetting um now i'm just wondering if this arrangement breaks this arrow instead oh god i think it does but it breaks it via you know it's horribly complicated to see why because if you put one here and here you now can't put one anywhere on this arrow so could you do two three and four is the question you can't do two three and four because a two there actually sees this square by knight's move so the best you're going to do here is put threes and fours on the arrow and that will most certainly make that too large so yeah all of this is just nonsense this is nonsense this is not helping us i'm afraid i don't think this is the way we have to think about the puzzle let's get rid of those um oh well one one sort of slightly fatuous observation is that these digits have to be different because there are nights move apart the same is true there um yeah actually so maybe that's what we have to do is rather than focusing on a single arrow maybe if i have to think of the symbols you know think of these two in a connected way because those cells are all they're all in the same row so they all have to be different so if we make those their minimum value they'll be one two three and four that's ten uh yeah okay that's a little bit more interesting because i can't make these two squares the same digit because if i do there are knights move apart so 13 is the minimum i can make these two cells add up to just sort of using the sudoku and the arrow rules sorry the sudoku and the knights move rules uh one two three four five six yeah okay no and the other interesting thing at least i find it interesting is that um so many conversations in my life where i've started like that oh the other interesting thing is and people just like basically go to sleep um but the other interesting thing to me is that these digits can't all be different can they because if they're all different this they would have to sum to a triangular number they'd have to sum to 21 1 plus 2 plus 3 plus 4 plus 5 plus 6 is the minimum we could make them and that adds to 21 and there is simply no way to keep both of these cells down to a single digit total if we're trying to make them add up to 21. so there has to be at least one repeated digit in these yellow cells and well it can't be yeah it can't be that one so this digit so whatever's in this i'm just going to get rid of the um sort of tentative digits there this cell can't repeat within the structure of the arrows because whatever goes in there let's color it in it couldn't be in those squares by sudoku this square is in its box so that's not possible and this square is a nice move away so this one doesn't repeat this one ah that's annoying this one this one could repeat here i think maybe by symmetry can we rule out this one because it's sort of the equivalent oh no bobbins that doesn't work i was thinking this one would work a bit like this one but it doesn't because the silly arrow dips down into box five ah so whatever goes in that cell can't go in those three or this one by night's move but this that could repeat oh no okay so all right that's that's not helpful so this one can repeat this one can repeat that one oh that one can repeat there oh lord okay so they can there can be many repeats i think that's what we can conclude i don't actually think therefore beyond oh so do i have to actually let me just think about that maybe i maybe i've been thinking too sort of micro and i need to think more macro maybe i have to rather than just focusing on this sort of symbol maybe i have to use both symbols together actually that notice that's not such a stupid thought because one two three four five these cells are all on arrows and the same must be true presumably in row four two three four five all right yeah let's look at this so those squares what's the minimum i could make those five squares that up to was 15. if i make those one two three four and five i get to 15. now this little five here means i can't make those five squares add up to 15. the best i'll do is 16. now that's already 31 and that is getting close to the maximum especially as i haven't used those two cells yet because what's that yeah this is good okay so what's the absolute maximum i can make those four cells add up to well because these see each other via a knights move they can't be the same so the maximum i can make this these two add up to is eight and nine and similarly here eight and nine again so eight nine plus eight nine is thirty four but i've already got 31 here so these cannot be large these have to be tiny 31. so if if these can't be a repeated digit if these can't be double one these have to be a one-two pair actually so let's look at that is it possible to put one in both of these squares the answer to that is maybe i don't quite know um yeah okay well if you do well one thing we can say for cersei actually let's just complete the logic is that is it possible for either of these strings not to have one in them well clearly not because if we try and make this two plus three plus four plus five plus six that will that will add up to twenty we know the minimum for the other one is at least 15 so that's already 35 before you even get to you get to these extreme extremities and we've got to keep it to 34. so there does have to be a one in this string there does have to be a one in this string so where does the one go if we try and put double one in the in the perimeters here or in the sort of at the top and bottom of the the arrow patterns one can't go there it can't go here by night's move so one would have to be in one of those oh no no one can't go there by knights move one has to go here so if these are both one you have to put one here and presumably that works by symmetry the other way around one can't go there or there from this one this one sees that one this doesn't work this doesn't work so if you try and put two ones in these two cells you end up with ones in those two cells which are knights move apart so that does not this is very good i'm very pleased this doesn't work why am i pleased this doesn't work well because if i can't put if i can't make both of those squares one i have to make them one and two and now this it's simply not possible there are no degrees of freedom left this is the only arrangement that will work for these cells because i can't make these bigger than 34 i've got 16 here which is a minimum i've got 15 here which is a minimum we can't put double one in there so we put one and two in and we get to 34. so this is it we've got eights and nines in the circles and that was quite complicated but we haven't we have at least deduced something we haven't got a digit we don't don't think we're a luxuriating in a digit yet but we have got pencil marks so what do the pencil marks mean they mean that there is no six here and there's no 5 here no no they don't well they do mean that but they also mean where do you put a 6 in row 3 of the grid it's not in those squares and it's definitely not in this domino so it goes there and i do have a digit um [Music] the five doesn't work the same way the three rules three out of those two squares so now these two have got to be seven eight or nine there's definitely got to be a seven in the domino definitely worth keeping track of dominoes that can only take one digit in the knights move puzzle because you can straight away rule seven out of these two cells if you try and put seven in that cell it rules a seven out of both of those um now those squares are seven eight and nine as oopsy i don't want to do it like that i want to do it like this um right so what do we do now um i've got this six there's a six up here it still doesn't feel like it's the time to do sudoku does it four given digits now um [Music] sorry about this let me think for a moment or two hopefully only a moment or two what's this six doing i mean does if you're going to put these givens in they must do something that's quite profound mustn't they not seeing what that is unfortunately is there a way of telling which way round the one and the two go if that's a one let's look at that if this is one we can't put one here or here so one goes into one of those two squares ah that's that's interesting you can't put one there ah ha ha look if this is a one now i can't make eight or nine work on the arrow because this square can't be large enough that's this is what this six is doing the if this had been able to be six you could have put one here but because you can't this doesn't work so the only place you can put the one if this is one you have to put the one there which means and i suppose we have to have a one in this string because we know this is one two three four four and one two three four and six there's no one here there's no one here there's no one here because of the knights move so you have to put one i will see that that works right okay you have to put one if this is one you have to put one here you have to put one on the same arrow as this one so this arrow will have a one on it another one on it and therefore it needs a six to get to eight and it can have one and this would be a two because of the knight's move constraint so that's all a bit well it's interesting but disappointing isn't it because it works does it work the other way around if that's a one let me just look at that hang on if this is a one you've got to put a one in this string can't go there there sorry it can't go there or there because of the knights move and it oh and it can't go here because this one can't be a five or a six so if you try and put a one there you can't get anywhere near eight or nine here so you have to put one here and you need a one in this string so you've got no ones in those squares ah there you go this is why it breaks so if you try this the other way around trying to put a one in here is possible absolutely it's possible but it has to go on the same arrow as this one and look look at the options for what accompanies it it can be no bigger than a five because of the six here so you end going to end up with two ones and a maximum of a five which most certainly don't add up to eight so this is this is progress now we've got more digits you can't put one here that's got to be two that must be one therefore because we know these two have to add up to three we know this can't be a one because then this would have to be a six which it can't be so there's no ones in any of those squares this is a one we know there's a one in this string of five cells we've got i need a one in this string of cells now so it's not here by night smooth from this one it's not here by sudoku it's not here by nice move from this one [Music] is there some other way we can do this now okay no this is this is a nice move apart i've got this wrong hang on why is that knights move apart have i made a mistake oh no one can't go here or here or or here or here because this can't be a six ah no i think i just put the one in the wrong place if one is here i need a one in these one can't go here here or here so one is oh this yeah okay this works now this works because one has to be in one of those squares but we know that arrow adds up to at least eight so it has to have a six with it because this arrow is going to be double one and then another digit and the only digit that will work oops see sorry that's a one these two squares are a one six pair this is an eight it's the only thing it can be which means this is a nine by nights move and we i know we're definitely not cooking with gas but we are at least we've lit the fire um and what do we do now having lit the fire we have to make progress so two so this one adds up to oh i suppose yeah we can remove six from here can't we and here we go two three four triple but this has to add up to nine and there's only two on the arrows so far so this has to add up to seven so this must be a three four pair and we get an another we get another digit in the grid we get we know there must be a two in this string and the two can't go here or here oh right so that so this this arrow has a repeated two on it just as this arrow had a repeated one you have to repeat two on this arrow and that gets you to four so you need at least oh right i see this is very clever so one of these two squares is a two and then how are we going to get to eight or nine we're going to need a four or a five not a three so neither of those two squares can be a three you get a two four five triple and that square is a three and so this could still be either total and this could still be either total so now we i've got the problem with knight smooth puzzles as well is that it's so easy to miss something simple [Music] i'm sure that there is a way of disambiguating these and it's probably a night's move is seeing something sorry about this what can we do is it no we've done that one we've used that one we've got a two here six is up here sorry this is just awful oh one look can't go here so one must be up there three three is a bit interesting here because it's quite powerful from a night's move perspective look it sees those squares by sudoku and these two by nights move so three is locked into one of two places three down here yeah and then it's locked into two places in box five as well and two places in box six because this cell can't be a three now because if that was a three you'd see that square and that square because the knights move so three's got to be in one of these two cells threes ah haha yeah okay there's another trick we can do with threes you can't put three in either of those two cells in box seven because a three here for example this definitely sees both of those squares because of the knight's move constraint and that three is that's just symmetrical counterpart so you can't have threes in those cells so where does three go in box seven in one of two places so three is in one of these three cells and it's not that one because of these three here would see both of those because of the knight's move constraint so actually we've done remarkably well with threes although i will admit it hasn't actually got us any digits [Music] i mean it really hasn't okay so so what do we do now we've got threes two oh two look can't go there so two is locked into those two cells what have i not looked at is there some extra constraint that i'm meant to be seeing here i've got a horrible feeling it's almost like i've missed off a rule is there some area of the grid that is is there a cell that sees a load of other things by night's move like cells like this for example it's quite easy well at least for me to miss the fact that this can't be three or four because if it was a 3 or a 4 it would remove both those digits from these squares so this square this square can be it can be 1 i think it can't be 2 3 4 i know this got loads of options five six seven eight this is not where we need to look that square might be better we've got actually that square might be better because that's c seven and eight and three and four and one and two what can that be this square actually i'm just going to put in all the options if you don't mind uh it can be look i've gone to the tiny font if that's apparently what happens when you put in nine options for a cell right it can't be one it can't be two and the numbers grow as we get rid of them it can't be six or nine it can't be seven or eight yeah and it can't be three and four exactly the same way that can't be three and four this can't be three and four so that is five and that was not easy to see that's not 5 therefore this is not 5 which means this oh lovely look that means this is a 2 4 pair on the arrow it means this square is a 5 and that gives us that arrow as well of course so we get the nine and the eight into the grid we get five oh we get no we actually get five because of the given five it has to go there in box one five is in one of those cells in box seven we uh what else do we get do we get anything else can we resolve the two four pair we can well i can't i can't resolve it and then there's probably a way that one's not nine anymore look that one's not nine anymore this is now a seven eight pair so seven and eight can't go into this domino um eight here and here so eight can't go there because of the knights move it's got to be in the domino at the bottom check the eights in the domino positions you can't put eight into those squares but we don't know anything about eights you can't put eight into these squares oh that's evil that is pure evil a bit like sam kaplan lies the other day look this eight you can't put eight into this domino because it would rule an eight out of those squares so where do you put eight in column seven of the grid you can't go there there's already an eight in the box you can't go here it's a nice move away from an eight can't go there so it only goes here that is not pleasant that is difficult that's a seven that's a seven that's an eight that's an eight eight looks like it's oh it's not it's very restricted in box one but just two places um eight in box nine is two places it can't be here because of the knights move seven has got to be on the left hand side of box nine oh no it's quite interesting actually after this beautiful logic at the start with the symbols now we've basically pencil marked the symbols it's effectively become just a night's move puzzle and not not a very tractable one i do quite a lot of night smooth puzzles because of our chest sudoku app and you would think i would be better at them somebody even left a comment the other day to say that um they think that i i deliberately don't spot numbers just so that people will comment that is not true i promise you i have no wish to appear to look stupid in these videos um [Music] yeah like there's a trick you can do there these four squares have got to be one two three and four so this square all of a sudden it's very restricted it can't be one two three or four because if you try and put for example three in there you now can't put a three in box three at all so this square can't be one two three four or five it can be six it can be seven can't be eight it can't be oh can't be nine because of the knights move so that one is very restricted um that one cases two and four so if you try and make this square two or four it would see both of those squares so this one oh this one's interesting it can't be three i'm just sorry i've just noticed we've got three's pencil mark there so if you try and put three here it sees both of those squares so this one can't be one two three or four or five six i've got oh six is given so it's not six it's not eight it's not nine oh that one is a is a naked single it can only be a seven and that's going to give me that one ah this is lovely so this square is really strange but i think it can't be anything other than seven i'm just going to double check that one it definitely can't be two and four it can't be three it can't be because of the nonsense here five six eight nine that's correct so this is a seven this is a six a seven is lovely because this one can't be seven because of the knights move to this one so that becomes a seven in the corner that becomes an eight um that means there's an eight on the left hand side of box seven nine nine now where does nine go in box one it can't go there so it must go there this square must be a two or a four nine must be in one of these two squares so this box now needs two three four and nine that this one sees two and four oh it's and it's he's no comments about me not scanning to the bottom of the grid please i know it's because i'm quite close to the screen this is the only reason why and i don't have like enormous yoda eyes so i can't like just look downwards and and see everything um [Music] otherwise i'm sure it would be fine but look this square here is is a naked single it can't be 1 2 3 4 5 6 seven eight that's a nine these are two three and four two no uh i'm sure something is what is disambiguating this now the answer is i don't know 9 is a bit restricted um in box 5 by this 9 this 9 takes care of the central cell this 9 locks those squares out so there's a 9 in one of these two positions which means by said oh no it doesn't it means by sudoku 9 can only go here in box six can't go there because that because of that nine and this nine is in the pencil mark of a three so let's just make sure we don't go ahead of ourselves here nine can't go here by knight's move so nine is in two positions in box nine this square has to be a three now which fixes that this square is a four that's not four threes aren't here so three is definitely in one of these two cells so it's not here that gives us two four pair which means this one is three there's a one there as well so we've got a two four pair in row 2 a 2-4 pair in row 3 and gibberish in row 1. now can we keep this going yes i can 5 where does five go in box nine box five i should say it goes it can't go in those squares because of the knights move so it goes in the same positions as the nine which which gives us a five in box six which means there's a five down here in box nine this five bounces back again into uh box five by the knights move constraint this is nine this is five nine is now in one of those two positions in box eight and in these two positions in box eight for five three oh oh yeah hang on look at some stage i think we locked three into one of two places in this box and i think the four took one of those positions it does seem i've only got one left and this three let's just double check this threes yeah yeah three is just by sudoku locked into that square but this three is actually seeing that square by knights move which gives us a three here which gives us a two here that two is going to be oh it's all kicking off it's all kicking off now this three has to go here that's gonna i'm gonna come back to this it's gonna give me fives look in this box but let's just deal with the two here while we're here so two four two four two get rid of the twos from the top row this one sees that square and i don't know how to do that but anyway let's come back down here again now what did i want to look at i think it was fives because if you look at where i've got fives pencil marked in boxes seven and eight they're both in row seven and row nine so we can ask where five goes in row eight of the grid it's definitely not here it's definitely not here in this box it must be in this position so because it can't be here it would be a third five in those two rows five two one one must be in one of these two squares in box four so ah in fact this box so we've only got one six and seven to place in this box and that can't be one anymore seven is definitely in those two squares 7 isn't here 7r 7 isn't here because if there's a 7 here it rules 7 out of both of those cells 7 is not here either so 7 is in this domino which means seven is in this triple this box what do we need over here we need one four and six one four and six that's not six still haven't got this arrow sorted out that must be possible to resolve there's almost certainly a random one or six pointing at this stuff uh i don't know where it is one four six seven this square oh that's useless one four one four six seven along here four this square is interesting this square c6 by this square is fascinating let's look at this one four six seven this sees six by nights move so it's not six it sees four by sudoku it's not four if it's seven you can't put seven in that domino and you need to put one a seven in this domino so if this square is a one that's not one whoopsie i mean not one i've just done the wrong thing there i don't want one in that square this is a six seven pair so ah now that's how we resolve the one six is not by knight's moves but by sudoku moves so that's a six six is in one of those squares this is not six anymore so we've got a one four pair in this column and this triple here is a six eight nine triple so let's change the pencil marking that can't be eight by sudoku or well knight's move sudoku nine can't go here and very slowly we're whittling away at codex puzzle aren't we um [Music] okay what now what do i need in this box i need four six and seven oh there's a six seven already in column one that's a four this is a six seven pair deadly pattern alert but presumably a night's move will sort this out where is it where is the six or seven poking into this dunno oh look four four is pencil marked into the same position as five oh and this five sees that one so we we resolve this immediately this has got to be four this has got to be five that's got to be five four is given now by sudoku it's got to go here four is either that is in one of two positions in box nine these squares are six seven and nine in some order these squares are one two and eight in some order let's do some tidying up we can get rid of one there and two there we're heading towards a fully pencil marked grid aren't we one look by sudoku has got to go there these squares are six eight and nine it's the same as those there's two six eight nine triples at the bottom of um these columns now those squares have got to be two and seven what sees those anything uh no this column we've got one three four and seven ah that's quite interesting look there's a lot of stuff over there that can't be in these squares one three four and seven are the options this can't have one or four in it because of the one four this can't have three or four in it and this one can't have three in it and that means that one three four seven oh okay well one question we can ask is where does two go in row eight and i think the answer is there it doesn't seem to be possible to place it anywhere else it's definitely not there definitely not here yeah okay we've got rid of two here because of the knights move so there is only one position for two which gives us seven oh the seven is enormous look at this seven look at the damage it does to this this triple you can't now put seven here or here so you have to put seven here but not that also gives us the three that gives us the four at the top the one and the three the one and the four this square now must be a one by sudoku that's not the one over there the only place for one in box seven is now known this is a four again sudoku helping us out that square should be a two this two is lovely it's our friend it fixes this two eight pair this eight sees the six over here that's a nine therefore that's an eight six eight means this is nine which means this is seven this seven's this seven sorts out the six seven uh problem at the top look that's now six six seven seven in order to keep things a nice move away and we should be able to do this yeah the eight's gonna fix it all isn't it eight goes here six goes watch it eight goes here six goes here six goes here nine goes here we click check yes wow that is a very very clever puzzle just three given digits and some real thinking that i had to do i'm i mean there may be another way of thinking about that but the way i found was very very nice indeed that you know you have to think about both symbols together it's really clever i mean it's what we've come to expect from codec he is absolutely first class constructor and i really enjoyed that i hope you guys did too forgive me the slowness around the night's move parts um i just find them difficult to see consistently and we'll be back later with another edition of cracking the cryptic

Channel: Cracking The Cryptic

Views: 62,633

Rating: 4.9311457 out of 5

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Id: _ROvoT2eh0Y

Length: 45min 32sec (2732 seconds)

Published: Mon Feb 01 2021