How Can This Sudoku Exist?!

[Music] hello and welcome to Saturday's edition of cracking the cryptic I move my microphone a bit closer to me now it's Saturday but of course it is also international pi day it's the 14th of March today and those mathematicians out there or people like me this is a lovely day of the year 3.14 and many of you many of the viewers of cracking the cryptic seem to be well aware that this state was coming as well we have literally been inundated with puzzles based around pi day I would say probably about 20 puzzles we've received from you guys so thank you very very much for sending those to us and creating them now when I'm what we've had to do is decide which puzzle we are actually going to show today and that has not been easy our testers have loved a lot of the puzzles you've sent and I feel I feel bad actually that you know some of them won't get the publicity they deserve but we had to choose one of them and we have chosen this one because visually this is quite stunning I mean it's unbelievable you can see that we have 20 decimal places of Pi in a circle around this grid 3.141592 I check this earlier on it's absolutely right goes all the way up here and then the 20th digit is that six in the very center of the grid and believe it or not this is the creation well you will believe that it's the creation of art Van Deventer in the brilliant Dutch setter but it does have apparently a unique solution now a unique solution there's one variation that you need to be aware of before we start to solve this and that's a nice tie-in with the channel at the moment because this puzzle is actually a king Sudoku so those of you who don't watch the channel regularly may not be aware that last week we released chess sodoku which is our third app it's been very very well received we've been absolutely delighted with the feedback but one of the puzzle types featured in the app is kinks Doku now how does King Sudoku differ from regular Sudoku well let's try pick a digit here them is seven let's look at this seven this seven ordinarily would rule out these three squares from being a seven but in king Sudoku it also rules out this Square and that's because if this seven was a king in chess it could move to this Square it's just one away it just moves one diagonally so that is the extra constraint with King Sudoku and yeah apparently this puzzle solves I say apparently our testers have tested it they tested all the puzzles we got and they have confirmed that this is indeed it does have a unique solution and it's not easy apparently so I would let you into a secret which I was told by our thorne our Bandar Veterans friend when he sent this puzzle in he said that the the eighth digit is it is a struggle so I think we're going to be able to get seven digits in this grid and then we're going to struggle so we're going to have to put our thinking caps on to finish it off and with that let's get cracking and have a go now if you want to have a go you can always do that on cracking the cryptic you just click on the link under the video and that will take you to this webpage where you can play along with that let's let's see how we get on so we'll start with the ones look we can put some ones over here threes over here there's these threes back and in fact we get a three look because of these threes in the grid that means that square must be a three that puts a three over there now immediately my eyes are drawn up to the pencil marks threes I just made and whenever I get this pattern I always focus on it now why is that well it's because if we look at this box you can see the three is locked into column eight or column nine if you look at this box the three is locked into call or column 9 therefore we've got enough threes already in this puzzle in column a and column 9 in column a and column 9 there will be exactly two threes and we know that they must fall in those four squares so where do we put the three in column seven whoops it must be in one of these three positions in fact we have a three over there so in practice in one of those two positions now let's carry on we can pencil nuts and falls there choose and Center nines up here cuz of these nines ah ah now look we can pencil mark sixes into those two squares because of this six and this six but that is not as far as we need to go because this six if it was a chess king could move to this square so this cannot be a six so the six must be there which means one of those two squares is a six now in placing this six we took the pencil mark of a three so that must be a three that must be a three now because of the threes dotted round the grid this one means this must be a one it's the only place of one can go in the box and how many digits forgot I've got one two three four five so far so we haven't reached the sticking point yet five so we can place a five there these three squares have got to be four seven and eight in some order we don't know anything about four sevens and eights from the left-hand side of the grid there yet so let's just check the rest of this column why we need a two three five and nine so this square can only be a two or a three this square can only be a two or nine 5s must be in one of those two squares now I've been quite careful so far to only - only pencil mark in in two positions in boxes I may have to move to three positions sometimes in Kings move sodoku three positions is actually important the eights though look we can place an eight this must be an eight because this eight is going to force an 8 into one of those three squares so this square can't be an eight and this eight removes those eights so that's one two three four five six seven so we've now got seven digits so it's this next digit that's going to be the struggle can play our we can place eights and those two squares look now look at that this square can no longer be an eight because if I put an eight here I would remove both the cells in box nine that could be an eight so that cannot be an eight ah sorry about this just one second I am gonna moved yeah I'm gonna start pencil marking threes in just in case this is gonna be helpful so sevens you can see must be in one of those squares one of these three squares six is in one of these three squares falls in one of these three squares because of these Falls interacting none until are no nine we can do better than three squares because of course this square sees this nine so nine is actually in one of those two squares which means it's in one of these two squares because this nine rules out that square ones in the central box look can be in one of three positions and the reason this this sort of thing can be important is if we look at this box now a one can no longer go in this square because this one would see this square and this square in the column but it would see this square by Kings move and I mean I'm not seeing how that's immediately useful but this is why we might need to pencil three digits in a box what am I missing here eight look these eights interact so the eight must be in one of those squares which means it's in one of these two positions at the top and again these eights are interesting to me because that this rules out an eight from either of these two squares if I try and put an eight in one of these two squares I remove both of these squares as options so so the eight in the central box look can't be in any of those squares so that eight must be in one of three positions ah fives look this 5 here and this 5 here that's going to give us a little bit of a pencil mark in this box because 5s ruled out from there but this 5 sees that Square and that means the 5 is in one of these three squares in box for now again we've got an interesting pattern there that means this Square can't be a 5 because if this is a 5 it rules out that one that one and that one because of the Kings move and that gives us the opportunity to pencil mark 5s in the middle box now this 5 and this 5 so the 5 must be one of those three squares so we've got we've got quite a lot of pencil marking done in the middle box now we've got we haven't pencil marks for all the sevens or nines whoo-hoo right now that is important this is very hard to see but let's have a look at this square this square has suddenly become magical because we can see it can be a - from our pencil marks but the only numbers we've not pencil marks yet in the central box of four well it can't be a 4/9 well it can't be a nine and seven well it definitely can't be a seven because look there's seven here would rule out this Square and this square by Kings moves and that one and there would be nowhere to place a seven in this box so this is not seven the only digit this can be is two it was sitting there as a naked single the whole time but that seven there rules out of seven from that square but that doesn't change what we just did so we have found our eight digits now what does it mean the numbers Mason what do they mean oh well I thought that would be more helpful ah but hang on let's look at this column you need when you still need one five six seven and nine we'll look at this square that sees a five six seven and a nine it sees the nine because of the kings move so this square can only be a one now that's gonna look a one up here I mean I just want to pause just for a second and say how on earth did our van der bettering figure this out I mean this is absolutely absurd that you can put PI to twenty decimal places in a circle around a grid add a kings move constraint and it's a unique sodoku it is mind boggling I mean you wouldn't even think to try it you just assumed it wouldn't work anyway let's carry on these ones look I can see they look a 1 into one of those two squares but that square sees that one so this must be the one now that force is this to be a while which means this must be a 1 and all of a sudden we are starting to make proper progress aren't we now in placing this one we displaced a pencil mark 6 so now this square must be a 6 desperately trying not to miss things here in eights are here the 5s are here the sevens are here we've not placed a 4 I'm going to pencil mark falls in actually I know that's a bit naughty 2 pencil mark 4 falls in a box but just to make it clear to me that I've all of the digits have been sort of addressed but that actually this square look can't be a 4 because if I put a 4 here I'm removing a 4 from both those squares so this square has to be a name which means that's not an 8 oopsy it's not an 8 so this is the only place an eight can go this 8 removes that square from being an 8 so now we've locked the eights into one of these two squares that's not that helpful actually ah but the 9 is helpful now because the 9 now shifts up there which hits this 9 so this must be a 9 must be a 9 in one of those two squares now also when I put that one in yeah there's a one over here look I meant to put that one in as well so the one here and in placing that I displaced a 3 which must now be here which means that's a 3 good grief now we've done all the threes now we've done all the ones now and in this room ah now in this row in this row we need two four and eight but this square can't be a four because if this square is a four I can't put a four in the middle box because this four would rule out those three squares normally it would rule that out by Knights move and that four rules out that Square and there would be nowhere for a four to go so the four is not in this square which means this square can only be a two can't be an eight because of the APA so that's a two which means there's a two in one of those two squares so these three squares now are four six and seven so let's do some pencil marking that's four six don't yet know about seven let's just pencil mark them all in sevens and fill in the two here which means one of these two squares must be a two now let's finish off this row as well because we still need to place four and eight and you can see we can do that now because of the four up here so this square is a for this force he's the four seven here sees this square this square can't be a floor anymore so that's a seven and that's of four this four rules out that from being a four so it must be a seven because we fully pencil mark that box I remember doing that now this is a four five pair that means that this can't be a five now seven means these three squares can't have seven into the seven shifts up into one of those two squares where it meets its friend the nine so these these are a seven nine pair which means that's not a seven at the bottom and one of these squares needs to be a for now the four here means the four must be one of those two positions so this square can only be a five and look up five is gonna fix the five in the for their this four C's this square can't be a for now so this is the four this is the seven that Square down there must be a six this square here must be a four good grief now this must be the age we've had that hanging there for a while oh now they ain't sees this for eight pair so this is the age this is a four this four here sees the bottom of the grid so that's four seven six this eight sees the eight at the top is all coming together now it's I mean it's mind blowing this absolutely incredible you can see this is a two seven pair so we shouldn't label that up and just check whether we can see how to resolve it now down here we need 2 7 & 9 so this is a seven this is two or nine I'm just trying to check the diagonals as well to make sure that we're not missing a trick there these sevens mean this is a 7 this 7 not only sees this two seven pair but look it sees the 7 9 which we could have resolved anyway because we had eight numbers in the row just having focused on it at that point that means that's a 2 this is a 2 this is a 5 that Tuvix is the two nine at the bottom that should be 9 that should be a 9 that should be a 9 this square must be a 5 this square must be a 6 I think so we need 6 and 5 into these squares and as I've made a mistake that looks yes what a stunning puzzle that's ridiculous absolutely ridiculous so happy pi day to all of you let me know in the comments what you make of that that is one stunning puzzle and we'll be back tomorrow with another edition of cracking the cryptic [Music]

Channel: Cracking The Cryptic

Views: 532,541

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Id: N41yZsxIsK8

Length: 21min 1sec (1261 seconds)

Published: Sat Mar 14 2020