The Hardest Sudoku... And How To Solve It

[Music] hello welcome back to cracking the cryptic where I'm in a good mood at the moment because I had a few emails over the last few hours with some amazing looking puzzles attached to them so I think it's going to be a treat this next week on cracking the cryptic but today this this Twitter poll that I perhaps foolishly instigated has produced a clear winner you want to see the hidden clone Sudoku from Sam's test in the Grand Prix apparently I shouldn't have said in the video where I advertised the poll that I really didn't want you to just hit back because do you all then chose it so originally the tic-tac-toe was winning but no you can see it's a pretty clear pretty clear majority so what what can we say about this hidden claim before we start with it let's have a look at the results from the GP here we are so if we scan down here yes this is quite interesting there were a lot of top solvers who have solved 13 of the puzzles and who have scored 505 points out of 600 so the puzzle that they have not solved is the hidden clone so it's clearly caused trouble even at the very top end of the world ranks I mean teets time here I mean his his reckoning that's ten points a minute he's taking less than 10 minutes for the puzzle we're about to try so let's let's once we've understood the puzzle and solved it let's think about that time and think about whether it's mind-blowing or not I suspect it will be where's the puzzle now ah here it is so this is the hidden clone how do the rules work well this gray shape in the grid whatever numbers we put in the gray shape just let's put some numbers in to illustrate whatever numbers these are this exact sort of shape of numbers so let's say it went up here like this would have to appear identically in this one so you can see actually that shape wouldn't that's interesting actually that shape would not have been possible because the two would have shared a box so we need to reproduce this arrangement exactly as it is here not reflected not rotated somewhere else in the grid and that's the only rule apart from that it's normal sodoku now if you want to have a go and please do click on the link under the video and that will take you to our software and you should see something very similar to what I'm looking at here by the way the Akari video that I did when did that come out on Tuesday I think that seems to have worked in terms of the software so do check that video out if you've never tried an Akari puzzle they are fabulous to do and we found a way that you guys can actually solve along at the same time which is I think tremendous with that I'm gonna have a look at this now I mean the first thing to say about this is this is a ridiculous construction I mean what have we got here we've got I mean it's ridiculous you've got 14 given digits and very little interconnection between these digits so you can see that even where we have even where we have digits that are repeated in these these two sides sort of clusters of digits in the top right and bottom left I mean these twos how do they interact they they just don't really they just don't right okay so I do think we're gonna have to think about this shape we're going to have to think about the geometry of the grid ab initio and try and understand what it is that sam what is the restriction that this shape implies so how do we do this logically I mean there are obvious I suppose there are obvious orientations of the shape that won't work so if we focus on this square just for a moment and we say is any transformation of the shape that brings it this way possible and clearly it's not the same is true of this way and how do I Ella straight that well let's imagine that the whole shape just shifted one cell horizontally to the left what would that then look like you can see that it would look like this and why is this not possible well it's because this digit here has to be the same as this digit so it would repeat in the box and the row so any lateral shift of the shape is ruled out and by the same token I guess any vertical shift is also ruled out so in fact I think what I'm going to do is I'm gonna focus exclusively on this cell and how it can move in the grid so we now know that this cell here in the transform shape cannot come to any of these cells and it can't come to any of these cells and well more to the point I can't come to any cell obviously in this box because it's already in this box so we can rule out those cells as well ah yeah okay so and that's interesting because although that is interesting because anything that I say is true for this cell is also true for this cell around the symmetry here so I also can't yeah this is very interesting this is very interesting so I was just thinking what happens if I move this square into this box but the thing is moving into this box is not allowed not because of what happens to this cell but because of what happens to this cell and by symmetry if these cells are not possible these cells are not possible because this cell will end up with a repeated digit okay so that is a little bit interesting isn't it that is a little bit interesting right okay so now so I think what we've got to think about oh this is fascinating actually I'm spotting all sorts of things now so can this cell for example move down to this square here and the answer's no and again it's not because of the effect of this cell this cell can move here it wouldn't be in the same row column or box as it is originally but that knight's move of coming deficit from this cell to this cell would break this square here because this square would come down to here a knight's move away where it would share the same 3x3 box so we can also rule that out now can we go further than that I can't move it down here a knight's move what about so I'm gonna remember we've got these six to rule out and in the central box well it's interesting actually because any shift down this way so all these are ruled out in turn by because they're too low in the grid so this what about this transformation so why is that not a valid movement of the shape from there to there what what what is the problem with that so you can see this one would be okay this one is the problem isn't it that a nice move of that one takes it to here so that's also ruled out okay so we are really running out of room now we've ruled out or it can't come laterally this way it can't come down here it can't come here so we're left with transformations that come can't come here because there wouldn't be enough room in the grid so that's ruled out so it actually has two if it comes this way it's got to map onto itself and if it comes up here we can rule out this square as the mapping because that square is a knight's move and that will break this square so that's not allowed so we've still got these squares to think about that one's obviously that one's definitely impossible because that would if we try and shift this one to here it takes this one outside the grid this one is impossible because that by a knight's move this one would move to their be in the same 3x3 block so we're left with those squares there that ones ruled out because it's a vertical shift that ones ruled out sits outside the grid wow so the only two positive so it so we now have locked this has to shift diagonally either up or down good grief okay sorry that's a very long way of getting to that result but I wanted to explain that slowly for myself that's what it's with you guys but I think I've convinced myself it must move along this diagonal now does it move one or two well it can't move one because if I shift this to here although this cells shift would be fine this cell shift would not be this estelle with map to this cell and these would have to be the same digit so in fact this cell Maps either to here or to here in the finish grid Wow okay so which way should we go first let's go let's go upwards so we're going to say that the this cell is going to map like this this is going to be our transformed clone and what does that mean that means that this digit is the same as this oh right I see so that means this digit and this digit are equal to one another but it doesn't just mean that because as this clone shape shifts of the grid this cell will map onto this cell so actually these three squares are all the same digits okay so that's fascinating isn't it so similarly these three that the right are any different colors here so let's do let's do some different colors these digits colors mean it's the same digit and we must have the same thing going along there so we get a very pretty pattern like this and now can we make progress oh this is so clever yes it is so clever haha I mean sometimes when you solve a puzzle you just think I am in the presence of a greater mind here because I mean not only as Sam had to sort of have the idea but to execute it like this because now once you know these three digits are the same effectively they are all subject to massive restrictions now because I mean look at this square for example that square sees these three cells but this one also sees those four cells so actually the range of possibilities for these three cells here is quite limited so all of the highlighted digits are not possible so it's got to be a 2 a 5 or a 9 okay I'm slightly disappointed that it still got three options but I think it does so let's do the same now for these three digits we've got those that seize that one those two this one this one sees that one as well and that one okay I think I've got those highlighted so what do we see now we've got oh that's right that's much more restricted that can only be eight or nine let's look at this one so that's those three gosh dot that one c-47 this one sees the two and one so looks like one two three four five five or nine I think oops I pacify the added five or nine and then these ones see imagine doing all of this computation in a test in under ten minutes and finishing the whole grid as well just imagine that okay so that one has to be seeing everything apart from seven eight or nine so we have to remember here that when we when we're thinking about each of these possibilities we're not just saying this is eight or nine if this is eight it will be eight eight so for example ah yeah okay so look we can't have seven in any of those position or in all of those positions because watch if that's a seven that does that and now I've got to put a seven here in this box and there's a seven there so that instantly rules out seven from all of those positions oh yes which gives us an eight nine pair which means this is a five so this is a two now it can't be it can't be a five or a nine because there's an eight nine in the box holy moly now this is a five good grief that's a - that's a to - in one of those squares - in one of these squares now of course so far I've not figured out why this doesn't work but it it's a bit disconcerting because we I'm not sure whether there was a way of me eliminating the shape transforming down there before I started on this path but there may have been I tell you what we'll do if this does work we'll go back and we'll check Y the other way didn't work right hang on let me look at this so five here is cool because that rules out of five from this square now that means there's a five locked into row eight and row nine in this bottom box here now that's nice because it maps with this five these fives here also in row eight and row nine so where does the five go in row seven but the grid well it must be in one of these three squares and actually we know we must be in this one three four here locks A three and a four into those two squares and that's nice with the six now so the six now has to be in one of those three squares in that box so it must be in one of these two positions in the top left box that means it's here and what next so there must be a six and a seven in those three squares because we know this one isn't seven so now there's a seven in one of those two positions seven in one of these two positions ones are in one of those two squares 7s are in one of those two squares similar thing going on down at the bottom there look ah now hang on oh hang on yeah look at this this Square and this square they are a six seven pair because look we've got eights and nines aligned in column four and column six and in this box we've got one two three four and five so these two squares are in fact the 6 and the 7 let's remove the other pencil markings so this square is an eight or a nine to complete the box now is that enough to give us anything useful eight nine maybe but I'm still not quite hang on that we can look do more work with the eights look so we've got eights here and here and here and here so that's an eighth opportunity over there and nines are also restricted so this has to be a nine she looks nine over there and the nine down here must be a four in one of these two squares now because of the four in this position and hmm okay so we make I'm sort of making slow progress certainly not crushing this though it's not easy we can put another eight in the grid because of this eight nine pair here we've got a similar thing to the logic I explained it down there with the fives eights are locked into one of those three squares because they can't be here and that marries up with the eights there look so now down in this box the eight must be in one of those two squares two sixes what's the next step that we need to find here so up here in this box we've yet to pencil mark one's threes and fours oh oh so that square sees a 3 and a 4 look does that just been sitting there the whole time yes it has this is a one oh that's important look that's going to give us a one on a 7 there which means this is an 8 9 pair this must be a 3 or a 4 sevens can be pencil marked at the bottom now and can we get any further from this logic so we've got the eight nine pair here the eight nine pair here the seven is resolved this square must be a three or a four still can be either I think we look down this column and ask where the one can go now it must go here so this square is a three or a four these squares down here have got to be well the three is very useful now isn't it because that's going to give us a three a nine hopefully five and that locks a five here look wow so now we might be starting to cook with gas four three four three four now does this we've got threes are the fives a resolved now just the three do anything yes the threes are resolved now that locks three into one of those two squares what a puzzle how do you get this puzzle done in under 10 min how do you get it done in under 10 minutes it's absurd anyway I wasn't get distracted by that so what because it's upsetting me this three six and seven here so this can't be a seven can't get any further restriction here we still don't know which way around these eights and nines go as soon as that written as soon as I can get one of them I can get all of them so maybe I should focus harder on trying to do that yeah look we've got an eight nine pair here that sees eight pencil marked so maybe I can get an 8 into that square is that gonna be enough no seven this square here has to be a three or a four seven threes here feel like I'm in one of those situations where I've almost got too many pencil marks now we've got one four six where does a one go in column 4 look these two squares can't be one in fact a better way of looking at that might be to say those two pencil mark ones here so this square has to be a 1 which that gives me a 1 2 pair over here look so I've managed to pen some are the same digit into two squares this one could no longer be a 3 so 3 must be here 3 1 2 so these squares have got to be 4 6 & 9 and you can see we the fours are pin Tsering those two squares so this one has to be the 4 which gives us the 9 and gives us the 6 now 6 allows us to tidy up this square these two squares form a 3 7 pair in the row which is resolved by that 3 so finally we get a bit more done this square here that's got to be a 3 I think and these two squares here I've got to be 4 & 6 just still not as I don't believe it how can that not be resolved yet these squares have got to be 7 8 & 9 these two these squares are therefore got to be 1 2 4 & 6 six is forced to be here on to four into gaps that again the fours our pincer in local force are operating on these three open squares and forcing for two and one like that which gives us the one in the two as well now this has to be a 1 this can't be a 9 this is a 7 or an 8 I keep coming back to the colored squares thinking I must have got them now and I still haven't uh but now I know well now I might have because now at least I've got another 9 in the grid this square here has to be a 9 look because we sit need a 7 and 9 for the row there's a 7 here so we can go 9 7 8 9 ah ah ha ha look now last I know what this digit is NaN the moment I get this digit I'm gonna take advantage of the logic fill 8 up there and nines back the other way just to show I've understood the puzzle and now that's a 7 which gives us 6 7 these two squares have gotta be 2 4 & 6 as usual so rack is resolvable now so that's a 6 and that's a 4 this is an 8 this isn't a this is a 9 now I think let's check yes that is the solution to the puzzle so I am just briefly how am I going to do this I'm gonna pause while I unwind the puzzle to the very beginning and we're going to prove that the other way didn't work what a puzzle right one second okay so it would have been very simple to prove it the other way round so what I've done is I've labeled the squares up and highlighted them by reference to what they can be using exactly the same technique we did the other way so if we have a look down at this box for example you see we have an 8 9 pair and a 5 9 pair so there's far too many nines in this box so we could immediately actually have ruled this out as the other option so we would have known then for certain we were working on the right iteration when we should the clone up to the top left what a puzzle that is what a puzzle I am lost in admiration the teat and the others who solve this puzzle under exam conditions so fast and for Sam of course for creating what is an absolute work of art amazing I hope you enjoyed it let me know in the comments and we'll be back soon while I'm back tomorrow with another edition of crack and cryptic [Music]

Channel: Cracking The Cryptic

Views: 550,923

Rating: 4.939363 out of 5

Keywords:

Id: 8s7LPmQyWHA

Length: 29min 45sec (1785 seconds)

Published: Thu Feb 13 2020