The Final Boss Of Thermo Sudoku

[Music] [Applause] [Music] hello and welcome to monday's edition of cracking the cryptic and today we have a debut on the channel for the set of garford with this rather beautiful puzzle he calls the tree now this actually has been suggested to us several times by other people as well as garford as being um sort of just a brilliant sudoku and also a very interesting new rule set so this is a completely new sudoku variant and you'll understand what i mean when i run you through the rules i'll do that in just a second but in fact just before that let me just show you this is what it looks like in all its coloured glory so mark suggested we needed to pair it down so it's become a rather i don't know a well-wintered tree should we say in order to allow us to put pencil marks in the grid as we solve it or as i solve it um so if you want to see it in resplendent glory like this you can see look this is a sort of very healthy looking tree um but we're doing the the winter version um now before i read the rules it's a huge day for anyone who supports the channel over on patreon obviously big thanks if you do do that and at 4 p.m this afternoon which is a couple of hours ago um we released our brand new sudoku puzzle hunt so please give it a try and we've tried to pitch it this time just slightly easier than some of the recent hunts um to make it as accessible as possible while still being a challenge and there's a lot of puzzles to do and there's a whole and then you have to having solved the puzzles you have to solve the meta puzzle in order to generate the the solution word now if you find the solution word do send it to us you can email it to us at crackingthecryptic gmail.com and for the next few days at least we will read out uh correct solvers on the channel so very good very well good luck and i hope that you enjoy the puzzles um also on patreon we've got my solve of fistimophel's yin yang philomeno puzzle which i tried last night that is a beautiful logic problem but boy oh boy is it challenging um so that video is about an hour long to give you an idea and i'm not ashamed of taking that long to solve it so if you enjoy some of the battles you've seen on the channel over the last few months i think you'll enjoy that video but most importantly do try the puzzle um i'll put a link under this video um to the puzzle so that you can have a go and it is it's definitely worth your time it's so it's an incredible incredible execution um as always from vistamafel now what are the rules of garford's puzzle let me read them to you because they are unusual normal sudoku rules applies that's good now the tree branches are populated by two digit numbers where the tens digit is placed before the units digit seen from the stem which is the bulb in box eight so this is the bulb that's being referred to and then as we move up the grid everything has to be viewed as a two-digit number where the tens digit appears first now the bulb includes the first number red from left to right so that means that's the tens digit that's the units digit and the two digit numbers must increase along the branches so this is like a mad thermometer sudoku but instead of involving the normal sort of one-digit numbers everything has to be viewed as a two-digit number when a branch separates the two-digit numbers on all new branches must be greater than the two digit number on the preceding parent branch and the two digit numbers must not repeat across the whole tree so the way i think this works is let's imagine this was 27 for example the next two digit number which would be read from this square to this square so this would be the tens digit has to beat 27 so obviously can't begin with a 2 it could be a 31 that would be okay and then as the thing branches the next two digit number along this branch would be this as a tens digit and this bit as a units digit so that could be 45 something like that and along this branch on the other hand this branch has to just be the 31 that came before it so this would have to be i don't know well we don't know what it would have to be but it could be 69 for example so and we have to keep building the numbers as we move up the tree so it's a fascinating idea um and yeah we'll see how i get on with it do have a go yourselves the way to play is to click the link under the video as usual now i get to play let's get cracking um and we've got obviously no given digits and presumably yeah okay if this is a tens digit we yeah okay at the start of the puzzle you know where all the tens digits are that is something i can appreciate because if this is a ten digit and it is the next tens digit along this this branch of the tree is this one then that will be a units digit that will be a tens digit that will be a tens digit so what we might do is highlight all of the tens digits because they are going to push the did push the overall numbers up um far more than the units digits are so that's 10 that's a tens digit oh but coming along this yeah this the tree already branches at the bottom look so whatever that digit is then there's another yeah oh yeah okay so each branch is an even length which makes sense because it must be able to be viewed as a series of two digit numbers so this might make it quicker for me to to fill in all of the tens digits although this feels very peculiar then so this is a units digit tens digit units digit 10 10 10 10 10. now look at where they come it's really strange how they the pattern of them is very counterintuitive to me at least units tens tens tens tens this so this was a tens this is units this is tens units 10 10 10 10 10 it feels a bit like nori nori this sorry um 10 10 10 now that must be 10 10 10 10 10 10 10 right i think that if i've made a mistake god imagine how bad that would be i'll use actually if i use greens it turn it into a tree again yes it does all right so i've re i've refoliaged my tree now um and i think i'm i hope i haven't made a mistake but i think that that those are all of the tens digits and that means oh bobby's i've broken this already sorry i've done something wrong ah what did i do wrong there maybe i've not understood the rules i've the reason i've broken it is that row 2 must be impossible because this high up in the tree is like the end of the thermometer and the ends of the thermometer will have to be very high digits so looking along this line you can see we've got seven yeah we've got seven different tens digits i have to place in this line which implies that i must have one of the green cells must be three as a maximum well how can anything this high in the tree be three be a thirty number it can't be so i think i've misunderstood the puzzle let me just check the rules again [Music] so first digit read from right left to right the two digit numbers must increase along the branches when a branch separates the two digit number on all branches to be greater than the two digit number on the parent branch i thought that's what i did um yeah you can see this well i'm just going to check this breaks but look if that's a one and that's the minimum it can be immediately as we come along the sort of main branch of the tree this square is a tens digit that can't be a one so we're already at the twenties and we're down here [Music] so if we come up here this this has a minimum value of three already so you can see as we sort of come up this branch of the tree yeah if we come up this branch of the tree to get to these these three squares in row two the minimum i could put in this square is a four so these definitely these have to be at least equal to forty something 40 something is greater than 30 something this has to be at least equal to four so this one can't be a three um this one oh now oh oh well this is good this is good i've just noticed something that i should have appreciated before and that's that this square doesn't actually need to be a 30 number that could still be a 20 number because the twos are not in the same column ah so if this was a one and this was a two you can keep this as a two so maybe we can put a three in one of those squares somehow so we're at 20 something still all of these three squares come through this branch so we get to 30 immediately so this is 30 something that therefore can't be 30 because it's already in the column with a three that one ah that one can be 30 and therefore probably must be 30 because this one can't be 30 because if this is at least 30 and this is at least 30 this one must be at least 40 because it's in the same box as this tens digit here but this can be a three and it's the only one that can be a three and given we need a three um or a one or a two in these green cells and we definitely can't get a one or a two in them this is a three so this is a three this is a two this is a two this is a one and we are off and running um and actually we can fill in the one and two as well because we can't put the one or the two in any of these tens digits here was about to say that must make that a four but that's complete bobbins um i have no clue what that is just because it's bigger than 30 doesn't mean it's 40 something ah but rather that's rather beautiful let's look at this square so these two squares are both 30 somethings but we can view this a bit like a thermometer this 30 something has to be a lower number than this 30 something because it's lower on the tree now this 30 something is a tiny thirty number i mean if this was 31 this would have to be 30 and it you can't put zero into a sudoku grid so this must be 32 and this must be 31 and that gives us more digits and that's what i like more digits this two gives us a one here um [Music] two by sudoku oh this is good two by sudoku is in one of those two squares well it's not going to be there because that cell must be at least it must be 40 or 50 or something because well yeah especially now the minimum value of that now is 40 because it sees three and then these branches of the tree come up to the top through these nodes which are both tens digit nodes and they have to be greater than four so the minimum value i could put in either of these would be five so if i even if i anyway the point is this definitely can't be 20 something it's got to be i think it might even have to be 70 something but it's definitely not 20 something that's a two two goes in one of those squares what are the same same logic one can't go here it would be too big um [Music] uh well no it you know making this a teenage number is not going to be a good idea so this has got to be a one in one of those squares three actually three is just as uh useful because through these threes mean a three is in one of those squares but this can't be a 30 number because we know that this is at least a 40 number so three is in one of those two cells and therefore it's in one of those two cells now all no that could be a 30 number because in fact yeah that could be a 30 number i was going to say it's higher up on the thing than a 29 but it's not actually it's just higher than the the teenage number here but that doesn't really matter it's still got to it still could be 30 something well this is very interesting and i suppose what the other thing i've got to do is keep track of the fact that i've used 31 and 32 which is that is a terrifying thought because they can't repeat anywhere in the tree 31 and 32 i'm never gonna remember them all okay one ah yeah yeah yeah the greens basically all greens in this puzzle apart from this one have to be not one because they can't be teenage they you know yeah i mean this is definitely a two so everything higher up in the tree than this is at least a 20 number so this box where does the one go it can't go in a green and it can't go in those squares so it must go here one therefore is in one of those two squares both of which are units digits which is a bit uh annoying if one of those have been green we would have been in clover we've got ah one oh actually hang on can i do the same in box five yeah one here and the none of the green cells in box five can be a one okay i mean this one can't be a one because it needs to be greater than a twenty number so one is in one of those i'm just wondering actually if that's a 1 that's a 21 that's impossible because if that's a 21 this would have to be a 20 and again i can't use zero this is really clever this is really clever setting so that gives us a one up here one now i'm going to get the one in box six because these ones and this one and the fact that this can't be a what the tens digit must mean that's a one so one is in one of those two cells i've actually done i've done seven of the ones just by focusing on the low digits i think this is the key i'm going to look at twos more carefully again um [Music] twos so twos in this box uh twos in this box in theory can go in four positions but i don't think this can be a two because for this to be a two one of those two squares would have to be a one and that's impossible so this is not two this one this is interesting this can't be a 2 because that will create a 21 number on this branch but we know that this number is bigger than 21 because this square can't be a one two or a three and in fact it has to be greater than that as well so this is not two and now i've got twos locked into those squares i bet i can't put two into those and i can't because these have to be at least equal to forty so two goes here this is absolutely beautiful now two's ah all of these are units digits that's not fair two's over here now if i can rule two out of those two squares these are both tens digits so yes you can rule two out of this one because if this is a 20 number what is this number which is before it on the thermometer or on the branch it would have to be a 10 number because it can't be a 20 number and that's impossible because it's got to be greater than that number so this is not a 2 now this one can that be a 2 no it can't because then this number has to be lower than it and it can't be so actually 2 in this box is in one of two places that's not two two must be here i've done a lot of twos now um well i've done a few i bet three three is just placed in this box it's exactly the same logic given we've got the four going into the spaghetti junction here everything that's a tens digit in this box has to be higher has to be at least four so it's not three and therefore the three must hide in this position so now oh can i rule yes i can i think oh no yes or no um three is in one of those two places i'm just wondering i think maybe it can be here 30 something i think is possible isn't it bobbins right okay um but this definitely paid more dividends than i thought it would sort of check trying to focus on the tens digits placement of placings of the lower the lower digits but it seems to have run out of run out of room a bit doesn't it so what do we do now maybe i think about this digit now because this digit i still got to put like four into row two and if this is a minimum value of four surely the four can't go in any of those squares that come through the spaghetti junction because if this is a minimum of four these are a minimum of five yes so i can't put four in those so four is in one of these two now if four is oh no i think you can just i think you can just put four in either of those what about five then let's come back over here and think about five because five's also tricky because five will have to mirror in order for you to let me try and articulate this in some sort of coherent manner in order to put five in one of these squares you'd have to be okay with putting five in one of on on its branch because if you don't put five because this is four minimum the best the lowest you can put on either of these branches is five and therefore to put five in one of these squares you need to preserve you know you need to put 51 or something early and then have be able to put 52 or 57 or something as one of the as one of these limbs so if this is five now this is this is gorgeous this is gorgeous this definitely can't be a five number now because for this to be a five number this would have to be a 40 number and that's not possible now this can't be a five either because this is creating a 51 number and this square well what's this this has to be a lower than 51 and it can't be 50. so you can't put 5 here and you can't put 5 here because it's just in the column with the 5. so 5 does not work in those 3. now the quest and 5 doesn't work in this one if that's a 5 you can't put 5 here so 5 is impossible in those uh oh did i just get rid of a i think i just got rid of a green yeah i did but this can't be five um we can delete that well no that's not right these can be five but the point is that these can't be five so five is locked into one of those two which is the same as four and this is a four five pair but but let's just think about this again because i couldn't whichever one of those i put five in i couldn't rep this is very this is lovely this is lovely whichever one of those i put five in i couldn't repeat that digit on its branch so when i tried to put five in here remember i couldn't put five there because it would become 51. well that logic holds whether that's six seven eight or nine you you simply cannot repeat whatever is in here cannot repeat on any of those squares and whatever's on here can't repeat here so whatever yeah so i think what i'm proving here is there has to be a five in one of those because i know one of these squares is a six and i know it's not possible to put six am i getting confused here maybe i'm getting confused if i put six here yeah i could put six no i couldn't put six on that one because that would be it yeah the point is i've got to put six in one of these squares and the only square you can put six in is the one you've put five in in one of those two squares that's the point and if one of these squares needs to be a five and it does in order to allow a six to go into any of those squares this must be a four so we get another digit because this is lower on the tree than the fives i think that was a very long-winded way of saying there has to be a five here but at least i think it's true right okay we can keep going with this though because these this square for example can't be a nine because that two digit number there would then have to be lower than this two digit number which axiomatically would have to start with a nine and that would repeat nine in the box so that one could be a 9 i think that one can't be a 9 for the same reason that one can't be a 9. if this is a 9 you need a 9 here and i guess thermometer logic works the other way around you can't put a 60 number there given that this would then have to be a 70 number or an 80 number and that will be this digit will be higher than this digit so that's not a six and this has all been a great deal of effort for nothing at all hasn't it i've got no actual progress this square has to be higher than this one so i think this has to be seven eight or nine therefore because it can't be if this is six you couldn't repeat the six in the box ah oh dear sorry um now what do we do we can i've got this is one of these puzzles i fear i'm going to get this sensation because i can feel it dawning on me of having no real feel to where i should look next um can i assume if this is a four that i can't put four in these tens digits no that's not right is it because this could be like 45 and then i could have a oh no that would make that 42. but i could have a 4 here and then this this could be 46 or something so you can put 4 in a tens digit yeah you can but you i think you've still got a bit of a restriction because four can't go in those by sudoku now can four go here the answer is no because we know that this tens digit has to be at least a four so this can't be a four this tens digit also can't be a four because 42 means this would have to be 41 which it can't be so the four is actually in one of two positions which is a small breakthrough means four's over there so the other thing we should think about you know is is where we put high digits low down on the tree so we worried about how where we put low digits high up on the tree but putting high digits low down on the tree will be very difficult especially if there are lots of tens digits to be avoided so i was about to say nine in this box is troublesome but it's not is it nine nine could even go here with another nine there oh nine in box five well what you can't do you can't put nine here because that digit's lower than nine a ninety number you can't put 9 here because that digit's lower than 90 number oh this is good this is good you can't put 9 here because that's a 29 number and then what what 20 number am i gonna make this one that would have to be 29 and a half and that doesn't work yeah okay so nine in box five is in that domino and that means it's not in those cells that gives me a six seven eight triple in this box oh and and in and in row two where does nine go in row two only there um [Music] does that matter i want to restrict 9 in here but i don't think i can i think the 9 could hide it hide in a white cell or it could just be there for example and just be a very big number at the end of this branch of the tree six can't be here because we've got a six seven eight triple you can see the six in that six seven eight triple is definitely in that domino so that's not six this can't be eight because if this is eight you need this to be nine which it can't be so there's an eight in this domino ah yeah this is nice um eight eight is not there eight can't be here because that's creating an 80 number and this can only be a 60 or a 70 number so eight is not in any of those squares and eight goes here in box five create ah creating a 28 but this has to be higher so this has to be 29 and we get a nine in this box bobbins nine can go in three positions there ah that's interesting now nine has suddenly got restricted in box four a bit more nine is now in that domino let's take a look at that can we rule one of those out uh yes yes yes we can in fact both of them are a bit tricky but this one is is is terminally tricky because if that's a nine we it's creating a 92 number here but this is on the same you know this this then has to be bit bigger than 92 and we can't repeat nine in the box so that can't be nine that's huge so that's not nine which means that's nine which means that's nine so we get two nines for the price of one that's not nine anymore and oh lovely look this this is creating a 90 number and there's still more of its thermometer to cut it's branch to come sorry freudian slip so this this is 9 here 91 is impossible because if this is 91 what this would have to be 90 that doesn't work so this is not one this is one that's not one so 91 uh okay um let's check nines then so nine yeah hang on that can't be nine because that will create 29 here and 28 needs to be lower than this so nine not sure looks like nine can be in one of three places i'm sure that there are reasons i could eliminate these but see this one for example looks like it could go 90 something and then 90 something back that way and i can't immediately see why that's not valid oh here's something simple um where does seven go in box five the critical thing is it can't go there because if it goes there what do i put into this square the answer is a six so we'd have a 70 and then a 60 higher up on the tree so the 7 is not there so that means 7 is in one of those two squares which tidies up this top bit look so that's an 8 that's a 6 that's a 7 that's an eight eight must live in this domino [Music] um now what is that done i'm sure it's done any number of very incredible well it's good i tell you what it has done it's given me a six in this box there and that's six means that's a five and that's a seven so that is actually lovely and that means these two squares are a three four pair i almost feel like we need to take stock here yeah okay look 49 and the we can't put four here now because this this cannot be a 40 number that's bigger than 49 so the four goes here these two squares now have got to include these are a 7 and an eight i think oh that's that well that's easy there's an eight here so that gives us a seven and an eight figured out that gives me an eight here eight's got to be in one of those three squares at the bottom these squares now are five ah eight here let's just do some sudoku simon come on eight nate there and in fact this yes this is 83. so this has to be an 80 or a 90 number and it can't be a 90 number so that's eight that tidies up the 80 from over there eight yes yes eight where does eight go in box um box jobby here box eight in fact it goes there and that oh no it doesn't give me that i was about to write the nine in thinking i'd only pencil the nine into one of two places but in fact i hadn't done that so there's now oh there's now a three nine pair at the top of the grid apparently that means this is a four or five pair this square is a five i think i've not put five into this column so i'm going to go with five here creating a 25 which is lower than 28 so that's good this eight means that's an eight look this is not eight anymore five six and seven into those three squares these two squares are five and five and six but well yeah this is a thermometer though isn't it because 49 whatever i put in there has to be lower than there so i can't do 62 followed by 51. i've got to do it the other way around 52 followed by 61. this square's therefore this square actually is a 7 because it has to be a higher number than 61 and it can't be an 80 number or a 90 number so i think that is a seven that gives me a five six pair in the box five six ah which means there's a seven there i think seven in one of these two cells that we need let's actually look at this we need six seven and nine to complete box eight now that can't be seven that can't be nine that one might be able to be anything but oh this can't be a nine because that will create 98 and the only number that's bigger than 98 would have to be 99 here which would repeat any number of nines in any number of rows columns and boxes so don't do that that's ah so this is nine nine is therefore in one of those two cells we're slowly but surely inching our way towards the top of this tree um now those squares look are three four and seven i think three is not here i'm not sure if i can eliminate anything else those two squares are five and six i've got a horrible thought i've just had a horrible thought i bet i'm going to have to learn all of these digits to see what what's repeated and what hasn't repeated oh i'm gonna be terrible at that um [Music] i'm going to be absolutely terrible at that these three squares are two three and four that's not two um [Music] you know because it's perfectly possible we've had a 92 93 or 94 somewhere in the puzzle already and i wouldn't have a scooby-doo about it that's oh that's not a 90 number that's a 29 number oh dear this is i think this is going to be what i'm going to have to do isn't it let's look down here though i've not put 2 3 4 and 6 into this column so these squares are 2 three four and six that's not two there's another 90 number here that's so i've definitely had 91. i definitely had 81 by the looks of it i've had 83 i've just seen i've had 83 here so this one can't be 83 that's not a three um now that's mean that that didn't give me anything oh i've got a bad feeling about this this square is interesting actually looking at that because that's this digit here is a minimum of 68. so this oh yeah okay look this square has to be at least 60 at least a six and it can't be a seven eight nine that's a six creating a 69 which is a very memorable number for some reason um so that's a six now and that's a five six goes here by sudoku that fixes the six and the five over there five is now locked into one of two positions in box three and one of two positions in box nine okay and we can go back to hunting for repeated digits again we've got this row we still need to place two three four and five into the open cells let's look at that so that's useless that one can't be two that one's useless oh dear oh 80 no that's not an 83 that's a 53 or a 54. ah 69 is a memorable number and we can't have it repeated in the grid so this square is not 69 that's 63 that gives us a 9 at the top oh oh good my pencil marks i have pencil mark three nines into there so that's the nine that means that's the nine i feel like i must have done all the nines yes i have this three is giving me a four here look four two three the four and the two are looking at that square which is a three this is now a six that fixes the six and the seven so those squares are now two four and five in some order and we can get rid of five from this one two from this one nothing from that one 84 or 85 we've probably had before somewhere um i keep looking at this one that's not 84 is it that's something else that's 81. four here gives me the four and the four and the five there that four fixes the five here so that's another five at the bottom these two squares now are a seven and a four i was about to say that's problematic for this but i don't see why that that that could be 44 presumably oh um [Music] this is 29 this is something and then it becomes a 60-something number so this can't be a 70-something number that's got to be a 3 or a 4. two three four um hang on that three is eliminating threes from those squares three four five this is a three four or a five oh ninety something ninety three ninety four and ninety five look for green nines that's the way to do this green nine ninety three can't be 93 we've already had that let's get rid of three green 91 96 9 oh that's the one i'm looking at 90 oh sudoku helps me four five pair in row eight that's gotta be a three that's a four that gives me a two here look the two fixes two in the corner so these two squares now are three seven three and seven is that what i'm looking at here this is four five so don't tell me is there's like a 63 somewhere is there or a 44 or a 47 oh good grief ah um is there a simple way of figuring this out or not the answer is probably not i think i'm going to have to let's look for 60 numbers first so 60 i need green 6 63 63 yes that's got to be 67 therefore that fixes the four that fixes the seven the four the three and the seven and the three and i've just got a deadly pattern left so there's going to be another repeat that's going to have to deal with this so 9 94 or 95 look for green nines 93 uh 91 90 so i've done this before i'm having deja vu 90 is no use 84 or 85 8 82 8 no 81 it's i have to read it that way 8 80 no 83 you're joking i don't know this but this one better be it 74 or 75 green sevens seven no it's red that way 79 i thought i got it then i haven't got it that's a 79 this one 76 that's not it either oh no i 74 74 here it is 7 4 is 74. so this can't be 74 it must be 75 5 5 4 4 tick yes did it that is not an easy puzzle at all my goodness me um well welcome to the club garford that is some debut very colorful very interesting and very hard let me know in the comments how you got on um and i will read them with a great interest and thank you so much for watching and we'll be back later with another edition of cracking the cryptic you

Channel: Cracking The Cryptic

Views: 163,212

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Id: tBuEpFbZpxA

Length: 50min 31sec (3031 seconds)

Published: Mon Mar 01 2021