Groundhog Day: The Sudoku

[Music] [Applause] [Music] hello and welcome to tuesday's edition of cracking the cryptic and a brand new puzzle by the constructor shy today um for those of you unaware of um who shy is shy is a brilliant but terrifying setter to me at least because she seems to think in ways that cause my brain to have to bend into uncomfortable places um anyway this puzzle has four stars out of five for difficulty on logic masters germany and a whopping 97 approval rating so it ought to be brilliant um it's called the hive by the way i don't know why i hope it's not a blatant attempt to cite me out by reference to the current op nature of the zerg in starcraft 2. um i'm sure fellow terran players know what i'm talking about here if i just say the word lurkers um now i trust you all woke up this morning to your radios blaring i got got you babe um because today is of course groundhog day now bad news is that punxsutawney phil apparently emerged from his hole or his hibernation uh spotted his shadow and that means that there are six more weeks of winter in store for us all um although i am grateful to uh peter graham um for the following knowledge bomb which is that an albino groundhog day in wyatton ontario did not see his shadow and therefore the canadians are due for an early spring i have no idea how this relates to climate change but it seems pretty profound to me um well one thing one thing anyway whether we've got spring on the way or not one thing that will make us all feel better is groundhog day sudoku how do i know this well no fewer than 200 of you have successfully completed the puzzles we released yesterday groundhog day sudoku over on patreon as fabulous uh solving by all of you i don't know how we're going to announce it we might have to have some sort of star wars style scrolling of the names um but yeah it's brilliant and the feedback's been terrific that's warmed our hearts so big thanks for that and um if you are a patron of the channel go over to patreon and try the puzzles and we know you'll like them and a huge thank you to said hollasan for helping us to set them um still no use for from sting or selena gomez or steve martin i'm afraid on how mark did in his crossword off versus sting um we we well we live in hope we live in hope that there will be an official announcement soon um but we shall see anyway what are the rules of shai's puzzle very simple today we've got normal sudoku rules apply we have two mark diagonals you can see the diagonals marked in blue these need to contain the digits from one to nine once each so a sudoku x constraint and then we've got killer sudoku so basically 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 those three squares need to sum to 20. these three squares need to sum to 14 and if that square was a four you couldn't put another four there because although that seems to work sudoku wise the four repeats in a cage and that's not allowed um that's all there is do have a go yourselves the way to play is to click the link under the video now i get to play let's get cracking first thing i notice as i stare at this grid is that as usual it seems nowadays none of the cages have much of a restriction in them do they um yeah you know when i used to do killer sudoku there would always be a 2 cell 17 cage or a 2 cell 3 cage and you could feel good about yourself by pencil marking things in no longer i mean the thing that strikes me when i look at this grid is this strange pattern down there down the diagonals here with these cages maybe this is why it's called the hive is this meant to be a honeycomb pattern maybe i mean we can do a little bit of math so i've mentioned this on the channel once or twice before but let's look at this box um these yellow squares we know what they add up to because a complete box of the sudoku will contain all of the digits from one to nine and if we add up those digits we get the number 45. so if the yellow digits sum to 45 but those squares sum up to 31 those squares add up to 14 to get us to the 45 total now 14 is absolutely useless because it's almost well it's almost averaging five and five is of course the average digit between one and nine so we know very little you know if these had summed to 24 or to six or something like that would have been happy days but as it is it's not um down here oh down here we've got exactly the same we've got two 15 cages which means these three squares do have an average of exactly five because they must add to 15 as well so 15 here 14 here means these three squares add up to 16 bobbins um [Music] bobbins bobbins bobbins do we have to so how do we do this puzzle do we have one thing i don't think i'll just mention it in case any of you are thinking about it it might well if this is relevant we shall yeah this will be a very long video but there is a variant of fistomaphel that uses these 16 cells so it's possible to show that these 16 cells here are the same as i think it's these cells in any sudoku so this the 16 digits that you find in the purple squares are the exact same digits set of digits you'll find in the green squares i think there are 16 greens there are so you know that's just that is a little bit interesting with these overlapping cages in the perimeter as well is it worth checking this the reason i'm hesitant is that you know there's there's such lack of clarity over these the sum of those cells to some of those cells and indeed all four corner squares that it's like we're going to end up with a simultaneous equation with about 18 unknowns and two equations and that's going to be very hard for me to solve and probably embarrassing for me to try to solve i think i'll come back to this if i think this is if i can't find anything else i will come back to this i'm not convinced that is the way in um [Music] although now it's niggling at me i've deleted it as it seems like i've done even less now [Music] i suppose the other thing that's actually just well it occurs to me thinking about these cells in the perimeter we do actually you can always approximate the value of the perimeter of a sudoku so we know that these yellow squares will equal 180 minus the four corner squares and that's just uh that's just an extension of the arithmetic we did on box one we know those squares will add up to 45 those will add up to 45 that's 90. add on those squares that's another 45 but obviously i'm double counting those corners and on these that's another 45 double counting these corners so the perimeter of any sudoku is equal to 120 180 i should say four lots of 45 minus the four corner cells now here the interesting thing is that we can actually work out the value of those perimeter cells there because because of the 20 cage and the 12 cage so we've got 25 there and 33 there is that going to be worth looking at it might actually i'm not sure let's well let's at least do the maths and then we can then we can convince ourselves it's not important so we've got 40 there 60 72 uh what was that 25 there 97 33 130. i've got 130 in those yellow squares and i know that once i add these squares into that i'll have a hundred eighty my ah no this is no good i just don't know enough sorry i just don't know enough about the corner squares i think if i knew what the four corner squares were either fisted fell or that perimeter thing might be worth thinking about so i've waited the first 10 minutes of the video getting absolutely nothing um okay what do what do we do to crack this puzzle we can we can a 12 k just got to have a one and a two in it at least i've got i've got pencil marks there we go that's a breakthrough um can i do anything with the one and the two here you can't put a one or a two in a 21 cage actually so maybe that's what i meant to think about oh yeah okay well i still i'm still nowhere near a digit don't worry about that but that square i can actually pencil mark with a middle pencil mark that can only be a one or a two and that's it's quite a beautiful idea actually look these squares can't be one and two because we know the one and the two in box seven are in these four squares you can't ever put a 1 or a 2 in a 21 cage because the other two cells will have to add up to too many so there's no one and two in these squares which means that the one and the two definitely are in two of these three squares in box nine but if i put them both here this square would have to be a 12 which it can't be there's a knowledge bomb for you so this square is a one or a two and that feel that feels like amazing progress after what's gone before it so 12 can be one two four five or one two three six five one two ah three you wouldn't ah got it got it i've got it look this can't be one two three six because if it's one two three six we run into an even bigger problem in row nine where do we put the three now you can't put it there you can't put a three in a twenty one cage either so the three would have to join its friends the one and the two down here in a one two three triple but now i can't make this domino high enough even if i make that two and three this would still have to be ten that doesn't work so still no digits no but at least now i now know exactly what this is this is one two four five and you can't put more than one of those digits in the 21 cage because if you put four and five in the other square would have to equal 12. so this either has four or five in it these two squares are one two four and five so there's exactly one a four or five in here and exactly one of four or five in here so there's all uh okay so there's always a 9 in the 21 cage because whether it's got a 4 in it and it's 4 8 9 or a 5 and it's 5 7 9 there's a 9 in it which means there's a 9 which means there's no well let's do this slowly look there's a 9 now in box 7 in this domino um which means there's no 9 in the 19 cage which means there isn't 8 in the 19 cage because i know that 5 6 and 7 add to 18 and that is not the same as 19 it's too few so there is an eight in there that bounces back down here again so now oh and that fixes oh this is beautiful this is such a clever idea honestly it really is so shai has done let's just think about the process of setting this puzzle assuming that i'm thinking about it in the way intended is to use the fact that this needs to have a one and a two in it to force one of those well to firstly do some stuff over here then you can narrow this down to exactly one two four five then you can prove there's a nine in here then this beautifully works around the corner here forces eight in here bounces back down here with the eight now there can't be an eight in the 21 cage so the only way of getting to the total is with five seven and nine which means this cage doesn't have a 5 in it which means it must be 2 4 because if it's 4 1 you'd have to put 10 here and now i have a digit um in fact i have two digits that must be nine now what does that mean that means i get three digits that's a nine as well four digits there's a seven in there that's a seven these squares here are three six and eight that's not eight because of the eight up here oh the 19 cages now yeah yeah look the 19 cage has an eight in it and it needs 11 more well it can't use two nine it can't repeat the eight so that domino that adds to 11 is not three eight it can't have four seven in there so it's five six eight and that's three in the corner that's three in the corner that's three in the spotlight losing its religion there um there's a three sorry there's a six eight pair now one two four pair up here that's probably going to matter for this is it i can't put one and two in a 14 cage because that would have to be too many so there must be a four in it so there's no four here and there's a one yeah look there's no f there's there's no four in this square because i need the 4 and the 14 cage whoops pressing the wrong buttons and there's no 1 on the diagonal so this must be 2 which makes this a 1 4 pair and fixes that this is a 9. good lord um it's absolutely brilliant isn't it it really is now what did those have to add up to 14 didn't they oh okay so these were 14. now there's a two in them these have to add up to twelve can't be four eight or three nine these are five seven now five seven get pushed yeah okay now five seven get pushed into the 15 cage so that must be three five seven here these squares have got to be six and eight yeah and that does work because those three squares had to add up to fifteen so suggests we haven't made a mistake yet um okay so those squares those squares are also three six and eight i feel like i've just said that three six and eight so now there's a three six eight triple in column three that can't be a three therefore because the three in this three six eight triple is definitely in this domino so that gives us a six eight pair in column two uh these three squares we know them they are three four and nine three doesn't go in the middle because of the three in the corner um [Music] oh this okay we can do something with the 12 cage now can the 12 cage has not got a 1 in it so is it possible it doesn't have a 2 well if it doesn't have a 2 it would have to be 3 4 5 and that gives well it makes this a schrodinger cell it would have to have two personalities at the same time it'd have to be three and five well it can't be both of those at the same time so this does have a two in it two that locks two in the 20 cage in box uh three here by sudoku of all things two and you ah okay now look you can't put nine in fact you can't put nine or eight in the twelve cage now if you put nine in the twelve cage along with the two you need a one in there and you can't have it if you put eight in there with a two you've got to have another two also impossible so these are eight and nine in two of these three squares nine can't be in that one look eight to nine are now not in the 20 cage which means the three cells that are not two needs to add up to 18 without using eight and nine that's only one way to do that this has got to be um five six seven along with the two which uh which might be good um what does that mean it means that one has to go in those cells by sudoku no one in the 20 cage now there never was a one in the 20 cage there never was a 2 in the 20 cage there could could there be a 3 in it it would have to be three eight nine that would be nine that would be eight not sure maybe it could be three eight nine um [Music] the 12 cage now oh sorry look the 12 cage we know what it is because we know it's got a two in it and it its other two cells must add up to ten well they can't be one nine or two eight so they're either three seven or four six well if they're three and seven that square has to be both of those at the same time again so this square is being asked to do too much work in this puzzle so so this square this has got to be four six and two which surprisingly doesn't seem to do much oh it locks a four into the same cells as one in box three so this is a 1 4 pair now so the 20 cage now doesn't have one two or four in it and these three squares we now know the value of these are these are three oh oh that's good yeah that's good hang on these have to be let's go to central pencil marks these have to be 389 which very nicely rules that out as a possibility here so this 20 cage now cannot contain one two three or four so it's got to have a five in it because if it doesn't have a five either six seven and eight add to twenty one so there's definitely a five in here there's no three on the diagonal look let's not lose sight of that in fact look three eight nine is seeing these squares let's there's a bit of tidying up i've got to do here three is in that square uh there you go i've done the tidying up already that didn't take long um [Music] is that all i get for this 389 okay let's come back over here so this is either oh there's got to be a 7 in here there's no i haven't got a 7 in the row yet so there's a so this must be five seven eight that's a simple way of doing it there you go five seven eight that's really nice that gets me an eight here a six here three here this square is now a nine look this square is now a three that's an eight there's got to be a three in one of these cells this eight sees the eight and the six at the bottom of the column well scanned simon um and oh self praise is no praise oh dear let's hmm okay so we've got a few digits there and those digits were handy but they do seem to have we seem to have dried up a bit don't we not uh nine though yeah okay nine in the middle we get the four in the center of the grid is that helpful i've not put eight on this diagonal yet so it's got to go in one of those squares we can okay i don't know what we can do we can we know there's a three in one of these three squares threes threes are sort of pencil marked into these triples all around the central box there two five i don't know it feels like we might have to start thinking about some of these cages maybe 18 cage there so we've got yeah okay hang on this 18 cage hasn't not got a 9 in it because we've got nines in those positions in the central box and the nine here oh i was about to say so eight if it's got an eight in it would have to be down there because it can't be in the top square if it hasn't got an eight in it has to be five six seven which it can't be there's a five seven nine triple in box eight so if you try and put five six seven in here that square has to be both five and seven another schrodinger cell which is impossible so this does have eight in it which means that eight is definitely here in one of those two squares which fixes that square blocks a six into one of those cells eights in one of these squares six is not in those cells look and this needs another ten to go with its eight um what is possible 1 9 is not possible 2 8 is not possible so we're looking at 3 7 3 7 doesn't work again we get schrodinger cell problems 3 can't go in there 7 can't go in there so this would have to be three and seven at the same time it can't do that in fact it can't even be three anyway you can't put three in the 18k that's a simpler way of looking at it so this has to be four six eight i think and if that's true there's a four here so this is four this is eight this is six that's not six therefore four is not ah hang on four in the 12 cage is now known it can't be in any of those three because of the diagonal um still don't quite know where eight goes i don't think in the middle box four must be in one of those two positions oh goodness i've missed this look seven can be there and five that's not five therefore doesn't seem to have done anything this square's got to be one two or five can't be five this is one or two ah bobbins um now what do we do we can six no six here no six here 3 9 17 here 17 in three cells now what kind what can and can't go in the 17 hasn't got an 8 in it look so if it ah so it must have a 9 in it because if it doesn't have a 9 in it it has to be 5 6 7 which is impossible because that adds up to 18. so there is a 9 in here which must be in this domino so it needs it needs another eight right and again schrodinger's cell time we can rule out three five as the option because look three can't go in those squares and five can't go in those squares so if this knee did three five as well as the nine this square would have to be three and five which it can't be in fact you can see it can't have a three in it at all so it's not three five it's not two six you can't put a six in it at all so this is one seven nine that's not nine this square is now interesting because this square sees the entirety of the 179 triple um through the medium of like what's in its box and what's in its row and it can't be 5 6 8 either so this square what can this be it can be two three and that is it this is a two or a three ah that must i've got a bad feeling that something's looking at this um [Music] i can't see it okay so this square is very restricted but i'm not sure i'm not sure how let's let's keep going around this circle so we've done this one we've done we've looked at this one let's look at this one this is a 14 that can't contain a nine or an eight i don't think yeah no it hasn't got nine or eight in it so it's got to have seven or six or both i suppose so if it's got seven in it where does the 7 go it doesn't go in the top so 7 would go here and then these would have to add up to 7. is that if these are adding up to seven they're not two five if they're one six this would have to be six this would have to be one if they're three four this would have to be four this would have to be three we're running into a few options here i think if there's no seven in it there needs to be a six because five four and three only add up to 12 so the six would have to go here these two would have to add up to um these two would have to add up to eight without repeating the six without using the seven because we've already looked at the option which involves the seven so this would have to be three five which means that would be three this would be five bobbins that seems to work as well doesn't it um oh diagonal sudoku don't forget diagonal sudoku there's sixes off the diagonal here where does six go on this diagonal it can only go there does that oh that might affect this no it doesn't oh no it doesn't two five seven triple but it doesn't resolve this domino the two in this triple is in this domino so this square can't be a 2. so maybe it's the 13 cage that's going to resolve this for us so the 13 cage can it have a 9 no can it have an eight yes i think it can um if it's got eight in it the eight would have to be here oh and you can't put 4 in it so if there's an 8 in the 13 cage it has to be 2 3 and 8 which would make this a 3 8 pair and this a 2 that would fix that one so 2 3 8 looks interesting if it's not got an eight in it what's the option then it would have to have it can't have a six in it actually and three four five is not enough so if there's no eight in it it has to have a seven in it so if it's got a seven in it we can [Music] it can't have a four in it go this is really complicated so i think if it's got a seven in it it has to be one five seven is there a problem with that one five seven in here let's just have a look at that sorry let me just put it in and see if i can see a problem um [Music] this square is therefore restricted by in exactly the same way that one was because this sees the whole of the one five seven triple so this square couldn't be one in fact this square could be very few things what could this square be it could it can't be one two three four five six seven eight it'd have to be nine oh and it can't no it can't be nine ah look this is this doesn't work if this is nine which it will be forced to be if this was thirteen you get this those four squares would have to be the digits one five and seven and you can't make four digits from three different numbers so this doesn't work so this is 823 which means this is a 3 8 pair which means this is a 2 which means this is a 3 which means this is a 3 i think that's an 8 this is a 6 by sudoku 2 4 here this is a 5 by sudoku that's an eight this is a six uh three here sees the three nine on the diagonal eight in the middle box now can't go there anymore so it has to go here get rid of the 3 8 pencil mark there and it must be about to crack isn't it we've got one seven and nine into this square i don't think i can resolve that we've got i don't believe it this central box needs one five and seven into this square oh come on this diagonal must do i don't know if it does one five seven the one look has this can't be one so the one is in one of those two squares which does actually fix the two here that might you'd be useful yes that is useful this 2 forces this to be a 2. that makes this a not the 2 5 pair a 1 5 pair 2 on the diagonal sees that cell so this square's a 2 the 2 ah that gives me the two and the four well scanned at the bottom again simon that gives me a one here one disappears from this cell um okay good has this cracked the puzzle it might have done um [Music] i'm sure it has somehow i just have to spot how that can't be 8r we've got a 5 7 pair at the top that square becomes an 8. gosh that's that squares and i've got a five seven pair in column six now as well so this column i've not placed one three and ah i've not placed one three and six in the column that's square c's three and six this has got to be a one one and four go in this is not four which means this is four if i trust my pencil marks that's great is it because that ha these have to sum up to ten now so the only way they work is with three seven that's a one now this is a five the five on the diagonal is important it gives me all sorts of treasures seven and five go in there look seven and five going at the top of the grid this square by sudoku's got to be a six that means that square's a six this square's a three this should be a one now hopefully if we scan down this column that's a five this is that means that's a seven that's a nine we need a two in one of those and a nine in the other we need a nine here that's going to be seven that's a nine and i think we might be about to crack the puzzle and what a puzzle it is uh seven and five here over here i need a one and a four there we go that's what i would submit and it's correct brilliant brilliant shy again so elegant the star is just to die for and the um yeah and actually it was very tricky i might have been might well have been many better ways of resolving what i had to do around the central box with these cages so let me know in the comments if you found a better way i do read all the comments and enjoy them especially if they're nice thanks for watching and we'll pack later with another edition of cracking the cryptic

Channel: Cracking The Cryptic

Views: 41,516

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Id: a81c9BD5D9o

Length: 37min 33sec (2253 seconds)

Published: Tue Feb 02 2021