The Empty Sudoku

[Music] [Applause] [Music] hello and welcome to thursday's edition of cracking the cryptic and this colorful new puzzle by quinn looks that we're going to take a look at today now quinn looks appeared on the channel a few times before always with absolutely brilliant sudokus and the testing reports tell us that this is another of those gems so this ought to be a real treat um although i am noticing as i stare at the grid that i've got no givens no numbers at all in any of these cages and no numbers at all in these little killer sudoku clues outside the grid so quinn looks has not been overly generous it seems to me although he has been uh extremely uh charitable with his uh use of colors and this is called build your own little killer sudoku so that's our task and we shall turn to that in a moment um first things first do have a look at what we've got going on over on patreon at the moment it is it's quite staggering we're closing in on 4 000 patrons so that's a lot of people who seem to enjoy the content that we're putting up over there the latest of which is this wonders of the world sudoku hunt that we released a couple of days ago it's getting great feedback an incredible number of correct solutions which is fantastic and if you've not tried it and think you know your christ the redeemer from your machu picchu or at least their sudoku equivalents then check it out you won't regret it um and then over there we've also got sort of on the more extreme side of things myself of fistimaphel's yin-yang philomenopuzzle which you can play at the link under this video and then you'll be able to empathize and or at least sympathize with me and the suffering i go through in trying to solve that beast so that's over there we've also got the solution to groundhog day which is uh february's reward um by said hollison that's definitely worth looking at as well um now let's get back to quinn looks what are the rules we have got normal sudoku rules applied today the contents of each colored cage in the grid are either a single digit or form a two-digit number read left to right or downwards these numbers act as the arrow clue of their color such that the digits on the indicated diagonal which can include repeats sum to that number okay ah right so that i think is saying that these are not normal killer sudoku cages these are right okay these cages are to be read as numbers that we then use for the killer sudoku clue so if this is a four or three i'm going to type in four you won't be surprised if this is a three and a four that's not we don't worry about the fact these add up to seven we have to read these as the number 34 left to right and then we go to the blue little killer clue and that's telling us this set of cells which can include repeats have to add up to 34. that is crazy well and that that is enough to solve the puzzle that seems incredibly unlikely to me um so the down i see so the down clues work the same way so if this was actually better make this a small number because the little killer clue is small let's make that 19. so if this is 19 well this is 1 and 9 that's how we would read it we would read it as 19. we would come to this clue and we would say the purple diagonal clue sums to 19. that's our task oh now mark has put in an another thing saying that there is a color blind version of this puzzle so we're going to put two links under this grid the first one will be to this one the sort of chromatic festival that we've got going on the second one i'm not sure what we'll do but we're going to somehow indicate um which little killer clues and which cages are connected in a way that doesn't use color so that if you if you do struggle with your colors and i i i actually struggle a bit with mine although you'll know that i do like colors as well um but if you do struggle with your colors there should be a version you can still play under the video so definitely have a go click on one of the links whichever one you like under the video to play the puzzle now i get to play it let's get cracking and see what we have to do here so so i think it feels to me we must focus on the short little killers so although that one is the shortest and that is not helpful because that seems to only have a one digit total yeah so this these two cells could add up to as little as three or as much as nine so this square can be three four five six seven eight or nine that's not a great restriction the yellow one though has a two digit total so there's no way those squares can add up to anything other than a teenage number or a twenty-something number so that square i think has to be a one or a two and the same is true presumably of purple here those three squares have to sum to a two-digit number that two-digit number will either be a teenage number or it'll be a um [Music] or it'll be a 20-something number so that square's a one or a two the next one looks like it's the red red is the next ah hang on red is the next shortest but there is also a very long red diagonal ah right this is where i should have started right let's look at the red what's going on in red because assuming i've understood the rules correctly we are now being told that this four cell diagonal sums to the same number as this nine cell diagonal there's no i don't think no there's no coincident digits so there's these don't overlap with each other but the maximum i could make oh actually i could make this quite large total because i could use three nines and an eight so this could be if we do something like that although that's my i know we can't put eight there can we so sorry what i'm trying to do is get a handle on what the maximum size of red is but it's not 35 because this would imply that 35 is equal to a number that begins with an eight and it doesn't yeah in fact this just doesn't work at all you can't actually you can't make a total of 30 on this diagonal well you can you can with a three here but that doesn't work for the sudoku reason that that would imply that digit has to be a zero because these three squares sum up to 30 and i can't put zero in a sudoku however much the software might like to accommodate it so yeah so this now adds up to 30. now in order for this to work i've got to increase this away from three zero so i'd have to increase one of these digits at least by one or more which digit is it that i can pick well the only one that has any flexibility is this one but as i increase this one by anything it changes the tens digit of the red clue and that won't work because increasing this total by one does not increase its total by 10. so yeah so this i think this is a long-winded way of saying that this cannot add up to 30 so this square is also a one or a two which presumably puts a lot more pressure on this diagonal because now that this diagonal cannot add up to more than 29 well actually there is a bit of freedom isn't there that's not as bad as i was thinking ah but ah okay but ask the question can it add up to a teenage number one plus two plus three is six another one plus two plus three is another six so that's twelve so we're at twelve before we get to those three squares well those three squares cannot be less than another 12 i can make those three four and five so these together have to be even if we take the absolute minimums in each position they have to add up to 20 something so this is a two this is a one this is a one and we are at least we have some digits um [Music] now what does that mean it means one is in one of those squares maybe we should do some sudoku when we're doing a sudoku puzzle you know i never like to but sometimes needs must um so this is adding up to 20 something that's at least 23 now as well so those are adding up to at least 21. these adding up to at least 23 therefore oh i see i see what's going on here quinn looks you are very very smart this is lovely this square is the one we need to focus on because this square doesn't matter for the purpose of this diagonal at all we can make this whatever we like it doesn't affect the total what do i mean by that what i mean by that let's imagine this was a 5. if this is 25 the 5 is contributing the unit's digit to this total so these eight squares here have to still add up to 20. let's make that an eight what do those eight squares now have to add up to it hasn't changed the 8 the 28 contributes the 8 itself so these squares that are not in this position the rest of this diagonal still has to add up to 20. now that is almost it's almost beautiful well no it is beautiful it is beautiful but it's almost it it almost sort of completely gets us into the puzzle but it doesn't quite does it because i now know that these eight cells have to add up to 20 but those have a minimum of six those have a minimum of six those have a minimum of seven because they cut they've got a one and two in the box so these can be three four and look that adds up to 19 which means there's one degree of freedom on the diagonal bobbins that is it was almost completely completely forced but it's not no it is it is because i can get it with the greens i know what i can do the greens these four squares have to add up to something do i know what it is i haven't got a scooby-doo but i can say with some certainty that the green does not add up to 40 anything because there are only four digits on the diagonal so this square has to be a one two or a three now if it's a one two or a three these squares cannot be one two and three but i can only increase these squares by exactly one because if i increase this total of six to eight the diagonal's broken because if this added up to eight eight plus six is fourteen plus seven is twenty one but i know the eight cells have to add up to twenty so this has to be one two and four and that means this has to be a three and that's going to mean that those have to be enormous but hang on let's just settle back on this diagonal because now we've actually we have learnt that this is definitely a one two three triple this is definitely a one two four triple this digit bizarrely enough i think it can just be anything it doesn't matter maybe it's going to be this diagonal that tells us what this digit is this is absolutely fascinating isn't it it really is it's so clever that you can build a puzzle out of colors like this and domino's numbers it is just so clever and it's actually extremely fun to solve which is you know it would i imagine it would be very relatively easy to to create a puzzle like this that was monstrously hard to solve but this is actually very cool you know what the green this green total can't even be 31 it's got to be 35 at least that's going to be it can't yeah okay this has to be a five because how on earth do i get those to add up even getting them to 35 is quite a challenge but they definitely can't add up to 36 because that would require four nines and you definitely can't do that so this is three nines and an eight which means those must be nines this must be an eight nine pair um not sure what else it means it might mean something this one is the oh gray is now forced because gracie's one two three on the diagonal so what's the minimum i could make those two squares it's four and five and i can't make them anything else because they have to sum to a single digit total so this nine actually comes back in here gives us nine and eight nine has to be in one of those three squares well i can say with some certainty it's not here because there cannot be a way of making cells on a diagonal of a sudoku add to 90 something i'm not even going to prove that because hopefully it's self-evidently obvious um [Music] now those two squares are six and seven to complete that box one can't be there by sudoku in fact maybe i should just take a step back and think about sudoku for a moment or two um [Music] which clues have i not used i've used green i've used red not used orange i've used oh yellow yellow might be good now look i've got 13 or 14 here and a 9 here so this these two squares have to either add up to four which will mean they have to be one and three or they add up to five oh bother that doesn't work so these have to be one two three or four that can't be two that can't be one but i don't think we actually know what the order is unfortunately orange let's come back to orange orange has got to be yeah this this digit is very restricted because the maximum i could make that diagonal would be nine eight seven nine eight seven so 48 so this square has to be a one two three or four and it can't be a one or a three so it's a two or a four it forms a pair with its friend there so these three squares to complete the row have to be six seven or eight that can't be eight six seven pair in column seven now it's definitely an eight in one of those two squares the purple diagonal so the minimum value of these two squares would be five and six so eleven plus three is fourteen so this has to that's not that great actually is it this just has to be a digit that's greater than four i will pencil mark it in a slightly uh good lift moment okay this is ground to a little bit of a halt this no this diagonal i don't think is where don't feel like that's restricted this one can't be restricted i suppose i can get the tens digit though roughly can't i so one two three four not even sure i can get that with much certainty so if that was eight nine that could be eight and nine as well i think nine here eight here so that's 34 35 39 48 so this has to be one two three or four yeah that's useless [Music] um let's come back and look at orange again so we've got orange oh it's the same trick isn't it ah yes it's the same trick look this square takes well this diagonal includes the units digit of its own clue so whatever goes in here let's just put eight in here for the sake of exposition if this is eight it doesn't matter for the purposes of this this is either 20 or 40 plus this unit's digit so these cells on the diagonal have to add up to the 20 or the 40. it doesn't matter what we put in this square yeah that's it you can't look this square here can't even be bigger than five let's make it maximum this is a five the maximum of those squares can be is 24 with seven eight nine twenty four and fourteen is not forty so this is a two uh it's lovely again oh how do i go back i want to i just want to get rid of that um this is a 2. it really is it's so clever to use these units digits like this it really is it's just classy setting um [Music] now let's keep this going so this square's a two not a two i should say um that's not a two uh come on um i suppose we can keep using this diagonal because that means those four squares now have to add up to 11 because we know these together add up to 20 so these add up to 11 which is that important not sure no i'm not sure um i think starting to lose track of where the best place to look on this puzzle is we've got ah i've got twos here and here this had to either add up to four or to five either way either way it needs a one yeah either way this needs a one these have to add up to four or five so it's either one three or it's one four because you can't use a two and the one can only go here so this is a one this is not a one this is the most peculiarly useless one isn't it it's not doing anything we've got ones down here yeah so hang on those had to add up to 11 didn't they so if there is no one in this position those would have a minimum value of 9 which couldn't go with a 2 because 2 is already in the box so these would have to if there's no one here these would have to add to ten this would have to be a one these would have to be two three five i think that's possible ah but this square has a minimum value of three look now because it can't be one or two this has a minimum value of two so the minimum value of those squares is five so the maximum value of these two squares is six but that we already knew that for that one this one already couldn't be um couldn't be higher than five this one can't be three this one's on the red diagonal um that's it that's it this square this square is where we need to look because this unit's digit of the red clue is not one two three or four this has to be at least five so this total here is actually pretty high which i think means this can't be it certainly can't be one or two if this is 25 those three squares have to add up to 23 which means this 23 minimum so this can't be one two or four even if this is four you've got to make those two add up to 19 and i can't do that in two cells this is five and in fact i'll max these out with nines and that only just gets me to a valid digit here because now this i think has to be 25 and that's the absolute um it can never be lower than that because the ones twos threes and fours are not available so we get a five in one of those two squares we get we get these nines that gives us a nine up here look we get a five in one of those two positions we get a nine in one of these two positions we get a five in one of those positions we get six sevens and eights in those positions we still don't know which order these threes and fours are in i've got to get rid of those minimums they're going to confuse me and we go we go what do we do now oh i tell you what once this is a five it it really is yeah these three squares i got rid of those minimums i'm going to put them back because these three squares have to add up to six well this has a minimum value of two this has a minimum value of three and this has a minimum value of one one plus two plus three is equal to six so these must take their minimum values um and that might be important because that feels like yeah this 2 gives us a 2 and a 1. this 1 gives us a 1 at the bottom of the grid there's a 2 joining its friend the 5 in this domino has a 3 up here um there's a two in one of those squares one must can only go in one position in box three now six seven ah yeah look at look down column seven we've got to place two three four and five well that square can't be two three or five so this is like a naked single that's a four it gives us a three here that three tells us that the yellow diagonal is 13 so that must be a three that's a four that's a four by sudoku four lives in one of these squares um two two by sudoku goes here two and three go into the grid three goes here by sudoku three's in one of those cells and all of a sudden this two fixes the two and the five we are actually doing a little bit better aren't we suddenly a flurry of digits have gone in this column needs six seven and eight must have done most of the nines yeah look nine goes here so nine goes here and that actually means we've done the nines this square these squares are six sevens and eights that's squares six seven eight six seven and eight is the new nori nori by the sounds of it in fact that's square six seven or eight um ah six seven pair here this square's a five it's a naked single those two squares you've guessed it they're six sevens and eights we've got okay purple oh no purple is still not done purple purple has a minimum value now of 17. now we can click we can tidy up our good lift pencil mark that becomes oh actually that can't be nine either this is now really restricted this is seven or eight ah look six seven eight triple and where does the six go in this triple it's definitely in one of those two squares i've also got eight pencil marked up here well it's the same effect yes the six being up here forces this to be a seven once this is forced to be a seven we can remove seven from those put seven in here this becomes 17 which i know is going to fix this but i'm also noticing i've just got to tidy up do my bookkeeping up there so i'm going to do that as well if you don't mind so i don't forget to do it um [Music] this 7 forces this not to be a 7. okay let's come back down here because now if purple is 17 the only way i can make this work is if i remove eight from both those positions so eight eight is placed in box seven okay um [Music] now what do we look at one and two are looking at that square so this has become three or four now it's definitely not one um is it this column at least we've got six digits in this column three five and six to pl yes look that's a naked single that's a five because it can't be three or six that fixes five and four blocks four out of this square i feel like i've got a lot of fives in this grid if i got enough yes i do have enough fives this is a five that must be a two you can see again look double click the fives where does the five go in this box it's got to go here these squares have got to be a three four pair the four fixes the order so four and three go in this square should be a 6 by sudoku 6 is in one of those two cells we might be able to fix this value now because i've got a lot more real estate on the blue diagonal i've now got 23. these two squares i just need to get yeah i mean well the simple way of doing it is saying given this can't be a 9 there's no way of getting to a number that's 40 in fact look it's just kind of you cannot put 4 here because 41 and 42 aren't even available so you the best you do is go forward in fact best you do is go about 46 by the looks of things and there is simply no way to make those squares high enough so this is three which actually doesn't do much for us i don't think so how do we do this we've got can i place yeah look for in this box by sudoku has to go there this square's a six or an eight this square is a six or an eight we've got six sevens and eights in fact the whole of the bottom six rows six sevens and eight that we haven't placed we've got four six and seven along here i think presumably i've got to there must be some sudoku i can do at the top here i think maybe this digit let's check this digit that can be four it can be six it can be seven i think i'm not sure digit here can be four eight can it be one two three five can it be six oh no it can't be six yeah just four or eight so it's definitely even but this can be odd so we can't get a parity trick on this square what am i missing here um [Music] six seven this quest got to be six or seven this squares can be anything again ah is it's i'm not sure whether it's sedu i think it must be sudoku i'm missing because seven here that can't be a seven oh it is sudoku i'm missing ah right got it now this not being a seven is very interesting because look whatever it doesn't matter which way round this six and eight go these two squares will be the opposite they will be opposite of each other these cannot be both six or both eight because if they're both eight you can't put eight into either of those squares if they're both six you can't put six into either of those squares so these are different digits and they're both looking at this square so this is i think it's a technique it used to uh pincers and pivots is how we used to describe it we've done videos on this but they are they're years old um but yeah this square can't be six or eight that's seven that gets a seven here that gets us a six here ah good here we go maybe we are we are on the home straight we've got no sevens in there i don't know why i said that thing about the home straight when i hadn't actually hadn't actually proved that we were these two squares what are these oh three i could have got that look three eight at the top these are one four and seven that's not four that's not seven oh but the seven is on the blue diagonal this is very clever isn't it so now we've got now we've got 30 on this diagonal not including this square so these two squares now finally have to be equal digits and you can see the only option that's available that's common is four and that gets us the one that gets us all of this done look two was i think that two didn't feel like it's uh what am i saying i'm saying that two i think could have gone earlier that is not a four don't put a four there why am i putting a four there um this is a seven this is an eight this is an eight this is a six six and seven six eight seven eight six eight six eight six click check i can't see what that says yes it says it looks good so that's how to solve it it's a fascinating puzzle it really is so clever just so clever i loved the way that these unit stitches this one and this one affected the logic um i mean it's a stunning idea stunningly executed and it's so much fun to solve you couldn't ask for a better sudoku i hope you guys enjoyed it let me know in the comments i do read them as you know and thanks so much for watching and we'll be back later with another edition of cracking the cryptic

Channel: Cracking The Cryptic

Views: 130,423

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Id: wszx7_3cDwc

Length: 37min 6sec (2226 seconds)

Published: Thu Mar 04 2021