The Sudoku That Broke The World's Best Solvers

[Music] [Applause] [Music] hello and welcome to tuesday's edition of cracking the cryptic and on screen we have the puzzle that mark has persuaded me to try it didn't take much persuading to be very honest with you um it's this puzzle that richard stolk has has recommended to us and it's by arvid bars the dutch constructor and it has a very interesting history um so i'm going to tell you about it now i mean the way the way we came to hear about this puzzle is that i got an email from richard uh basically saying that he'd seen we'd done a few xv sudoku's on the channel and we're enjoying them and had we seen what he described as an incredible incredible gem of a puzzle uh by arvid and and we hadn't seen it and we looked into it a little bit now this puzzle comes from the 2017 world grand prix final which is something that happens at the world sudoku championship each year and basically they sit down the uh the very best solvers in the world who've competed in the grand prix online over the year and they let me just find it they all have to sit at a desk exam style they are presented with a series of puzzles you have to do them in order so initially you can see they were given a classic puzzle and look at the times taken for the classic puzzle here it's quite it's quite indicative i think of the level of competitor we are talking about here sonja quack under two minutes and now this isn't this isn't you know a new york times easy puzzle this is a world championship level classic sudoku and we have a time here of under two minutes i mean all of the times are frankly incredibly quick for what will be a reasonably difficult classic sudoku and what happens is you solve the puzzle if you get it correct the marker takes one minute to check and then if you're correct you get the next puzzle which was the xv puzzle which is the subject of today's video now here we have something quite quite extraordinary going on and i cannot think of another example of a puzzle i've ever seen in a competition of this nature where the times for solving it have been so incredibly varied and at the top end mind-blowingly long i mean well we'll get on to it but just just let's just have a look at some of these times sonja quack was the fastest he did it in what's that about seven seven minutes but that includes a minute of checking so six minutes for sungjae quack for this puzzle which is it's still a long time don't get me wrong for solvers of this standard six minutes is a long time for a sudoku and then we have the vast majority of them taking well over 10 minutes i mean kota morinishi three-time world sudoku champion has taken over 15 minutes to solve this puzzle you know you know kota is a bona fide genius so already we're getting to problems but the one that really stands out for me is this one um now thomas is a friend of mine and he is i mean he is a bonafide genius um three-time world sudoku champion world puzzle champion regularly used to finish the uh the us puzzle championship each year and if you've ever tried that to finish it in the time that you're given is absurd i mean it is brain power that is off the scale and thomas you know i mean he would have a claim to be the best sudoku solver that ever lived in my opinion uh certainly when he was really able to devote time to puzzles he was almost unstoppable uh nowadays thankfully he's off sort of curing medical very very difficult medical problems and you know i can think of no one better to do that no one you'd rather be working on those sorts of of questions because you know he is just phenomenally clever um now just look at the time 50 minutes and that includes one error so i imagine what what's happened is he must have he must have made a mistake on the puzzle or something and then found it very difficult to unwound unwind what's probably you know a sudoku with lots of pencil marks all over it but i can i i well i mean thomas i know he watches the channel sometimes he may he may comment but uh for thomas to take this long on a puzzle is absolutely unheard of so this this puzzle is something else altogether um and you know for that reason it's slightly daunting to try it in a video but the fact that sanjay's done it in as quick time suggests there's a trick so if we find the trick hopefully we'll be good to go if we don't find the trick this is going to be a very long video and quite embarrassing although if i do beat 45 minutes i still beat probably the best sudoku solver that ever lived so happy days shouldn't count my chickens though that's what my parents always said to me do not count your chickens before they hatch so yeah i won't do that um but yeah this puzzle is i mean it's stunning the standard variation in the time solving times here is something you very rarely see in these competitions um it tends to be far far more regular and yeah this this this is really very very interesting um so here's the puzzle now we've done xv on the puzzle on the channel a bit recently so hopefully you'll be familiar with the rules but let me read them to you anyway we've got normal sudoku rules apply all horizontally and vertically neighbouring digits with the sum 10 are marked with x all horizontally and vertically neighboring digits with the sum 5 are marked with v there's actually no v's in this puzzle look so what we're looking at here is dominoes so if a domino adds up to 10 there must be an x if it adds up to 5 there must be a v if it if there is neither x nor v dividing the cells in a domino it cannot add to 10 or 5 and the negative constraint often in these puzzles is key to solving them efficiently do have a go i mean how often do you get a chance to do a puzzle that's you know that's flummoxed one of the world's great intellects very very rarely the way to play of course is to click the link under the video and with that with the aeroplane going overhead let's get cracking um now oh i tell you what before we get cracking though can we just take a moment to settle back and admire the construction the beauty of this setup we've got symmetrically given sort of pattern of digits in the bottom of the grid laid out x's in the top of the grid no v's at all i mean it is a gorgeous looking sudoku um you know and when you get constructors like richard stock who is one of the very very best constructors in the world specifically taking time to write and say look this puzzle is something else you i mean it really is a testament to how how good the constructing powers are that have been sort of focused on this puzzle anyway we're all with that let's go let's go what am i going to do to start with enough jibbering um we can right yes we can i can enter a digit actually i can enter a digit by thinking about box nine now why is box nine catching my eye well it's this one that sits in the middle of the box because the one touches all four of those squares now uh if any of those squares was a four you would have to see a v between the one and the four now as there's no v there's no four so the four must live in one of those cells and that means by sudoku that square is a four and we are off and running chasing down one of the finest soldiers who ever lived um [Music] okay now let's do it again actually the one in row seven is also now very restricted it can't go here and if it went there there would have to be a v again dividing the one one and four because they add up to five so the one goes here seven eight is also disambiguate so there's a bit of a gimme at the start here i i'm absolutely sure this wasn't what held thomas up so you can see where does seven go in in row seven of the grid if it went here it would be next to a three and there should be an x between them so it doesn't go there that's eight that's seven and we're off and running um [Music] okay now can we do any more tricks regarding this square can't be a two because it's next to a three so the two must live at the bottom of the grid and therefore it lives in one of those two cells similarly with seven seven can't live here because it would be next to a three and there should be an x dividing it so 7 also lives at the bottom of the grid if you've watched me solve these before you'll know that i do tend to miss these negative constraints so i am really trying to focus on them today um oh no hang on look if we look down column eight we've got a one two and a seven in the column so what can this ten be well it can't be one nine two eight or three seven so that's four six same in this column look similar thing one nine two eight four six all ruled out that's gotta be three and seven this one maybe as well yes that one this one can only be one nine two eight three seven and four six ruled out this one ah now that one's not quite as constrained that can be 2 8 or 3 7 so this one's a bit less a bit less good um now ah no i see i see right okay so there's a trick going on here this is very beautiful very beautiful let us consider in fact it's gorgeous yeah these dominoes what can we put in them well you might look down here and go well this one could be three seven well it can't be and neither can this one either now why from a sudoku perspective it's absolutely fine for this to be three seven there's nothing in the column preventing it nothing in the box preventing it but there is a problem here because this would add up to 10 and there should be an x dividing the cells and there isn't and it would be exactly the same if you try and put 3 7 here there's no x dividing the cells so in fact um in fact this must be one nine or two eight that plane is getting lower and lower i wouldn't want it to crash um one two eight nine i think it's the same for this one isn't it yeah this can't be three seven for the reasons we talked about so it has to be one two eight and nine therefore we get a quadruple here and we presumably this trick yeah this well no okay the trick that is not necessary here look because we've got one nine three seven in the box already so this one has to be two eight or four six just by sudoku same thing must be true of this one because this cell can't be one three seven or nine so that's two four six eight that's uh oopsie two four six or eight two can't go here anymore therefore uh okay so let's look at this column because where does one go in the column one's got to be in one of those cells because of this one here so apart from that we're left with what is it five seven and nine seven can't go ah is this a naked single then let's just double check that oh you know how another way of looking at this is though where does where does nine could never go next to the one this beautiful nine can't go next to the one because there would have to be an x between them so nine is in one of those two cells and it can't be there because there's a nine so the nine goes here so that forces those two so this was a naked single that's a five these two ah these two squares are one and seven and there's a three here so seven one we mustn't connect the seven and the three these two squares let's delete those they've got to be two and seven uh sorry let me just try and spot something i'm not racing today don't get me wrong i'm not racing um five look that's got to go in one of those cells at the top there just because of its options within this box so five is in one of those cells down the right hand side five therefore is in one of these cells five is the most useless digit though in xv sudoku because the x's and the v's just never apply to it so you don't really get much use from it [Music] okay so one thing i've noticed if we look at this column now we've got to place 3 4 5 and 7 and there's a 7 there so the 7 can only go here in the column which means there's a 7 in one of those three cells now three where does three go in this column now three can't go next to the seven so three must live down at the bottom there what else do we need to put in we need to put this uh well two is up here so two is not there is it so we could just get the two the two's been sitting there lonely for a while this can't be oh this is a naked single because there's a four five in the row so this can only be a three so these two are a four or five pair let's put that in so we need these squares here to be four five and eight ah that one can't be an eight because it's next to a two so i think this this square here has to be an eight it's the only valid position for an eight in the box that's not a two oh it's not a two undo so this is not an eight and we can actually look we're going to get these digi oh we are we are in fact going to get these digits because of the two here this square has to be the eight because we can't put the eight next to the two so we get the eight and the seven and we need to put one three six into the row this can't be three because it would be next to a seven uh in fact there's a three seven here i've just noticed look it's scanning upwards three seven there means this is a two this is a seven this can't be a three oh so three goes there in this box because it can't i can't go next to either seven this three helps me out at the top this has got to be a 2 8 pair now and now now we can do the trick on here again because now we've got the same thing going on down this run that we've got going on down this run these squares have got to be four six three seven in some order therefore this square is a one this square is a six this is a two-nine pair we can do it the two is going here um okay well this has been a marvelous start now it's probably going to grind to a halt but never mind at least at least we've had the joy of a marvelous start so those squares have got to be four and six i'm just looking to see whether i can get anything from the negative constraint i don't think i can so what i think i'm going to look at now is these i've got loads of columns here with effectively six digits in them yeah i'm not saying much better than that so let's have a look we need one six and seven into those squares so i'll label it up and then see if we can spot anything that can't be seven because there's a seven here okay not seeing anything better uh this one we've got one we need to put two five and six in here so that that's gotta be five or six two five six two five six i'm not sure this one we've got to put four five and nine again i'm not seeing anything here i'm so sorry if i'm missing what's staring me in the face it's very i was watching one of mark's videos yesterday and you know it it's so interesting i mean mark's a brilliant brilliant solver but sometimes he isn't seeing things and i'm getting so cross watching the video and then i'm thinking but hang on this is exactly what happens to you all the time um it is very strange when you're recording these videos because basically your power of sudoku solving disappears trust me uh these are three five and nine um that's ah now that one can't be three look there you go there we go three cells have got to be four five and nine so that's a triple oh this is beautiful it's going to give me these two cells if these cells have to be made up of four five and nine that can't be a five so this is a six and this is a one and now we might be cooking with gas let's see um six can be removed from this square and this square and this square and therefore four gets removed from that square can we go can we do any better that can't be three look i don't know why have i got that can't be three because this is two so that therefore can't be seven now if i look along here you can see that we've effectively got seven digits and we just haven't placed three and eight and annoyingly i don't think we can place the three and the eight yet maybe we can but i'm not quite seeing how um so we're gonna have to try and do something else i feel like this six and this one are important so ah they are important look um one nine one nine pair in column two and column three now that means ones and nines have to go into two of these three squares well can they be in a domino of course they can't because if they are you'd have to have an x between them so this square is not one or nine this is a brilliant puzzle isn't it the geometry here is just gorgeous so this is a one-nine pair and i've not put a 5 in the box yet so that's got to be a 5. that means this is a 5 look yeah the fives here all ruled out the five from there i just didn't follow through on my pencil marks so but as usual five is not that helpful hmm i suppose it gives us the five four five at the bottom ah which gives us the six four so maybe i shouldn't be so disparaging about fives they've actually been useful typical um now that's gotta be four that gets me into my four five nine triple look if this is four we can use the negative constraint to remove one from this square therefore we can use the x to remove nine from this square this becomes a one or a two which means that we can [Music] probably do some oh yes i can do something that's a 1 9 pair in row 3. so that square's got to be a 2 which means this is an 8 because of the x which means that these are not two and eight which means this is three this becomes a five nine pair we still need to put a one in this box these two squares are seven and eight in some order that's gotta be a three by sudoku because it can't be a one or a nine that's not three that's not seven this three fixes the eight over this side i don't wanna put nines next to ones that's the only negative constraint so i don't want to put nine next to a one why do i look at this i mean that's an example why do i look at this square first rather than that square which is next to a one the mind boggles or at least my mind seems to so now this has got to be a five this can't be an eight now what have we got going on that's got to be a 2 because there's a 5 in the row that's going to fix the 4 fix the 9 fix the 6. this can't be a 4 6 pair i think we're going to solve this which is good this 2 8 pair fixes that this is a 5. that's a 4 because there's a 9 beneath it 4 ruled out from there so 6 is ruled out from here six seven pair means this square has got to be an eight that's got to be a seven we can't put a one next to a four so we can put the nine in the one in we can't put a four now this is gorgeous you can't put a four next to this one so that's six and that four get resolved i mean they could have been resolved by that but the way i did it was frankly far more beautiful um one nine goes in here and here one nine goes in here and here this square must be a three i think that square's not a four six seven ah how does all this get resolved then ah there's a three here that's how it gets resolved mustn't put a 7 next to a 3. so the 6 7 gets fixed the 6 7 gets fixed up there that must be a 4 because there's an x relationship this must be a 3 by sudoku the 3 and the 7 get forced the 2 8 get forced again i could do it by sudoku but i'm going to use this three to do it eight two eight two and that's how to solve of its wonderful wonderful xv that was gorgeous the start the start was to die for i hope you enjoyed it as much as i did let me know in the comments let me know what i missed there's probably a whole legion of things uh i do try i promise um and we'll be back tomorrow we might do i might try fisting fell tomorrow i think i've seen there are a couple floating around there and they uh they're yeah they're making me anxious they've not been solved yet so look out for that tomorrow and we'll be back soon with another edition of cracking the cryptic

Channel: Cracking The Cryptic

Views: 339,480

Rating: 4.9571257 out of 5

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Id: 9ATC_uBF8ow

Length: 25min 7sec (1507 seconds)

Published: Tue Sep 15 2020