A Killer Sudoku With No Numbers At All?!

[Music] hello welcome back to the cracking the cryptic now it's Thursday today miserable day in the UK but I hope we'll be able to cheer up those of you who watch the channel from the UK because we've got a really interesting looking puzzle this has come into the channel from Christoph Selig and the brilliant German puzzle constructor and he was inspired to make this by a video we did about a week or so ago called PI R squared which was a beautiful beautiful construction from Nathan Gilbert which involved the constants PI and E and sandwich and and killer Sudoku and Christophe thought he would try his hand at making a variant now this puzzle looks to me to be my lips an extraordinary construction as I was putting it into our software you can see that these cages are completely unlabeled and these are killer Sudoku cages but all we know about each cage is that it must sum to a square number so if we look you know this cage for example that must sum to either 1 4 9 16 25 or 36 and some of those you can immediately rule out but that's what we know and apparently this this is solvable crystal says it's quite hard and it might not be suitable through video so I might be I might be mad and attempting it but I'm going to try it and and if you want to have a go yourself then just click on the URL link under the video that'll take you to exactly this webpage you should be able to try the puzzle on whichever device takes your fancy quick bit about min for a try this and try and solve this those who bought the sandwich to take your app and firstly thank you I guess but also the next 5 puzzles are up and running they have been for a couple of days now so if you haven't tried the new 5 puzzles there's obviously five new puzzles each month the first year then do read the question you should find a nice surprise now with that let's take a look at this now I want to start this well I think I've got to start either in this box or this box simply because at least I can at least there are complete cages within these boxes you can see I can see that in in this box there are four square numbers that add up to 45 because we know that every 3 by 3 will add up to 45 Inessa said okay because it will contain the numbers from 1 to 9 if we add those numbers up that's what we get and this one also therefore this is three different squares must add to 42 five so mmm let's just think about this for a moment for four cell cage here and so if we don't try and make three cages bats so if two of these were 16 that would give us 32 that would make the other cage have to equal 13 which is not a square so we're not using 216 if we use 16 and 9 that's 25 so the other ones twenties that's not going to work so we have to use 25 and the only cage that can be 25 is the four cell cage because the most I could make a 3 cell cage add up to would be 24 not that square but that that is the maximum so this must be 25 and these two cages must therefore add 20 which means they must be 16 cage in a 4 cage right so I can do the 4 cage this must be the full cage that must be a 1 and 3 this is a 6 I need to find some way of labeling these I think so I'm going to use colors so right for cages are going to be green in sixteen cages the six would transpose to that color so when you snap color for sixty 25 would be will use that color and nine cages therefore we're going to use that blue color and then if there are any 36 cages but let's let's come back to that if we need to right so we've got a 1 and a 3 here and I'm sure I can work out anything more about how these cages divide it is possible this one has a 2 in it but it's possible this one has a 2 in it as well well let's come back and look at this this box then here we've got 4 squares that add add up to add up to 45 and we've only got the maximum size of cages 3 cells the maximum square involved in this therefore is 16 so and that's interesting the most number of 16 we could have would be 2 because we could have a 16 in here and a 16 in one of these but after that we we couldn't repeat 16 again because a 16 is obviously a 7 & a 9 and then if we had a seven and a nine we couldn't make 60 in another way so the maximum number of 16 in this in this 3 by 3 is 2 and if there's one there's one 16 and three 9s that doesn't add to 45 okay right so this is this is definitely going to be 216 cages which out to 32 and then and then a four cage and a nine cage right now if we need to sixteen cages one of those 16 cages must be the three cell cage this is very clever so far not what I'd expect anything less from Christophe he is a brilliant brilliant setter good lord I mean I don't know how to have on earth my workout which is the other sixteen change I don't think I can okay now is this possibly even solvable I'm reluctant to get some of these other cages are so open I mean this this one is let's have a look at this one man this is more in desperation than anything else right so here I've got I've got three different squares and an extra cell and the moat I suppose the most number of 16 cages I could have would be I could have three sixteen cages here actually because this could be a sixteen cage and then these can both be sixteen cages although that's probably not possible cuz if this was seven and nine this would be it could be eight five three or eight six to the other cage couldn't add up to 16 so then I could only have two sixteen cages in here so two sixteen cages would be 32 and the sixteen cages could be arranged as one of these and one of these or the two three sell 16 cages goodness me to 16 to 32 and then I have another square cell which would be that could be 4 or 9 but it couldn't be 16 and if I had a 16 cage into 9 cages ah that is it okay right so if I have one 16 cage into 9 cages this grow would have to add up to 11 and it can't so therefore I do have two 16 cages as the base here let's imagine they're here just for the sake of me thinking about this so that we 32 these three cells would have to sum to 13 so this could be a 4 which would make that a 9 or it could be a 9 and that would make this a 4 so this square root of 4 or 9 and and I've got these three cells there's definitely 216 cages among them and so this was a 16 cage that would be a seven and a nine and then I need another 16 cage which would have to be have to involve an eight and then either a nine cage or a four cage but I can't if this was the 16 cage I can't make either of these two squares equal a former cage so that these would have to be a nine cage one of these two and this one can't no this one can't be a nine cage because look there's a 1 and a 3 already in the row so this couldn't be a 9 catch and this can't be a 4 cage so this one is a 16 cage goodness mate and that is going to be helpful if it's now look I've got two 16 cages and a 4 cage that adds up to 36 I know that row adds up to 30 45 so that square is a 9 Wow Wow ok now so this one this is a 16 cage that doesn't involve our of course I could have done this before this is a 16 cage that doesn't involve the 9 and it doesn't involve a 7 because one of these cages is a 16 cage so that means there is innate in here oops you need to do that it's not going to work on to 8 and therefore the other two cells in this box have to add up to 8 and they can't be 1/7 and they can't be 3/5 so this is a 2 6 8 carriage and I could have done that years ago so six-eight I wouldn't have got the nine though so suppose I made some advance this must be four five seven now less this is four five seven that's where either nine and that is useful because that means this is not a sixteen cage that means this is a sixteen cage without using a seven and a nine so it must involve an elite and it can't the other two squares add up to eight and they can't be 5/3 and can't be one seven so this is eight two six again and this must be one three right my goodness me this is this is incredible absolutely incredible that this is resolvable or seems to be actually resolving itself right so now this one three means this can't be the four cage this can't be the four cage because obviously I can't put a one or three in here so the only cage that can be before catch is that one so oh that's cage must be a 1 and a 3 this 9 therefore fix is a 9 here that means that's a 7 where's that now this cage can't add up to 19 it must add up to 16 and therefore this must be a 9 cage and it must be 4 or 5 this 16 cage still needs 7 more so it needs 2 and a 5 as it can't have 1/6 can't have 3/4 of these squares now our 4 6 7 8 obviously we can do a little bit of tidying up here this these two can't be 4 & 7 so this is six and eight therefore these two can't be six and eight they are four and seven this five points at that square there - that's five somehow we actually made some progress that is incredible now this nine is part of the two cell cage so in order for this to be a square this must be 16 let's color it in seven means that's not a seven but there's literally no way of making progress now unless we resolve something in the top of the grid so I'm going to look at this cage simply because we've got a number in it so I've got two three cell squares plus seven plus something have got to equal 45 so if these squares are both the maximum they can be a 16 the minimum they can be is 9 so if they are both 925 that would break the K in these two squares would have to add up to 20 that's not possible so there is at least one 16 if there are 2 16 32 39 these would have to add up to 6 that make that a 3 because we couldn't put a 10 in there if this is a 16 and 9 that would be 25 plus 7 is 32 this would have to add up to 13 and that would still be a 3 good good grief okay so that's incredible so that's always a 3 however these numbers are split so if that's a 3 that's a 3 and that's a 1 there's a 3 in one of those 2 squares and I don't I don't know how to resolve that I can't resolve it yet okay so let's have a look at this box now I know this box yeah I can we have to do something with this box just the same way again so you can see one thing I just want to say if you're solving this along with me oh you've already solved it this is just apps this is why I love handcrafted puzzles because we are being taken on a linear journey here you can see how this puzzle has been constructed you know it's clearly been designed we have to start down here we we ECAR way into some logic down here that eat-in now we're moving up this side and we're being led on a journey and it's a journey that is it's stretching what's stretching me it's making me think and it really is it joyful and just love puzzles like this now having said that I gotta finish it so this could be 25 this could only be 16 so okay but that's interesting isn't it because if we try and make that to lots of 16 we only get to 32 plus 3 is 35 that would make that cell a 10 which is impossible so this is a 25 cage and 25 plus 3 is 28 so if this this could be a 9 or a 16 ah if it's a 9 that has to be an 8 if it's a 16 that has to be a 1 so this is a 1 or an 8 we still don't know whether that's a 9 or 16 we don't know whether this is a 9 or 16 ah but look now this has beautiful that is beautiful this seven and nine suddenly become important because now the seven and the nine must be in the twenty five box seven at nine and nine add up to 16 so the other two squares are fantastic the other two squares have to add up to nine now look at this one eight option here that means one and eight are not possible as a way of making nine in the two cells two additional cells in this box so one eight we can't use that to seven we can't use that or repeat seven three six we can't use so this cage is four five seven nine for sure now that means there must be a two and a six in these three squares and that means that other square is a one or an eight oh but it's not look we can eliminate a 2 and a 6 from that square so that becomes an 8 so now the 8 must be here which means this contains a 1 so this is a 9 cage that is amazing that is amazing ok so this is 3 4 or 5 again it could go here and it could go here 19 minutes into the video I'm not even snipping halfway through right 8 so these are so this must be a 16 cage right because it can't be a 9 cage so these two squares have got to add up to 8 but they can't be 2 & 6 it can't be 3 & 5 so they are 1 & 7 okay so we've got these up to eight we've then got two more squares right the maximum these could be would be 16 if these were both 16 that would be 32 plus 8 this would be a 5 if this was 9 + 16 25 plus 8 it's too small that would make that square too big so this is a 5 therefore that's going to be a 4 because the only option then is for this to be a 9 and these two both add to 16 but this 3 means this one contains a 3 so the other two cells here have to add up to 13 we can't use 5 & 8 we can't use 6 & 7 so this is 3 4 9 that's not a 4 so this this is this is two six eight again that's come up quite a few times so far so that squares what could be a one can't be at or six and that can't be a four in fact look there's got if we look at this cage there's a four in one of those two squares so those two squares prom before this where is four and therefore these three squares are five seven and nine that count here look at this seven and nine resolving that this one has to be a five which means so this this five cell cage has got a seven and a nine in it now so now we know this Square this this is a twenty five cage because it can't be a sixteen cage obviously can't be a 36 cage and can't gets thirty six and five different digits so the other three squares here have got to add up to nine bunch oh no that is alright that is interesting because look at this eight so now where can I put an eight in this box given that I can't put an eight in the twenty five cage otherwise it'll break it must go here that's nice right down there this square must be a three this must be a sixteen cage so what have I got left here to put in I've got two in this box I still got to put him one two three and six so the only options for this to make this a square it's either got to be three and six or it's got to be one and three and is there a way of resolving that if it's one and three that would have to be a three that would have to be a one and that would put two and six into these squares ah that doesn't work look there that breaks because that will give three lots of two and six in the same rows this is this is not right that's not one three so it must be 6 3 which means it must be it must be 3 here and 6 here so that's six that's two this must be one and two into these squares that therefore must be a six this square cannot be a one anymore that's a seven that's a 1 that means that's a 7 that's not 7 anymore therefore this is a 7 and are we starting to make progress this is a 9 and [Music] and I'm stuck again okay well let's have a look down there must be a one in one of these two squares sorry there's a six there so that is it too so this is one and four one here eight three results of this is oh that's the wrong button then I mean to do that undo this must be the three here that's on one to one that's a - that's for lots of five six here is also the six and the eight do some tidying up with the colors before I get my new CD to me there we go that must be sixteen and we don't know about this one and we this one must be well for squares add up to at least ten so this can't be a nine Cage given it's got a 1 and a 4 in it it can't be a 25k so this is a 16 cage these two squares therefore must add up to 11 but they can't be 3/8 it can't be four seven it can't be five six so these two squares are two and nine goodness me it's incredible to nine that means that's nine seven this square now is in theory not six my scanning work that's gonna be a five these two squares now must be eight and seven and there's a seven here so that's seven eight there for these it's meant to put the colors in correctly these these squares are not part of square cells you can see that from the dots the dots are on the inside of a sphere of the cells not the outside so right how do we finish this Oh let's have a look at it so what are the options we know one of these square we know one of these squares is a three and it must be this one that's probably what I was missing this is not 3 anymore so if this is a 4 this would have to be a 2 which you can't be or a 9 which you can't be so this is not 4 this is 5 that's four that's five these this must be an 8 no it could be count abouts make mistake then we didn't I got away with it obviously this could have been a 1 but it can't be a 1 because there's a 1 there so it must be an 8 and this yeah maybe there's a restriction here we need 3 4 6 and 8 nearly so that's going to be a 4 or 6 that's where 3 and that's got to be 4 or 8 right we've only we've got very limited squares left to work with let's look at this one so this is I this adds up to nine this must be two and four which would mean that's a four and that's a two now is that even possible I can't see why that would be impossible if this is a sixteen cage this would have to add up to thirteen and then it would be 4 & 9 which means this square is always 4 and this is this could be a nine but that foresees that that's square forcing it to be an eight which means this is not an H and then to there is also that's a six this is just lime sublime puzzling now we need one two and nine into those squares now see if we put a nine up here I don't know maybe I'm being slow about this I don't feel like I am but maybe there maybe I'm missing logic that would have made this easier now okay so what are the options now for these two squares one of them nine one of them must be a six I still don't know which one and then the other square must be a two or a nine ah now look this one cannot can never be either a two or a nine so this must always be a six now this must be a two or this actually that can't be in these and that five resulta five and nine which I should have had before so now that is a nine that's a - not a nine shows that this that color that was a sixteen cage in the end and this square finally is a three these two squares must be six and nine and that does resolve and that's going to finish it isn't it because now we get six eight you get a 2 we get 2 1 one three we get three this is ridiculous ridiculous puzzle and these two squares are five and seven and please don't let me have made a mistake yes okay fantastic what a fantastic puzzle very difficult sorry half an hour video well I don't know I dunno maybe we will get loads of email saying that I should have I should have done it in 10 minutes or something but that felt quite hard to me to do let me know what you thought I have to say I loved it and we'll be back soon with another edition of cracking the cryptic [Music] you

Channel: Cracking The Cryptic

Views: 552,186

Rating: 4.9639955 out of 5

Keywords: free killer sudoku, best killer sudoku, hardest killer sudoku, extreme killer sudoku, deadly killer sudoku guide, most difficult killer sudoku, sudoku for experts, play sudoku for free, killer sudoku for dummies, simon anthony, christoph seeliger, nathan gilbert, pie are squared

Id: myGqOF6blPI

Length: 33min 26sec (2006 seconds)

Published: Thu Oct 24 2019

Reddit Comments

[u/PHPuzzler]

I think this was posted here several months back. But there are some puzzles worthy of a repost, and a killer sudoku without a single given number is probably one of those.

Fun fact: The author is on this sub.