The UNBELIEVABLE Sudoku

[Music] hello and welcome to thursday's edition of cracking the cryptic and on screen we have a puzzle that arrived a few days ago from the unbelievable setter advan de betering from the netherlands aard of course is the man behind uh the video that is our biggest video on the channel it has over seven million views would you believe it uh that that video is called a sudoku with only four digi given digits don't get me wrong that puzzle is an extraordinary puzzle and quite an interesting solve but this have you ever seen the likes of this because the answer to that is no um this looks to me to be absolutely absurd this is a normal thermo sudoku that is it there are no there are no tricks here no rinky dinks no nights moves kings moves nothing else this is apparently solvable and i saw the email when this came in and i i called up mark and i said we've just had a puzzle in from odd and i just don't believe it um and i said i've got to try on the channel so he has tested it now what i can tell you is it took him i think two or three days to test it i don't even know if he finished it but he's passed it on to me with a warning let me read you the warning and i've got it open on another window he says this is an unbelievably brilliant puzzle but it is also brutally difficult but you have to sit there until you solve it if you do it in a video so that is um yeah that's a worry isn't it so that means this could be a very long video but never mind i am i'm determined to give this my very best shot um and yeah well anyway we shall see how i get on um now before we before we kick off i've got two things to mention the first is thank you so much if you're one of the um one of the people who watched our first ever live stream yesterday i did indeed manage to get obs working i managed to tie it up to youtube somehow and i did a couple of times crosswords with the help of the audience um in an hour long video and what i'll try and do um for anyone who's interested who missed it is i will try and put that on the channel probably tomorrow morning uk time um it was a real adventure to me i loved it and it was a preparation because we've had a lot of a lot of requests to do or to try and so or try and play a game called the witness um or portal uh or even starcraft and even overwatch on on the channel we're going to think about all these things i can tell you i did download the witness last night and i did try and play it it does work on my computer i played it for five minutes and i still feel dizzy today as a result of motion sickness i do not know why i'm getting motion sickness from playing the witness but it is a bit of a worry um because um i don't i don't know whether i have to take medicine or something to avoid that happening or whether i can change the setting somehow so if anyone knows how to avoid getting motion sickness while playing the witness i know it sounds mad but um yeah i can't even go on the london eye without it giving me a problem so yeah i know i'm strange um anyway what else did i want to mention well just if you're a patron of the channel please do check out heatwave which is the incredible series of 10 thermo sudokus which is a topical uh a topical variant um created by grockles that we've got over there for all our patrons we've already had i think 200 or 300 correct solutions and the plaudits have been amazing so well done if you've managed to battle through all 10 you are doing very well indeed now let's get to this it's called checkerboard and let me read the rules it won't take long normal sudoku rules apply along thermometers digits must increase from the bulb end so we've got 16 one cell thermometers in this puzzle it is ludicrous so thermometers if you're not familiar with them whatever you put in the bowl then let's put a three here this square now just has to be higher than three so it could be anything apart from one or two or three itself um or indeed eight and nine by sudoku but that ignoring the sudoku aspects it just has to be higher than a three let's put a four in that would be a totally valid way of fulfilling that thermometer and that's it that is all we get we get five given digits 16 one cell thermometers symmetrically arranged in the grid and apparently this has a unique solution it is it is miraculous it is miraculous that this exists i can say that and i've not even started the puzzle yet but anyway let us do that the way to play do have a go yourselves the way to play of course is to click the link under the video as usual now i get to play let's get gragging sudoku may be our friend here look i can put a one in one of those two squares um right i've got two nines in the grid as well let's ah yes okay so where does nine go in box eight you can never put nine in the bulb of a thermometer because if you did you'd have to put at least ten in the in the end of the thermometer you can't put ten in a sudoku so nine look is in one of those two squares which means nine is in one of these two squares in box nine uh right i need to do rather better than that hang on a second nine is in one of three positions in box four this eight must be useless surely um [Music] what on earth is going on here this is absolutely ridiculous okay well i do not see anything else by normal sudoku so we must be looking for some jiggery pokery i think um [Music] i don't know whether to look at ones or nines i think i might look at ones i'm looking at actually i'm looking at the top row and wondering about ones because ones can never obviously go in the end of a thermometer because then you'd have to put zero in the bulb which is just as bad as putting nine in a bulb um so one in the top row is in one of four places yeah but because there's sort of a lot of symmetry here can we go further than that um one in row can be in one of these positions i think ah right okay right we're kicking off with something fairly extraordinary here looks like a jellyfish to kick off with um look at where one can go in row seven boom boom boom boom where can run one go in row nine boom boom boom boom well that is going to give me a digit actually good grief right so let's just talk quickly about what we've what we've found here we have found that in row one in row three in row seven and in row 9 the ones are limited to a very select group of columns i suppose either column 2 column 4 column 6 or column 8 and that's all we need to know to eliminate a one from this cell here why can i eliminate a one from this square well the key is to understand or to think about facetious simple questions how many ones are you expecting there to be in column two of this grid when we complete it when we complete it we're going to be positive well mental coach is telling us positive mental attitudes so how many ones are there going to be in column two there's gonna be exactly one how many ones are going to be in column four exactly one how many ones in column six exactly one how many ones in column eight exactly one so in these four columns there are exactly four ones we don't know where those ones are but we know there are exactly four of them but we know in row one there is a one contributed to one of those columns we know in row three there is a one contributed to one of those columns same in row seven same in row nine so the four ones that exist in columns two four six and eight are contributed entirely by these specific rows so if i try and put a one in here this will be a fifth one in these four columns and that is patently impossible you cannot have five ones in four columns of the sudoku so this cannot be a one and if this can't be a one that seems to suggest that's a one now that's pushing a nine up into row five ah that looks actually that might be interesting wow wow yes okay i think i'm gonna get a nine in box one as a result so this this is just ridiculous right let's look at this nines are in these squares so where do we put the nine in box six it's going to have to be in one of those two squares now look we've aligned some nines in a sort of x-wing pattern in boxes six and nine so the question we should ask here is where does the nine go in column eight it's not in those three squares it's not in these three squares so it must be in one of those three squares and it's not in the bulb so it's in one of those two squares now look at this nine and ask where nine goes in box two well the answer is we haven't got a clue except it's definitely not in any of those yellow squares because it can't be it can't be in those squares because of this nine it can't be in a bulb so it's in one of those oops this click lost my army one of those four squares now what does that mean now we ask the question where does one go in row two it's not in these three it's not in these three so it's in one of those three it's never in a bulb it's never in a column that already has a nine in it so it's exactly there which means that square is also a nine and we are off to the races so we've now got we've now got some digits in the grid um [Music] right what does that mean how can we make more use of our nines or our ah one i've not really thought about i got this one and then i started to think about nines let me just think about this one a bit more um let's just think about the jellyfish as well okay so which cells are interesting from a jellyfish perspective well because we know that the ones in columns two four six and eight are in the purple squares you can't have a one here you can't have a one in any of those squares we already know now we can't put ones in any of the central three rows because of the ones we've placed in the grid so the other interesting cells are those squares so there's no ones in any of those squares which means which means there's no twos in any of the end squares is this is this madness i'm thinking about here when i say that the end squares let's make those yellow actually just to sort of preserve the highlighting i now can't put a 2 here because if i do put a 2 there because of the thermo that's going to be a 1 which we know it can't be because of the jellyfish so you can't put a 2 in any square that is attached you can't put a 2 in any of those well this can't be a 2 anywhere you can't put a 2 in any of those but the problem is that you can put a two anywhere else in row one this is crazy this i i am really really surprised that no i'm astonished that this has a solution because i'm just thinking now even as i get some digits in the grid if i manage to get a thermometer digit filled unless it's a very specific digit like unless i get a 2 here for example which is a bad example because this can't be a two because of the jellyfish but let's say i did get a two in that position which would give me a one here that's giving me a very small inference if i get any other digit under than other than two here it's telling me very little about the bulb every time there's something i'm not understanding about this at all because i don't see how i'm ever to have enough information i mean obviously the place to start with any thermo is to think about ones and nines but we've sort of done that this eight is that eight doing anything ah oh good grief right i can actually get a digit from the eight i've now have now noticed because where does the eight go in box five it doesn't go there by sudoku now i don't think i can put it in either of those bulbs look because neither of these squares can be a nine from our pencil marking so that means eight in box five is in one of two positions which means eight in box six is in one of two positions and we still can't put an eight here because that would be a 9 which it can't be so that's an 8. so now 8 in box 3 look can't go here because that would be a nine which is impossible so eight is ruled out those squares so eight is in one of five positions i think in box three oh good grief what about eight in box one because a guy again you can't put eight into the bulb because that would be a nine so eight is in one of four positions in box in box one ah and that's almost it's almost gorgeous because thinking about where eight goes in box three eight's in one of those five positions which i can't really i hope oh maybe i've got to turn on my blue highlighting can i turn on blue highlighting somehow um [Music] ah my blue highlighting is back i don't know where it went but it went right so now those squares are the possible positions for eights in box three imagine this one is not an eight then you'd have to ask where eight goes in row two and it would have to be in one of those squares and it couldn't be in the bulbs it would have to be here still doesn't do anything even even if you even if you sort of get a deduction like that it doesn't actually do very much it gives you a digit everything we're doing is just giving us a digit and then we sort of have to leave it alone this is this is not going very well i don't know i've only had quarter an hour that's not that's not too bad um we need inspiration to strike i think here i'm almost wondering if you've got to sort of i'm always wondering if you've got to sort of try and parcel off the bulbs of the thermos and sort of do something set related relating to bulbs in the ends that's not a stupid thought actually that's not a stupid thought so what i'm just wondering is if i if i hive these off i'm going to look at that um let me am i gonna have to get rid of my jellyfish highlighting i think i am because i'm not gonna be able to see what the set is otherwise um let me go to colors right oh actually i can control a now can't i control a get rid of colors right what i'm thinking is can we hive off or separate the bulbs of the thermometers from the ends of the thermometers using set so if i highlight those uh that they do show up right okay so this these four are these four rows of the sudoku are clearly four sets of the digits one to nine now if i isolate four columns that can entirely contain um ends of the thermos like this are we gonna get anything interesting here so these four columns the four purple columns are clearly also four sets of the digits one to nine so we know in the greens we've got four sets of the digits one to nine and in the purples we've got four sets of the digits one to nine so if i was to remove this square which has both colors in it from both sets it would still be true to say that the purples and the greens would still be exactly identical because this digit is in this digit here is in purple and it's in green so i'm going to get rid of it now i'm going to get rid of that one i'm going to do the same throughout and then i'm going to stare at the grid and see whether we've revealed anything the problem is uh no maybe this is wrong maybe this is wrong hang on i've just seen i've got loads of real estate here which is so how many what have we got now we've now got what i was noticing is i've got all this real estate here which is it's colored in green not colored in purple but it's not in a bulb or a or a tip um [Music] have i got the right have i got the right number of digits in both sets now i've got yes i've got 20 digits in green 16 20 yes and i've got 20 digits in purple so so we can what right so we're now in a point where we can say the purple and the green sets contain the same digits and that is a little bit interesting because obviously yeah that's that is weird actually because all the bulbs are in green and all the tips are in purple you know as a sort of given that we know that the purples and the greens have to be identical that feels like it's clashing somewhat yeah that might actually be the trick we're looking for because what i'm thinking is that the purple tips of which there are plenty must be greater than that than their equivalent bulbs so whatever's in there it's got to be at least one greater than whatever's in there so we've got yeah we've got 16 bulbs so we've got 16 tips so if we were to hive off all of the purple tips let's just do that all of these squares from purple and all of the bulbs from green let's remove these as well then what we're left with which is just this strip of purples in row five and this column of per of greens in column five because we know that the purples and the greens together must add up to the same number because they contain the same digits but the ones i've highlighted in blue we know that the purples must be at least 16 greater which means that these greens must be at least 16 greater oh this is absolute done it i've done it i've done it right this is it because we know that the purples are at least 16 greater than the the purple tips are at least 16 greater than the green bulbs which means that that difference whatever it is whether it's more than 16 or exactly 16 it is exactly 16. i've just worked it out but it must be entirely catered for by the four greens in column five they must be greater than the four purples in row five by that amount so what's the absolute minimum i could put into these four squares absolute minimum well i can't put a one into them so the absolute minimum is two three four and five which add up to fourteen now what's the absolute maximum i could put into these four squares well the absolute maximum i can put into those three four squares is 9876 which is 30. and that's that's the biggest differential i can create between these greens and these purples and that differential is is 16. so so this is the trick this is the trick because now we have proved that with this is an eight this is an eight because we know that we have to absolutely minimize the difference between every bulb and every tip in order to allow this um arrangement here to take up the balance of the digits we cannot split the the columns in uh the greens in column five from the purples in row four by any row five purples in row five by any more than we have already the maximum we can split them by sixteen and that's the minimum i can keep the difference between the purple tips and the green bulbs too because there are 16 bulbs so so we now know that every bulb is exactly one less than every tip and that's why this has to be an eight and i hope that that oh it's already making some progress here um that can't be an eight look i've just noticed that that can't be an eight just noticed that this is late eight ah no okay um so what are we going to have to do here we're going to have to sweat these digits like nothing on earth aren't we so eight is in one of four places now i think in box three i've got this eight which i didn't have before i'm noticing that i haven't actually got many digits at all in bulbs or on tips so we're gonna have to work we're going to have to work hard to get to get the digits that we're going to need anything we can get on a bulb or a tip gives us the other digit as well [Music] um hmm okay no this is not it's not good enough because knowing that even if i knew one of those was an eight that would mean one of those was a seven but i wouldn't know which one oh maybe i've got to look at row five then because i've kept these to a minimum the the gaps here have to be six sevens and eights don't they and that's not an eight ah ah so now i've got a six seven eight triple in box five which means those squares have got to be two three four and five and that's interesting because if these squares are two three four and five the tips oh look oh this is just ridiculous this is ridiculous why does this matter well if i know these tips are exactly one greater than a number like two three four or five they've got to be the numbers three four five and six as a set so these are all different digits because these are all different digits and they are the set of digits three four five and six so this eight is not possible that's an eight so those are not eight anymore this can't be an eight for exactly the same reason because it if this is a that needs to be seven which it can't be so that's an eight which gives us a nine here which means those are not nine um my goodness me please let me be able to solve this from here i feel like i've done well i feel like i've found a um now eight look in box nine has to be in one of those two cells oh no it doesn't there's an eight here that's ah so i've now got an eight here and that eight is on a on a tip of a thermo so where does its friend live what's in there it's got to be one different from eight which is there for a seven which means this square is a six this square is a seven those two squares now are not seven this is a six eight pair um that means that squares are seven i suppose let's take advantage of what we can get so now now we know there's a seven oh hang on i've got this square this is ah i'd overlook this one this is an eight so that's a seven it's in the bulb we know it's one different so i've actually got a few sevens i've got a few eights now let's look at sevens in this box that's that's intriguing me because oh yeah this is good this is good because where does seven go in this box it's in one of those two places now if it was here because we know that the bulb would be one different this would be a six which it can't be so that's not seven this is seven that's a six that's a seven by sudoku and this seven is on a tip so that's a six that's a six that's an eight let's look at this these eights but an eight here which is why this has to be a nine that has to be a nine this is one of the greatest puzzles i have ever seen in my life i can tell you that now i am just i am so nervous i'm not gonna be able to solve it i cannot tell you because i've just got to solve this now come on what do we do now what do we do now the answer is i have not got a clue sevens look i can keep going with sevens that's what i can do this can't be a seven because it would put a six in the bowl which it can't be that's a seven so seven is in one of the two places in box uh ah no hang on no seven is seven in box one is forced it can't be here by sudoku it's there and if that's a seven we know that's a six and we know that's a seven as well and that gets rid of the two pencil marks that we had in there so now i've got quite a few sixes in the grid six are six in box one can only go in one of two places um can we can we limit six similarly in box three i don't think we can i think it's in one of three places which means weirdly that one of those three squares is a five i have no way of pencil are marking that in a way i'll remember what it means and i'm reluctant therefore to do it oh six down here yeah there you go six is in one of those two places in box nine which means five is in one of those two places one in box seven i'm jumping around a bit here as i see things but i can never put one in the tip of the thermo so one's got to be in one of those squares oh oh one in box three where does it go now it can't be in the tip of a thermo so one i think is in one of two places there which is almost interesting i'm looking at box one and thinking about where one goes it can't go in the tip again so one is in one of two places there and that does give me another digit that can't be a one this is a one oh this is just beautiful i i hope that if i get through this aard will write me write to me or make a video of how this was constructed because this is ridiculous you can't put one here it's in the end of a thermo one's got to go in one of those squares c is that square puts a one here because as oh look yeah and one one in this box has to be in one of those two squares whoopsie which means one is not here anymore and i get a one there because as as this was being constructed surely odd you must have been oh my goodness this is just the most extraordinary thing i've ever seen in my life um now i don't know if this is relevant but i am now noticing that i can't i'm now wondering about twos actually because cells like this can't be a two because that's going to put a one here where it can't go this is probably a leftover from the jellyfish that we found earlier uh can we actually make use of that any in any useful way though i'm not sure i can ah then maybe there is a useful thing to think about yes box three where does two go we can't put it in the ends of the thermos because that's going to force ones into bulbs where they can't be ones so two is in one of those squares same thing oh lovely i've got a one two bear in this box does that do anything though the answer seems to be no it rules two out from this square oh no hang on it does do a little bit in box seven you can't put two here and you can't put two here because that would be a one so the twos yeah this is good the two's in one of these squares and it's not there because that would be a one where it can't go so that's not a two and this is a two oh it's beautiful it's just so beautiful the two in box nine is now locked it can't go in the end of the thermo it's got to go here that gives me the two in box three that locks the two into one of two places in box six this two is ruling a two out of that square i'm just looking at this now there is a strange triple in column nine and why do i think that well look at look at column eight we've got threes fours and fives to place in those squares but they're all in bulbs which means that their tips have to be selected from the digits one higher than three four and five so that's a four five six triple which means that square is not a four or a five so those three squares here are going to be from two three and nine i think that's not a two so there's uh we already know there's a two up there so this what does that mean um i've got my four five six triple i've got my three four five triple i've got another three four five triple in row two look which means that square's a four five or a six no okay i don't know if that's doing anything useful or not um oh i was about to say i've got another weird triple in column one but i don't have look because because yeah it's not quite the same well it's the same geometry but i haven't don't seem to have got as many digits or something this this is a three four or a five which puts that as a four five or a six but this one is a three four or five but it doesn't have an equivalent bulb situation which is a bit annoying um okay what does this mean um oh i've got a naked single where does two go in this row it's got to go here oh so maybe i've got to look at column five now where again i've got threes fours and fives to place into those cells three that looks like a three four five six quadruple in row three which means that square's at one or two uh getting stuck aren't i i was not unexpected this is not unexpected um [Music] oh no come on simon um now maybe i can maybe i should use i think the minimum i've got to do is label all the thermos so this square here has got to be three four five or six which means this ah that's not a three because if that's a three here this square would have to be a two which it cannot be so that square is only three four or five i don't think that's good enough is it three in box seven has to be in one of in fact one of two places only that might be useful three is not here anymore and that's on a tip so if that's not a three this is not a two oh right okay let's keep going with this though because now in box nine the three is in one of those three places which means that is not a three and if that's not a three that is not a four and if that's not a four the four this is ridiculous this is ridiculous this keeps bouncing backwards and forwards because now if that can't be a four the four lives up here in box seven and that's not a four which means that's not a three and i've got this one down to being a four or a five oh please ah it doesn't do anything though ah no it does it does do something because what is this digit whatever this digit is where does it go in box seven the answer i think is there those two digits have to be the same digit by sudoku and if they're the same digit what would happen if they were five the answer is we've broken the puzzle because now i have to put a five here which by sudoku is fine but it's not fine for our one cell thermometer so those can't both be five they've got to be both sixes and they join with their friends here but that's not what's really interesting because what's really interesting is getting a six on the tip of the thermo gives me two fives in the bulbs i'm just sorry and i'm just pausing here to make sure that i'm not i'm not missing a trick because there is an awful lot every time i remove pencil marks from tips i've got to be so careful because removing six from these two means i've got to remove five from those two and of course removing or placing a six here means this is a five which means that is not a five which means that is not a six which we already knew but this being a six means that this has got to be a five and it means more than this though because also we know that this six we know those four digits were three four five six quadruple don't we so getting a six here means i must remove six from both of those squares now that oh hang on so getting rid of i've already removed the five because i got this five so that seems to be duplication but this six here is now no longer in that square so the six in box one is in this square that's not that's not a six anymore which means that's not a five anymore now i've got now i've got a three four pair somehow in column eight so that square's got to be a five and that's in a bulb that's not a five honestly this is as much fun as you can have with your clothes on this is just ridiculous two three four here five here means this is a six because it's on the thermo i feel like i've done an awful lot of sixing in the last yes there we have we've done all the sixes now have we done all the fives no by no means by no means have we done all the fives ah but look here we've got six digits at the start of row eight so these squares have got to be three four and nine and this is useful that's three four or nine now this square therefore can't be a four must be a five and of course what that means is that this is a four this is a three by the thermo logic this is a four by the thermo logic three four this is a five by sudoku five gets removed from those and here because of the we know this is a quadruple this square's got to not be uh if this can't be a five this can't be a four this can't be a four so the only place for a four now is here which means the squares are three please please keep going three that's a four that's a three that's oh no hang on i've just made an absolute horlicks of something there what did i do wrong i did something very badly wrong i don't know what it was i got the five here and then i should have written a four in here and i don't think i did so i've got to get rid of fours from there these have got to be one higher so those are not fives i think i might have deleted the wrong digit uh but something was going badly wrong there so i'm going back and on undiddling myself now two three four triple here means that's a five that's not a five anymore so i've got five four six five three four three four oh come on um oh no i'm grinding to a halt again now i've got a 2-3 pair here maybe this column is the is the key to the highway we need ones and four yes yes where does four go in this column it can only go there because of this four so that's a four and therefore this is a one and then this square should be a 3 and that 1 gives me a 2 here a 1 here and a 2 here and the 3 gives me a 4 here and a 5 at the top and this 4 gives me a three here which gives me a two here a three here and a four here and a five here and a four here come on three here this is a five oh i could have got that five from that six whenever i got that i just didn't spot it apologies please don't shout at me this is not the worst solve in the world two three this square's a three this square's a four uh this three is giving me a three nine in the bottom box this square is a two and this square looks like it's a nine and i've got just two more cells to do i need a one and i need a three and i'm going to click yes yes i am very proud of that that is an absolute masterpiece simply a masterpiece from the great aardvan deveitering um wow what what an idea so i mean i don't know where to start but the whole conceit of it i think is that you can lock in the difference between the bulbs and the tips of the bulbs to being exactly one and then somehow by some absolute magic the puzzle solves uniquely once you know that that that thing that fact it is quite quite extraordinary that is one of the most brilliant brilliant puzzles i've ever done in my life um let please let me know in the comments whether you enjoyed that i really hope that those of you who solved it will have got some of the pleasure so just even a little bit of the pleasure i've got from it it is an absolutely unbelievable puzzle i think mark the other day stood up to clap that's what i want to do um but that would prove i've got legs and i don't want to do that unnecessarily fabulous absolutely fabulous 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: 135,867

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Id: 5wtgymz5yjQ

Length: 47min 0sec (2820 seconds)

Published: Thu Aug 05 2021