The Sudoku With Only 2 Given Digits

[Music] hello and welcome to tuesday's edition of cracking the cryptic and yes i have managed to get the day right today apologies to those of you i confused yesterday by alleging it was uh sunday that is because it was a bank holiday here yesterday and that has totally discombobulated me um now you may be looking at the screen thinking how on earth can this be a sudoku and with good reason this is called the dutch miracle and it's by none other than aardvan deveitering from the netherlands now art is a mighty man in the world of sudoku an absolutely brilliant set of puzzles and in fact responsible for what i think i could allege fairly would be the most viewed sudoku of all time because we had a video a few years ago that has had eight and a half million views eight and a half million people have watched aad sudoku which we christened a sudoku with only four given digits well the art has trumped that here by halving that number to just a one and a two in the corner now we've seen miracle sudoku's before but i have to say i've never seen one with anything like this rule set it is absolutely fascinating and um i'll read these out in a minute it's a version of dutch whispers if you're familiar with that rule set so that's what we're going to be doing today in attempting to solve this rather sparse grid a couple of things to mention before we do that i've got two birthdays to say to talk about today so firstly kyle um or might be kyle um uh who turns 20 today so congratulations on that kyle karl from the north of england um and carl i was especially gratified to read that you actually enjoy our asmr sudoku video that we released a few years ago um that definitely uh that was marmite for people some people loved it some people absolutely detested it but we did do one asmr video and there is at least one person i now know who likes it so thank you for that uh now also um kyra um for uh over from over in south dakota it's your birthday today and your boyfriend justin got in touch with us to say you'd appreciate a shout out so i hope you've had a very splendid day too with of course very much cake uh that is always important on a birthday um so what else have i got to tell you about well if you're a patreon channel over on patreon check out the monthly reward uh we have had over a thousand correct entries so far and you've still got loads and loads of days left and the reports suggest that this one is well it really is genuinely approachable especially if you take on the normal version we release two versions a hard version and a normal version the normal version is definitely doable so do have a go and if any of you do get stuck um go over to the patreon chat over on discord and you'll find people who can help you um and other than that i have made a ricket i said a couple of days ago that we were going to be live streaming missed well i downloaded mist and i checked that my computer could play it which it could but i immediately got motion sick so mist is not on the agenda anymore apparently the game we might look at now is called goro goa i'm probably saying that wrong um it's not a word i'm familiar with but that is now apparently completely motion sickness free free and that's the one we're going to have a go at um maybe tomorrow night even wednesday night keep an eye on our twitter uh and also on the community page on youtube and we will we will firm it up then but if we do do it tomorrow night it will be at 10 o'clock uk time and we would love to have your company now what are the rules of the dutch miracle what does aard got for us let me read them to you normal sudoku rules apply along each positive diagonal ie from south west to north east which is from here to here so each of these diagonals two things apply firstly all the digits are different so all those digits are different and then all these digits would be different all these digits would be different etc and secondly adjacent digits i.e those touching at a corner so these two for example must have a difference of at least four so in this puzzle therefore this being a one this would have to be at least a five so it's a five a six a seven an eight or a nine and then let's say it was a nine the next digit would have to be five or lower five four or three it couldn't be one or two because one and two are in the box and that believe it or not is everything that is the complete set of rules necessary to yield a unique solution from this puzzle that's supposedly at least logically findable by a human being now that is what i'm going to attempt to do now do you have a go at the puzzle yourselves the way to play is to click the link under the video go down to the video description you'll see a link you can click that and play the puzzle on whichever device takes your fancy but now i get to play let's get cracking and i am tempted very much to actually highlight these diagonals it will make me feel like i'm making progress if i do this because because we know that on each positive diagonal we can construct in the puzzle um let's keep going this way actually and then we'll make a decision about with what colors we do the other way on each positive diagonal we can't repeat a digit so that's probably going to be worth keeping track of isn't it i'm trying to i'm trying to keep the colors as as well as crazy as possible it seems so now if we do that one again in yellow and then we sort of sort of propagate outwards we're going to have something very very beautiful to look at even if we can't do the sudoku that results from it so we need gray and then what do i go to then green blue and yellow and now what do we do so probably we start with the the main diagonal because at least we know that there's one of every digit on that diagonal and dutch whispers are awkward creatures um because german whispers i know many of you will be familiar with german whispers but in a german whispers puzzle the difference between adjacent digits has to be five and that leads to an oscillation by which i mean if you divide the digits up into the low digits one two three and four and the high digits six seven eight and nine then you know that a german whisper line oscillates from so if you have a low digit you then have to have a high digit because you've got to be five different and then you've got to be low again and you can never put a five on a german whisper now with a dutch whisper unfortunately you can put 5 in in a cell and that means you don't quite get oscillation you get oscillation i.e if we imagine the digits one to four and the digits six to nine as two parcels you do get oscillation unless you hit a five along the line and if you hit a five then the next digit has to be one and nine and the polarity can can switch yes so that's that's right isn't it so if this if this went five nine you can see that we we have changed if you like the natural way that this line would oscillate so normally it would go one and then a high digit and then a low digit then a high digit then a low digit but when you have the five there we we actually change that we get one medium high and then this is not low then so you can see if that's a seven is that a good choice yeah that works if one seven three would be absolutely legitimate and then you continue up the line from there but this is low but where five makes an appearance you have to switch to nine and that's that's going to be the challenge but there is there does have to be a five on this diagonal yeah that's that's interesting so does this have to be the 5 no because 5 could go in the corner bobbins ah that's annoying that was almost a sensible thought um obviously if if five does appear in the middle of this diagonal because it has to be flanked by two digits that are at least four away from it it would have to be flanked by one and nine and that would break the diagonal if you if you tried to put it here because we'd have two ones on the diagonal so the five could go here with a nine here but unfortunately the 5 could hide away in the corner with a 9 beneath it and then the problem with 5 goes away so that's really annoying actually um okay so okay so the next digits that we should probably think about on this line are fours and sixes um fours have to be connected with eights and nines and sixes have to be connected with ones and twos oh yeah right that's important that is important because of this one in the corner now so where does six go on this diagonal well the only place the only place it could go and be next to a one is here but then we'd have to put a 2 on the other side of it which we can't do so 6 is not here now if 6 is anywhere else other than in the corner it needs to be flanked by a 1 and a 2 and it couldn't be without repeating the 1. so six does live in the corner and it must be next to a two because it can't be next to a one and now five is problematic because we said five could go in the corner which it now can't so now five must go here and be next to nine and we are actually getting somewhere so we still need so now and now we've used the five we can use the polarity switching to help us so this has got to be a low digit now i uh a number lower than five then it's going to bounce up to a higher digit then it's going to bounce back down to a lower digit and then it's going to bounce back up to a higher digit but that digit must be difficult you can't you can't connect seven to four so yes so this can't be seven because it would have to have a four on one side of it and that won't be four away so this is eight this is seven this is three and this is four and we've done one of the diagonals that's quite lovely and therefore well now the problem is going to be that all other diagonals are far less clear in the sense that even if we take one of the eight cell diagonals like this one there's a digit missing from this diagonal so that so the sort of the restrictions that would apply to digits like four five and six will only apply to two of those three digits because one of them might just be missing altogether um right each box though has to have a five in it so the central box has to have a five in it and wherever that five goes it must be flanked by one and nine on the diagonal so if this was a five you'd have to put one here and nine here because of this nine if this was a five you'd have to put one here and nine here but that doesn't actually wow that doesn't seem to do much does it so maybe we've got to use the fact that we have a net we have now have two twos in the grid it's the only digit we have two of um [Music] so the two in box nine is in one of four positions and the problem with two is it's not very restricted at all from from a whispers perspective i mean if the two was here these two digits would have to be at least equal to six and that's not very constrained at all presumably the same is true up here in fact two could hide in the corner up here and a two in the corner is not uh subject to any whispers restriction so two isn't two is not where we have what is not what we have to think about we've got to put four and six in this box so that's probably worth thinking about so 4 4 has to be next to 8 or 9 on its diagonal so if four if yeah okay if four is in a yellow cell it must accompany eight within the box because it can't accompany nine but if four is here this could be an eight or a nine and six oh s ah oh right okay where does six go where does six go in this box sorry i didn't didn't think about this but like there's already already a one and a two in the box six can only go next to one and two so i think six has to go here because otherwise anywhere else it has to be it needs a one or two on the diagonal with it so this is six this is a one or a two and that is important why that puts a six into a two by two up in box number one and that's oh that's almost interesting because we remember wherever the six goes it has to be flanked by ones and two so if this was six you'd have to put two here and one here six ah no okay don't know if we can disambiguate that but we might be able to right let's have a look at where six goes in box four because it can't go there because that would need a one or a two here so six is in one of these cells and i want to say is there some reason there's probably a way we can yes okay but this is a one or a two so this can't be a six because that would have to be flanked by one and two so this is not a six oh this is not a six it's already on that diagonal good grief so six is that six is in one of these two cells now so six in the central box is in one of four places i think no that's wrong as well gosh this puzzle's strange okay this can't be a six because if that's a six you'd have to flank it with one and two and there's already a two on this diagonal so six is in one of those three cells now now let's just check all of these that would lead to a one-two pair in those positions might be possible six here one and two in those positions yeah we haven't got the ones and twos here aren't seeing these yellow diagonals so i think all three of those might be might be possible i'm not going to commit myself harder than that they might be possible now the six in here would cause a one-two pair here and we would know the order this would be one this would be two so maybe actually yes or maybe no ah i can't get my head around this at all if this is six you've got to go two here and one here which would stop this being a six if this is a six though you could go one or two here and one or two here and then you're not putting any pressure on this digit i don't think ah this is tricky this is really difficult um [Music] i'm not that surprised a puzzle with only two digits and with a very very short rule set is difficult i shouldn't be shocked at all should i um [Music] oh this has just died of death so six over here is in one of four places six inbox nine is in one of four places ah no six in box nine is not in one of four places because remember if we put a six in row eight here what digits have to be on the diagonal in column not in row nine we've got to put ones and twos in so you can't put a six here if you put a six here this needs to be a one or a two and it can't be either the same is true for that cell so actually six is not in those positions so six is now reduced to oh i've got it i've got it i've got another digit right six six in box eight is restricted because that that logic we've just done for the sixes in this domino applies identically for the sixes in that domino we'd have to put a one or a two in the bottom row and we can't so actually this is the six in box eight which now must be flanked by a one and a two so that's not a six now in box five um and so now i'm wondering about these two sixes so if whoa whoa whoa hang on a moment if that's a c oh no it's okay i think i was just noticing if that's a six i'm going to get a one-two pair in this row which is going to prevent these two from being sixes by the one-two rule but but that six would automatically reduce the possibility of these two being sixes okay let's have a think about this so if this is a six this square here would be a two and this square here would be a one now is there anything wrong with that answers on a postcard please i can't see anything wrong with that what about if that's a six if that's a six this has to be a two and this has to be a one oh so the two is always beneath the six on this diagonal and the one is always above it i'm sure that means oh no does that mean this can't be a six or am i confusing myself i don't think that can be a six because if that's a six where are we going to put the one on its diagonal if that's a six i can't put a one here and i can't put a one here and i can't put a one here because if this is a six this is a six and there's a one in this box already so that is not a six anymore now we might be able to repeat that trick if this is a six surely it's the same logic i've got to put a one oh no hang on maybe it's no it is the same if that's a six i can't put a one here and this is a six in box five which puts a one here so you can't put a one either side of it so here we go so now i've got now i know there's a six in this domino which means this is not a six this is a six which means this is a one this is a two and we are cooking with gas all of a sudden probably he says and then immediately comes to a complete and utter standstill um oh right this isn't a six now is it this was this was never a six because it's on the red diagonal i've only just noticed that right that's not a six so now i've got my six in box six and i've got my six in box nine and i know these are flanked by ones and twos so this cell oh that cell is a one it sees a two in the in in column eight already but these two digits don't seem to be resolved oh although i've got a one-two pair in the bottom in row six now oh so i can place it all right i can place two in box five two can't go there by sudoku it can't go here by seduce two goes there now that's probably got some profound implications for some middly digit along along this yellow diagonal um but also oh no hang on it's got other other easier implications look that's a one and a two this is a one why have i got a one in this cell is that in some way relevant yeah okay let's ask where six goes in this little two by two now it can't go in either of these two cells because it will need to have a one or a two lower than it on the diagonal and there's now one and the two in row four so those are not sixes if this all this is a six you have to have a two beneath it so there is definitely a two in one of those cells there's definitely a one in one of these two cells and that means this cell would have to have a 2 here and a 1 here i'm sure this is somehow resolvable i just can't quite work out how to do it um all right let's let's go back to having a look at box five we still need five sevens and nines what can we say about that five is going to be very important yeah five can't go here because that's going to require to be flanked by one and nine oh five could go there if that's a nine look that one might work what about this one oh this is beautiful right that's not a nine sorry i'm not a five because if that's a five what do you well your a is next to two which is that that's that's so depressing that's not what i was looking at i was looking at this cell and seeing it can't be a one or a nine so that was how i proved this couldn't be a five but there is a simpler way it can't be next to two on the diagonal so that means that five in this box goes here we need this digit to be four away from five and not to repeat the one so that's a nine that's a nine that's a seven by sudoku this is a nine now in box four good grief okay now does this keep going please keep going what should we say now there's a six in one of these two so if and this can't be a six because it would need a one on its diagonal so we can get the six here oh it can't be six because the domino here there's all sorts of sudoku possibilities that will help you if you evade them in the puzzle that's now a one um these are no longer twos so two lives over there oh two can't be here because these have to be different by four at least so this is a two um no okay this digit maybe maybe this row we need threes sevens and eights now that cannot obviously be seven or eight no this needs to be low in fact so that's got to be three leading to a 7 8 pair over there which doesn't seem to be resolved let's keep going down this diagonal this square has to be 7 8 or 9 and it can't be 7 it would repeat it can't be 9 by sudoku so that is eight eight must be um four different from a digit here yeah okay so that can't be three two or one so it has to be four so these two squares are three and seven and there's a three here so that's all fixed this is actually starting to get easier i think i mean it's not that surprising we're getting digits in but it's almost becoming yeah oh no yeah what's that digit that digit's got to be four away from nine but not five and not one two or three it sees all of them so that is four which means these two squares are three and five and that's three and that's five and that's five on the diagonal which requires a nine this square's got to be four away from nine and therefore it is five or no it's not five it's not it's not one two or three that's four as well these diagonals are all similar aren't they six one five yeah the cycling there's some sort of cycling going on don't quite yeah eight eight three seven two eight three seven two three seven two so oh because there's an eight missing from this diagonal which is why it's not eight three seven two so there's some sort of cycling two six one two six one two six one yeah this there's a pattern emerging i won't use the pattern because i don't understand it to to actually fill the puzzle in but it might be a quick way of doing it if you want to if you're minded to use that sort of thing uh this square is not a four so this is the only position for four in this column four must be four away from a digit so that's eight that's seven four has to be four away from this digit so it must be nine because it can't be eight this has to be um three four five it's not three it's got to be four or five it can't be four that's already appeared on the diagonal so that's five um this is three or eight and it's not eight so that's three by sudoku that's eight eight needs to be next to lowest digits doesn't it so this has got to be three because it can't be one one two or four and this square here therefore has to be one two three or four and it can only be four of those four eight three four eight three so again confirming our our opinion about cycling uh this is seven this is eight these two squares are seven and nine which is resolved this square here is a something five six one five six one five yeah all looking good that's an eight by sudoku that's a three by sudoku that's a five by sudoku um okay let's see if we can finish this off with some sort of a plum we need twos fours and fives along here so two four five that's not two that's not five and that's not four but this has to be four away from one so it has to be at least five so five two four get filled in now these squares have got to be six seven and eight and therefore that's got to be eight it's the only digit that's four away from four and this is six seven and there's a six here so then sudoku takes over and this column needs something uh what is it two and eight yeah i think it's two and eight so we can fill those in this column oh no let's look at that column one three five yeah one there oh sweet oh so that means that this six oh yeah we need to always flank a six with ones and twos i think there's going to be loads of ways we could go about doing this now because once you get a few digits in this it is clearly very very tractable um we need four seven and nine there so that's a four which is working this is seven and nine yes and the five helps us that can't be seven so that's got to be nine that's got to be seven and then we go four seven and eight here so that's four that's seven that's eight by sudoku we go three six nine here that's got to be six uh nine three and we go two five into those cells five two five nine four let's just check that that looks like it's cycling seven two six one seven two six one i've seen that before six one five nine six one five nine i think that's the solution yay that's just stunning isn't it it's just stunning it's yet another ridiculous puzzle from aardvan devatoring um i don't know how you come up with ideas like this oh you can put a one and a two in a corner box of a sudoku have some dutch whispers rules and a no repeat rule on the diagonal and the whole thing will result resolve but the clever thing is not just have all of those thoughts which are clever enough the clever thing is to realize that if you do have those rules the solve is actually very findable you know it's very logical you know all we did was sort of understand the constraint around which digits were going to be the most restricted and then think about those digits in relation to what we had and eventually we were lighted on the fact that sixes were very restricted in i think it was this box and it was it this box was it was really restricted in and that gave me the six here and then all of a sudden you're away and you can create these beautiful strings up all of the diagonals i hope you enjoyed it i hope you had a go let me know in the comments i do enjoy reading them especially when they're kind and we'll be back later with another edition of cracking the cryptic [Music]

Channel: Cracking The Cryptic

Views: 2,369,095

Keywords:

Id: wUnnXwLTbnA

Length: 32min 59sec (1979 seconds)

Published: Tue May 03 2022

Reddit Comments

[u/AtomicTaintKick]

I don’t even play sudoku and I watched that whole video. The patterns that start emerging are fascinating stuff.

Good find, OP

[u/Dthoulu]

i literally did this in like 10-15 mins, first try, im actually confused about how this was supposed to be difficult, not trying to gain clout or anything, but am genuinely curious as to whether or not im just stupid fucking lucky, vs too easy, vs really smard

edit:

i figured it out, its because there are so many solutions