The Most Beautiful Question Ever

[Music] [Applause] [Music] hello and welcome to saturday's edition of cracking the cryptic where today i am going to with some trepidation attempt the puzzle you've all been requesting for the last few days this is fistermephel's latest offering and it has absolutely melted through our testers none of them have even been able to place a digit in this one um and that makes it daunting to say the least in fact fisted fell himself emailed me to say that it would be a gamble to attempt this in a live solve um he thinks it's extremely difficult but he well touchingly he remarked that if i did spot the break-in i would like it so that's the challenge today um now this has been on logic masters germany for a few days and some people have managed to solve it including of course cwg 2000 now i don't know who cwg 2000 is but i do know that they are an incredibly good sudoku solver because they solve basically every puzzle that appears on logic masters germany um literally every puzzle now cwug 2000 wrote a comment under this having solved it to say and they used the word question instead of puzzle but they said this is the most beautiful question they have ever solved now that is praise indeed from somebody as prolific as cwg 2000 so i think this puzzle is probably a masterpiece i just hope i just hope i get to experience some of the wonder um so wish me luck um what else do i want to mention well quick mention those of you who follow us on twitter will already be aware of this um because i tweeted about it yesterday but i will actually be appearing in an upcoming audio sitcom called the night crew um i'm not sure when it's being released it's pretty soon it's um it's the work of peter c hayward who is obviously also a brilliant puzzle constructor and was helping us with our book um and um yeah he he asked me to play a part in this in fact he's done even done some graphics let me find the graphics where's the graphics here we go it's a cartoon me well some people said it was a cartoon mekong which is a bit harsh i mean i may look yeah a little bit like um the enemy in dan dare but not a lot like it um anyway the uh that's not the part i'm playing it's not a it's not a me con um but yeah i'll i'll put a link under this video and if any of you might like to listen to that i would recommend it not for me i hasten to add but there's a lot of very talented people uh in and behind the show now over on patreon of course we've got our wonders of the world sudoku hunt we're still getting correct entries which is marvelous if you are a patron and you haven't attempted that hunt yet you must do that it is absolutely you know it's great content and it's a lot of fun and so i highly recommend it um and of course tomorrow we're planning to release scott strosal's video where he shows you how to solve his sudoku challenge tracking the triptych um so that's definitely worth watching as well other than that it just remains for me to wish xavier a happy birthday and get on with the rules of this puzzle we've got normal sudoku rules apply the digits on an arrow add up to the digit in the corresponding circle so that's completely normal arrow clues a clue outside the grid indicates the sum of the digits on the corresponding diagonal on this diagonal digits may repeat if the other rules allow it so completely standard little killer rules as well so let's uh if you're not familiar with those that means those two squares they're obviously emanating from this circle here whatever those two squares add up to you've got to put it in the circle and then on the diagonals um basically this diagonal here has to sum up to 29 and you can repeat digits on the diagonal but not frivolously so you can't do that for instance that most certainly breaks the rules of sudoku don't do that you won't get the answer right now do have a go at this the way to play is to click the link under the video i suspect this is monstrously hard um let's get cracking uh now so what can i see immediately the first thing i can see is useless little killer clues which is no surprise i mean if our testers as i say our testers can't place the digit in this puzzle so there is not going to be anything straightforward here um and you know if we look at the little killers you know three cells with a total of 15 we're averaging five which is exactly what you don't want to average because it's completely the average um same thing here six cells adding to 30 that's averaging five as well two cells adding to ten that's averaging five four cells adding to 21 well it's averaging very nearly five that one that one's seven cells okay that one's averaging just a shade over four so that's nearly useless thirteen just a shade under five and just a shade under five again so these little killer clues are actually i would go as far as to say strangely average i'm almost wondering if that's where we need to focus for the breaking because they're so average let us do the other thing we tend to do with complicated puzzles which is let's just highlight all of the little killer clues and take a quick stare at that i've missed off that one there we go now does that pattern remind you of anything it doesn't remind me of anything there's no they should they should make this into a scientific study if you can see like you know the answers to the life of the universe and everything hidden in these yellow squares then it certainly says something about you but it doesn't say anything about me i've not got a clue what that is um okay right so let's i think it must be the arrows that we have to look to and i've been doing quite a lot of arrows recently because of our upcoming arrows app so well the first thing i'm seeing is look we've got spectacles everywhere it's like fistumaphel is deliberately haunting me he's got spectacles in every uh one of these corner boxes um hmm okay so i mean i can see these cells for example are all in the same row of the sudoku so they've got to be different so the minimum value of these squares is 10 1 plus two plus three plus four the minimum value of those squares is six with one plus two plus three which means that the minimum value of these squares is sixteen yes that is complete and utter bobbins that is no use to man or beast i was never expecting those to add up to less than 16 let me tell you um something very similar down here in fact it's identical isn't it we've got 16 there as well so that's no use um column nine look that does have a lot of arrows real estate in it so hmm that actually this is interesting the problem is i can't get too excited about this this is really sad because because i know the testers haven't been able to do anything i'm at a slight advantage i don't think this will be the break-in but it is interesting so i should talk about it because these squares the minimum i can include in six cells in the same column of a sudoku is 21. if i make these six squares one two three four five and six that will add to 21. so these squares have a minimum value of 21 and a maximum value of 24 because they could be seven eight nine now that doesn't even mean we need to have a nine in one of these because unfortunately six seven and eight add up to twenty one so but as they must add up to at least 21 you can't put low digits in there you couldn't have one two or three in these circles because that will that will mean you'll have to either repeat a digit in a circle or use a double digit number which is probably not a good idea um so if these if these are 21 this would be these would be 24 and if these are 24 these will be yeah okay there's something strange going on these the cells in the gaps in column nine combined with the circles in column eight i like the complement of each other they add up to forty five so these yellow squares add to forty five and by the way and if any of you are wondering how i know that that's because i know a secret if you add up all of the digits from one to nine and obviously column nine for example will include all of the digits from one to nine you get forty-five so i was eliding a bit over some of the logic there but that's that's how i know that so if these squares add up to 22 for example so 22 would be the sum of the yellow squares i must i know those three squares would have to add up to 23. so these squares together add up to 45 and that is i mean i can do something with this 10 arrow actually let's just have a quick look at that the 10 arrow how do we make 10 in two cells such that it meets the conditions that this square has got to be lower than this square because this square is the circle and it's the sum of those two squares the various ways are 9 1 8 2 7 3 and 6 4. so this has to be one of the higher digits oopsie this has to be one of the lower digits and therefore we will know the possible values of this square if this is 9 1 this will be 8. if this is 8 2 this will be 6. if this is 7 3 this will be 4. you always get an even digit there that's weird so maybe this is parity that we need to use parity parity is interesting in arrows because there is um there is a feature of arrows if you add up any arrow and its circle that will always equal an even digit because obviously even if this domino here adds up to an odd number once you add the odd number to an odd number you get an even number so i'm just wondering i mean those must add to an even number this is an even number therefore we know that those four squares must add to an odd number yes you're right that's useless sorry right i can do something if this if this is eight then these squares have a minimum value which is higher than it 21. the minimum value would be 15 plus 8 which is 23 and this would be a 9 so you'd have to have an 8 in one of those squares you'd have 9 here you'd have to have an 8 down here but this could be this could be 23 or 24 so you have something like this going on and i don't like doing this actually because this just feels like bifurcation i'm sort of guessing that this is an eight and then seeing what it does sorry now i don't want to do that i don't feel that that's elegant at all um right so what on earth am i meant to do here on earth am i meant to do i've got maybe i can could combine these arrows maybe that would give me 31 into the yellow cells which means that there's i mean there's a tiny relationship between let's color these in between these two squares and those four squares because i know the box will contain the digits one to nine and add to 45 so look at that that could be double one i suppose in theory if that's double one then we know those squares add 29 so we know those squares add to 16 to make 45 altogether and as we increase these yeah we need to increase these as well so as we move up from double one these become these gets 17 18 19 20 which is absolutely useless um bother um i'm not surprised i have to say i was fearing that this was going to be the case um now what else have you hidden in here vista mfl is it geometry can we do some geometry on the grid try and try and get maybe row one row nine column one column nine um so let me just explain what i mean here what i can what i can get is a relationship in fact i'll show you the relationship then i'll show you how to prove the relationship those squares there come out so these purples are equal to the greens and when i say equal i don't just mean they add up to the same number they are the precise same set of digits um and that actually might be interesting because there's there's eight circles there that have to fit into the greens let me just show you why this is true fill these in so if i was to ask you what the purple squares contained we could very confidently say it was two sets of the digits one to nine because this row obviously is complete set of the digits one to nine so is this one now if i wanted to remove from those two sets of the digits one to nine those two squares so let's imagine that i want to remove these two squares now those two squares are obviously different digits so i'm just going to remove them from one of the sets of the one to nine so we've got two complete sets of the digits one to nine i'm going to remove these two squares from one of those sets what will be left in that set of the digits one to nine if i remove these two squares from it well clearly it's going to be whatever's in the rest of this column because this altogether represents a complete set of the digits one to nine so if i remove those two squares from it i'm just going to be left with those so now we can come across here and do exactly the same thing on this column so if i want from the other set of the digits one to nine in the purples which is still complete remember because i've only meddled about with one of the sets so far i'm going to remove those two squares from the purples and in that set therefore i will be left with those exact cells so the purples and the greens are exactly equivalent and i just want to stare at this for a minute because i've got a lot of well it's a slight actually it's i'm slightly over egging the pudding here because there are two single cell arrows actually aren't they so this square could actually be a one so i was about to say that circles on average have to be relatively high digits because they are they are the sum of other digits which is not true for that one or this one but the others it's true for it's true for those those all have to be relatively high digits and in the in the green regions a lot of the digits are on arrows so in theory should be lower than there's something going on here isn't there arrow cells on average should be lower than the circles and yet do we we know we know that there must be we know these add up to at least 21. so so you can't so if these add up to at least 21 the yes the minimum these add up to is 21. so the lowest digit you can include in a yellow is a four so there must be one two and three in the greens which means i've got to put one two and three somewhere in these purples now in this column well you can't hide the one two and the three in column one in the corners you can't like make this a one-two pair because then this arrow and this arrow would have a minimum sum of three plus four and four plus five which is 18 which would require double nine which won't work so there must be a one and a two on these arrows or perhaps both which means the purples have to include a one two and a three from this side and at least a one or a two from this side as well which the problem is these are possible aren't they that's the problem is you can do you can hide digits in these squares and they can be low they can just be low digits the other thing you could do actually is you can i could just delete cells from these from the greens and the purples because this purple is equal to those greens so ah okay so at the moment we've got a situation where the greens and the purples contain the identical set of digits so they add up to the same number now i'd have to disregard the identical sets of digits if i start deleting stuff but that cell and that's those two cells add up to the same number so you can just delete them from both both sets now we know that the purples at this point still add up to the greens so ah this could be interesting same thing here same thing same thing in all of these corners the purple takes care of two greens these are the same sum so i'm going to delete them delete them so now what have i got now i've got six the six greens have to add up to the same number as the 10 purples but i know less about the greens than i used to because i'm not really covering the arrows we can increase the number from 10 though because i could replace that one with those two this is this is actually really interesting if i get rid of that square obviously these two add up to the same number as that circle so i could do that in fact i could force them all into box two and box eight is that that will allow me to relate them to 45 i can't quite see whether this is doing anything but i'm tempted to try and shunt all of the purples into box box two which i can do simply by mirroring that one in there and i can do it down here because that's got to be the same as that that's got to be the same as this so now we've got a situation where the six greens are equal to the 12 purples so on average a green has to be double the value of a purple now this is getting very constrained so that the minimum i could make the purples now would be 21 again it's the same as over here if i put one two three four five and six into those purples did the same at the bottom i'd get 21 21 is 42. 42 now i've got it yeah i have got it i understand how to start the puzzle and in fact i'm going to get a digit there because those squares what's the maximum i make these squares seven eight and nine now look here what's the maximum i can make these squares i could put a nine here no problem but this domino it's got to add up to a single digit number so the maximum this domino can be is 9 and in fact it will be 9 i'm going to get this digit as well let me show you why if this adds up to 9 9 plus 9 18 plus 24 is 42. so the maximum you can possibly make the greens is 42 and the minimum you can possibly make the purples is 42. so if you make the purples just one higher you can never make the greens add up to enough and you can't make the purples lower so everything the odd in fact the answer to life the universe and everything is 42 which i'm almost wondering whether fistamafel has done that deliberately he's so brilliant he probably did um i can well imagine he's a douglas adams fan that is absolutely i mean it's incredible absolutely incredible so now we know these digits are one two three four five and six we know these digits are one two three four five and six we know these squares therefore are all seven eights and nines we're going to get some of these we're going to get we can i can see i can immediately put nines into these regions because of this nine that's got to be a nine and then that's got to be a nine by sudoku um nine nine has to be down there nine has to be in one of those two nine can't be in this one because it would it's this is a short stubby arrow so if that's a nine this has to be a nine as well and this can't be a nine so that's not nine this must be nine nine's in one of those two i don't think that one is a short stubby one it's a little bit hard to see i think that's a two cell arrow oh but this is a little stubby arrow as well that yeah this is a one cell arrow so this can't be nine because that would put a nine in here so that's not nine this is nine which means this is nine and suddenly the puzzle is revealing its secrets now this square is not nine anymore so this square can't be eight anymore and that probably means that one can't be one no it can't because that would require a nine because of the ten arrow one two three i've got seven nines in the grid uh nine is in one of those two squares nine is not there so nine is in one of these two squares and right let's just sit back and think because suddenly we have a bit of progress like 15 there's a 15 diamond i'm not used i don't think have i used the little killer clues at all i don't think i will i've pencil marked that one a bit but i don't think i've really used them so those have to add up to six they're either one five or two four okay 20 21 has got already got 18 on it so these two squares have to add up to three so they can be very much restricted they've got to be one and two and they are different so we might even have to color them in fact i'm quite tempted to immediately is that worth coloring actually it's not it's probably not worth coloring because i haven't actually got any other cells in the grid that can just be ones and twos but we've got to try and remember these are different um 29 we've got no nothing 30 no 13 oh look we've got okay look we've got the short stubby arrows let's do some stuff with those so they look like they can both be one two three four five and six okay that's not a particularly good restriction um seven eight where does seven and eight go in box in box seven this seven eight and the seven eights here there's a seven eight pair so that means seven and eight have got to be in those squares in box nine don't think looks like with all of the options along this arrow that this could easily be seven or eight seven eight there's now a seven or an eight on the 13 diagonal so this can't be a six because if it's a six we're already yeah we're already going to break the bank so this can't be a six either so so the maximum value of this square is five oh but hang on i haven't used this arrow either these this domino yeah hang on this domino adds up to nine and it can't use eight one or two seven so this is three six or four five so the minimum value of those two squares together is now 10. so this can't even be three if this is three the best you'll do with this square is four and three plus four plus seven is fourteen it's not thirteen so this square is one or two that means this square is one or two now does that matter so now can that really be that can't be six so exactly the same reason this can't be six so if this can't be six this can't be three so this i know this could be three if that if that's eight and that's two so so we can almost get some stuff here the 18 diagonal oh yeah okay the 18 diagonal as well look this square is restricted because the minimum value of those two squares is 14 so this definitely can't be it can't even be four that's got to be one two or three 14 so the maximum value of this square is three so this is very restricted as well just wondering whether it's worth trying to put these together in the same sum because then i would know the sum of these two so if i if i look at this as a sort of you know two diagonals these has to add up to 31. i've got 15 there so these squares have to add up to 16. um can we do anything with that so if this was a minimum these would have to add up to a maximum of nine i'm not sure i'm not sure whether that's okay or not it might be i can't see why that's a problem i apologize if everyone's shouting at their screens now it does feel like this is quite restricted can this be nine if that's nine if i've got uh what have i got here 15 i need 16 into these if this is nine these have to add up to seven that could be done couldn't it if this was a one-two pair and this was three and one that would add up to seven so that's not proving useful i don't think i can restrict this at the moment um right let's look somewhere else we can look for where where do we look for something else we could this no that can be four different things one eight two seven three six four five uh do we know what this is i don't think so wow seven and eight is a bit restricted in row one seven and eight have to be in two of those three squares but that looks completely fine um i don't know what to do uh okay where else do we look here we've got to look at oh i know what i can look at i know what i can look at i looked at this column and this columns gaps these had to add up to 45 from the work we did earlier i now know two of them so these add up to 18. that means these squares let me get this right that one and that one have to add up to 27. uh yeah okay that also doesn't seem to be helpful what about if that was seven and eight if that was seven and eight these would have to add up to twelve is that possible it looks more than possible looks possibly even probable ah what on earth do you do next i thought the break-in was gonna be hard but it doesn't get any easier i can't believe it's these 20 this this 29 diagonal's got too much yeah too much optionality about it can i do more with these ones then 13 again 13 can that be five yeah it can five seven one that's absolutely fine eighteen so still so something about three is three here problem for some reason that would require these to add up to fifteen so it would require double seven and one is double seven and one impossible not seeing why let's try them together again we've got 31 now these have to add up these have to add up to 16 because we know they add up to 15. ah ah right i can i can eliminate a three from this square because if that's a three this has to be at least a four seven plus seven is fourteen and these two would have to add up to two which is impossible you can't double one them so this square is not three that gives us a one two pair here so i could ah yeah i am going to color this now because these two are the same so cells like this can't be a one or a two anymore because they see this square which is a different color from this square so let's have a look at this we can use red and blue so you can see this square sees this red and it sees this blue so it sees one and two between the two of those so this squares become a bit more restricted um i've now got these two squares have got to be three four five and six i'm clutching at straws a bit here i think one two one oh no hang on one two in this column are now forced into these three squares so those squares are one and two so this square can't be a one or a two and this square has to be a one or a two is that enough does that do anything for us i've got a yes i've got a one-two pair here now lovely so this square can't be a two i'm not sure if that rule oh that must rule one of the options out from there that does that rule six out from here six four two yes it does that's not six that's not four so six has come out from here four has come out from here one two can come out from here because of the one two pair this nine arrow now ah yeah hang on this square is restricted as well because this can't be one or this can't be one or two anymore either because this domino is either three six or four five now what do we do um i don't know there must be something else to do we can it's just it's always the way with vista mephil his puzzles are totally baffling they make me feel so stupid i cannot tell you um i'm sure that there is something very obvious i meant to see here actually i'm not sure it's very obvious but i'm sure there's something that is more obvious than i feel i'm making it look okay come on how do we make more progress in this puzzle we can if i could relate you see i can't i'm wondering whether i can connect the coloring of the ones and the twos somehow that might be helpful is there a way of doing that or is that see these oh these two are different aren't they ah i haven't used that these two are different because they of the 21 clue so this square sees both colors of the one and the two so this is not one or two this is not one or two oh now look now look at box two and ask where one and two go and the answer is we don't really know but they definitely seem to be in those three squares so there's no one or two here this square becomes a one or a two oh good grief now look these are on an arrow this is one and two are on this arrow so this is a three i've just look at what this three does look at what it does it removes three from these squares that's the first thing it does it removes three from this square that bounces back in here and now where does three go in this box on the arrow so this nine arrow is now three six that removes six from those squares and six from this square that removes three from this square that means we can color that one blue that's might be interesting down here for the stuff in the bottom left hand corner let's carry on up here for a second i've now got a four or five pair in row two the four five goes in here again this is absolutely ridiculous so this three locked to three in here which locks a six in here which then bounces back through here and gives us a one two four five quadruple in the row now now look at row one and where r square seven and eight can go that can't be seven and eight because of those squares so seven and eight are a pair in the end this square must be a six by sutoku six gets removed from these squares down here and and six being removed means this domino has to add up to nine it must be a four or five pair so get rid of three from here that means we get a three in the corner that's three in the corner that's three in the spotlight losing its religion that square's a six um this square is not a six i think it's quite clear we're going to have to be very careful with our pencil marking here because every digit seems to matter a one-two pair here so those are not one and two in fact that's not one or two either because of the one two pair there ah well actually it's obvious now there must be a three on this arrow because if it can't be a four or five pair because that would make this a 9 which it can't be so this this is r so this square is a 7 or an 8 now because because there's a 3 this is either 3 4 or 3 5. so this square is either seven or eight so there's well we don't yet know really what's going on down here i don't think three is in one of those cells i've got this four or five pair in row two six what have i not placed in here i need to place four five seven and eight so this square is a seven or an eight so it's different from this one so i think there's all sorts of coloring going on in this puzzle yeah okay this is lovely so this is a seven eight pair now so this can't be a seven or an eight that's a four or a five which means that's a seven or an eight so i'm not sure but we might have to think about coloring the sevens and the eights now all of those are the same all of those are the same unfortunately that doesn't tell us the coloring of those two squares or the coloring of these two squares this i'm just going to tidy up my pen spots how long have i had 45 minutes that's not i don't think that's terrible um okay now get rid of the ones and the twos from there okay what what have i not what have i not used i think i've used this 15 quite well i've not used the 30 and i don't really want to use that 30. that looks impossible oh it's going to have a look down here wasn't i i've got all of this coloring done now so i've got the same digit repeating on the 18 diagonal so if this is double one these two squares would have to add up to 16 so they could be uh it could be seven nine or double eight if if this is double two these have to add up to fourteen and they could be double seven that doesn't seem terribly good does it let's try them together then um what have i got there if i try them together it depends on what blue is so i've definitely got 15 and then if blue is two i've got double two plus one which is five so i've got fifteen and five is twenty these two squares have got to add up to 11 so they could be four seven if this is double one and two i've got 19 in these squares these have to add up to 12. right oh that's that easy that is useful there's no nine here ever these this domino what that proves is that this domino either adds up to 11 or 12 and you can see it's not possible for the nine to be involved in either of those sums so this ah she gives us a nine if my pencil marks are correct and then ah we've now got the nines i think we have got all the nines we've got a seven eight here now do we know the color of this one we do we do don't we because these two squares are either taking the total along this diagonal to two or four so we know that these two must be the same because they must be adding to an even number um now what does that mean do i know so i must know that this is green then don't i that's the point that's green i don't know what it is but i know it's green so this is purple this is quite beautiful i have to i have to say this is quite beautiful because now sorry brief pause there uh these things happen on the long videos especially at the weekends but um i was just about to reveal why this was quite beautiful and i will get the chance to do that now the reason is look if we look in this box here we've now got opposite colors in in these two dominoes and these two dominoes but we know the sum of those two dominoes because effectively we can divide the 18 diagonal now into 2x plus 2y because there are two greens and two blues in it so if we just take just take the two out we know x plus y equals nine so i know those two squares equal nine well if those two squares equal nine what do those two squares equal nine because they're just the complement of whatever we put in these two squares so if these equal nine what does this square equal well it's got to equal 4 to make the 13 square work so this is 4 this is 5 and we have more digits that's a 4. that's that's not a five this square is never a six because if that's a six um we could have to put three there minimum and that would make this square a nine um [Music] okay so okay can we go further with this i'm not sure it doesn't actually seem to have done very much unfortunately five i really don't think it has um bobbins one two pair here means that square's not a one or a two we've got a four five pair in this box so that's not four or five there's a one two pair in box two as well now it looks like we're stuck um we're meant to be looking i've got almost got something interesting happening in the 30 diagonal where i've got two greens uh so if that's 16 these would have to be 14. so these four squares either add up to 14 or 16 which i think looks very doable either way okay this square can't be a six because remember this domino here has two options left on it six two or three four if you put a six here you get a three there and neither of those options exist on that domino anymore because that would have to be a four three now but this square's just about to become a 3 to add up to 9 and we have a problem so that square on this diagonal is is now 3 and that square is 6. which does absolutely nothing um [Music] it means there's a six in one of those two squares we get a pencil mark we don't seem to get any elimination we get a three in one of those two squares you are kidding me um we had a three on this diagonal does that matter we've got so now we've either got 14 or 16. so if we've got 14 plus 3 we'd have 17 these squares would have to add up to 13. that would mean this couldn't be a 1 because you couldn't make those add up to 12. but it could be a 2 because you could make those up add up to 11 but only with a 5 6 pair here 5 would be there 6 would be there that looks doable oh bobbins um okay uh so what do we do now we could look actually we could have a look again at column eight and nine look because i've now got 15 in those two squares now those squares these squares together had to add up to 45 from the work we did earlier we've now got 15 and 18 33 these have to add up to 12. we know there's a seven or an eight in one of them now admittedly this isn't a massive restriction but i think these these squares therefore have to be from the digits four five seven and eight that means there's definitely a it's the same we haven't actually i've not done anything there sorry that's just completely useless uh there's a six in one of those two squares which i already knew if i'd thought about it so okay so what have i not looked at the 29 diagonal i've still got three cells that are pretty much unrestricted and could all well we could have eight seven eight down there for example and that would almost get us to 29 before we even consider the other squares 15 diagonal i've got to make sure those add up to six four six good grief all right i can do something with this square this square can't be a four and that's again to do with this domino here if we put four in here what happens well because because you get a six here and a two here so remember this square will be a two but because of the way that these two squares have to be if this is four and maybe i'll do it long hair if this is four that has to be a five one pair to make this 15 work so this is a 2 but i just said this square is going to end up being a 2 as well because once this is 4 the only way of making this domino add up to 7 or 8 is with a 6 2 here and look what happens there that is not easy and that's probably something easier than that to see here but unfortunately i'm probably best once we're reaching this length of video not to spend too much time trying to find it so this square is a five that's a four that means this is a two this is a one to make the fifteen diagonal work the four here look means this square's a five this square's a five this square's a four there's now ah we've now got a four six pair in this box two means this square's a one so this must be two or three let's get rid of the three pencil marks there so we're not doing too badly we've got ah 21 diagonal do not ignore the 21 diagonal these have to add up to three so this is two this is a one the two does absolutely nothing the one does you've guessed it absolutely nothing i don't believe it you rotten thing oh the 30 diagonal now look that's better than it was i've now got 5 on it 5 plus 14 is 19. 11. this ah look at that this five has made adding these two to eleven impossible so this this now this diagonal cannot be double seven in the greens it has to be double eight so just to show you that long hand again this is double seven now you can see we've got nineteen on the diagonal these would have to add to eleven nine seven sorry nine two four 3 8 are all ruled out so this would have to be 5 6 and this square here can't be either of those squares either of those digits so the we now know green is eight we know purple is seven that's going to give us that gives us a 2 here so red is 2 and blue is 1 and that this diagonal adds up this diagonal adds up these this diagonal now now we've got 21 these have to add up to nine without using one eight or two seven so this is three six or four five that square's got to be 5 or 6. this square's got to be 3 or 4. 1 3 4 into the balance of this column 2 5 6 into the balance of this column 5 7 8 into the balance of this column and surely this stuff down here is resolved isn't it we've got no what a puzzle this is it's ridiculous absolutely ridiculous even after the ridiculous beginning um it has remained ridiculous i mean just it's beautiful and barbarically difficult um okay what am i missing here what am i meant to be looking at that i've not looked at i've looked at everything that can be done surely this i still don't think this diagonal is in in any way restricted i've done all the other it's got to be sudoku of all things that's ridiculous that i have to do sudoku in a sudoku puzzle um where is the sudoku to be done are there obvious weak spots in this puzzle they don't look to be any um seven eight pair there two three five into those squares look that's not five this square maybe this arrow maybe this is the arrow i've got to focus on i've got one three four and six into those squares one three four and six this is not one um can we eliminate anything from this square if this is 4 this would have to be a 1 3 pair which looks possible if this is 5 a 2 3 pair looks possible this is 7 a 3 4 pair is possible this is 8 a 5 3 and a 6 2 look possible good grief um so we've got to find something else to do that's going to be some trickery we can i i'm not exactly sure what i'm meant to be looking at here what i'm trying to do is just uh is almost good lift this in my head which is a big difference between you know bifurcation as guessing and visualization which i think is fair enough but i admit it's perhaps not as satisfying as some things we can do let me just try and spot something uh three five two three two three two three two rules out four and five and seven that would force two six here three two six that's eight therefore so this becomes four that breaks it good grief right okay i have something but it's not very pleasant um this square cannot be a three now the reason it can't be a three is complicated and it's to do with this arrow this square and this square okay i thought it was complicated but if this square is three you can see because this is five you're going to get a two on this arrow so let's do this long hand three and two go into these two squares now the interesting question is what this square can be now in order to make a valid total with this arrow so we 4 is no longer possible here 5 is not possible because we can't put 3 here anymore given the 3 there 7 is not possible because 5 can't go there so this square would have to be 8. now if this is 8 and this is therefore 6 the question is what goes into this square well this square has to be a 4 because remember these squares were adding up to 27 and we worked out this had to add up to 12. so but once this is 4 we get a 6 4 pair boom that square is broken and that is horribly complicated i'm quite sure there's a better way of doing it but that is the way i found and i'm taking it that's a two [Music] um i'm taking it and it does nothing oh come on you are kidding is that that has literally done nothing um oh good grief what does it does it do anything in this column deleting a 2 from this square means this square can't be a 6 anymore because if this is a 6 we can't make this add up to 9. does it do anything else 2 and 1 sorry 3 and 1 is still possible this can't be 5 anymore can it i don't think no it can't so 5 comes out of there seven eight six can you put a six on this arrow oh no you can't hang on hang on look this is it this is it once you remove 6 from this square where does 6 go in the column you can't put 3 6 in here for exactly the same reason we couldn't have the 6 and the 3 interfering with this domino before three and six just utterly you know massacres this domino because it removes um it forces it to add up to six which this can't be so you can't put six in this domino so if you can't put six here look at the column where does six go only there and that might help not much else has but six yes six forces the ten arrow doesn't it so that forces the two forces to eight forces the seven gives us a three locks something out of this square now this this nine arrow can't be two seven or three six so it's four five or one eight um now i can see that three look is on this arrow so three is not there that's in just in looking at column nine so three is not here and has that done anything for us so hang on a minute i put a lot of digits in eight is not here anymore seven is not here anymore yeah there is there is stuff going on isn't there is i'm gradually whittling this away or whittling away at this um these two squares had to add up to 12 as well so once i remove seven from here i remove five from here which this already seems to have got rid of once i remove eight from here i have to remove four from here five eight so this is now either five seven or four eight i'm not sure the order of that come on simon there must be something we can do here so five actually five can never go in that square now that's it got it if this is five what do i put in here to add up to a valid total nothing nothing works this is not five this is three this is five that means this must be an eight arrow because this can be no less than three that means that square's a five we know this domino adds to twelve so that's a seven that means this is a four a six and a one and finally i think i might be getting somewhere um five is not in those squares okay that ran into a cul-de-sac quickly um [Music] one one is in those cells in rows five and six so i've not yet put a one in row four it can only go into this square that's not on the useful diagonal i think this 29 diagonal going gonna have to come into play at some point in a minute eight here means we've got an eight one figure figured out on this side actually that means this square is a one that means this square is not eight that still doesn't fix the eight though the eight can still be in one of two places in the column good grief um okay these three squares we know what they are yes we do three six and seven we know that's not seven these squares they are two four and five do we know anything about those the answer is no apparently oh no um i don't know what i'm missing here but it seems like the world is passing me by as i try and solve this puzzle um maybe i've got to try and get this diagonal sorted out now what have i got on it so far i've got 15 i need 14 from those squares incredibly average of course so this square is 4 6 or 7. six really i'm not sure what i'm missing here these squares are two three four and six eight ah eight by sudoku look in this box is that fixed i think it is eight yes it is eight goes there so this is seven this is eight that means this is five oh we are getting somewhere thank goodness for that this is not six this is not six this is not five so two three four and seven into this square that's gonna only be four or seven looking at the column four six here we've got anything else we've got i don't know if we do i really don't know if we do come on simon what are you missing here uh i don't know this video is one of the longest we've ever done i think i'm getting tired as well i hope that you'll forgive that it it's actually getting dark here such as the length of this video four six so this is definitely got two three into those squares oh dear come on what are you missing i must be oh i know what it is it's the 30 diagonal isn't it once you get this six you know this square has to be a three this is a four and does that do it for us it gives us more de ah yes it does this three sees a six here therefore we get a three seven pair this is not six two four five triple there two three four seven quadruple there two five pair here so this is not two this is not four either because of this four so the three six seven triple so now maybe at last this is going to be the key 15 i need these to add up to 14 yes this square can't be a seven if that's a seven you can't make those other two squares add up to seven because if even if you put six here you can't put one here this is three this is seven please please keep going that's a six that's a four that's a six that's a seven um this is a three there is a storm going on outside now so clearly fistima fell is angry that i'm about to finish his puzzle i think right now this diagonal again let's revisit it i've now got 15 9 is 24 this square has to be a 5 and that 5 is i think gonna finish the puzzle wow oh my goodness me click check yes i did it it took ages and it was monstrously hard but i did finish i did finish wow what the puzzle i mean even after the break-in which the break-in is beautiful and very clever and unusual um but what surprised me was after that it's just unremitting there's some beautiful logic all over the place as well and even when you find some lovely deductions um it you know they don't go you know it doesn't the puzzle never collapses it keeps sort of holding out on you it's a remarkable setting feat it really is i'd love to know how many of you solved that i'd also love to know if there was a quicker way of doing the whole back end of that puzzle i have a horrible feeling that i missed something and there might have been a more you know a swift away so let me know in the comments if you found a swift away let me know in the comments if i deserve a clap or not and uh yeah i enjoy reading them especially when they're kind 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: 65,605

Keywords:

Id: 3dVG6KfhMoI

Length: 75min 26sec (4526 seconds)

Published: Sat Mar 13 2021