The Sudoku With No Digits. At All.

[Music] hello and welcome to saturday's edition of cracking the cryptic and another another puzzle from the brilliant akash jane um who compiles under this under the name eudacos a name that for some reason i find it impossible to remember in terms of the ordering of its vowels and consonants and even when i remember it's not just a reversal of the word sudoku it still seems to flummox me i'm hoping i'll finding his puzzle a little bit easier now amusingly akash wrote us an email about the puzzle on the screen and you can see there's rather a dearth of uh digits at all um not even in the killer cages absolutely nothing uh but akash was concerned he said that this this puzzle was is some of his best work and it should be a joy to solve but he was worried that we might find it too easy well i'll let you into a secret our testers some of whom are completely brilliant solvers did not find it easy um so i don't think akash needs to be too concerned now before we get into the rules of this um do check out our kickstarter book if you've not done so yet the campaign which still has about 30 days to run is doing so well that we're going to be able to make what was already going to be a fantastic book even better so it's incredibly exciting and we we have more planned more planned for this book so check out on the screen there's a card there there look at the card there on the app front by the way if you own our classic sudoku app then do make sure it's updated as we very release recently released new puzzles for it and we're currently working on a big puzzle update for thermo sudoku as well at the same time as trying to test some incredible puzzles we've been sent for the upcoming killer sudoku app this app is going to be uh it's going to be absolutely sensational but testing lots of killers by the likes of vistamafel is how can i put it it's not an activity that passes behind the blink of an eye and so bear with us we have a lot to do um and we have a lot on but we are we are getting to it um now let's go to akash's puzzle i'm going to call it sorry akash i know i should use your pseudonym but it's easier for me now the rules are normal sudoku rules apply uh normal killer sudoku rules apply which means within cages digits have to sum to a total i'll get onto that in a moment and you can't repeat digits in a cage now within every three by three box marked by the thick black line so in every box of the sudoku all the killer cages have the same sun also killer cage sums are unique for every three by three box i.e if box one the top left box had killer cages each of which sum up to ten then none of the other boxes can have killer cages with a sum of ten okay the killer cage sums are not given and have to be deduced how kind right and akash actually produced an example let me show you here's the example this is a smaller grid um but okay so you can see that the killer cages in box one here sum to eight then to seven then to six nine okay so i can see how that's working that's fairly self-explanatory i don't know if that sudoku works you're welcome to try it um i'm going to try this one the way to play is to click the link under the video as usual and with that i get to play let's get cracking and see how to do this now um okay right well this this box must be resolvable because there are the cages in it exactly encompass all of the cells in the box so we actually know that um well let's let's get back to basics if we looked at the solution to this puzzle what digits would we see that were in yellow in this box obviously the digits one to nine so we know that this box the yellow cells must sum to 45 because that's what we get if we add up all of the digits from one to nine now if three boxes add up to 45 each box must add up to 15 and that is not quite helpful i mean we know that this two cell cage adding to 15 must either be six nine or seven eight but that's all we know i think uh but at least we know what that one is and that's the only box in this puzzle that is completely resolved everything else has gaps like this one uh okay so what are the values of this we know i suppose that this this is a single digit number and what's left when this is removed from 45 must be divisible by three because there are three boxes or three cages left in this in this box so um this can't be zero obviously so it's going to have to be three six or nine isn't it and if that's the case these cages here are going to either sum up to 42 divided by 3 it's 14 39 divided by 3 13. so these add up to 12 13 or 14. okay now this this ah that's interesting look that is exactly the same in terms of profile as this one so this must be also three six or nine this one is different though look at that this one has only one gap but this time we've got four boxes that need to take up the remainder so we need to make sure that 45 minus this equals a number divisible by four so that can be a 1 obviously because 44 is divisible by 4 gives 11 so it's got to be 1 5 and 9 presumably so the totals for this one are either 11 10 or 9 i'm sorry about the way i'm doing it i don't know if there's a quicker way this is this is the way that i'm i'm sort of doing it very bitterly i'm well aware of that this one this one has a small total because it has a single cell cage okay and this can't be a six because if it is the cage cells would only add up to 24 which would mean these two would have to add to 21 which is impossible so this seven seven fours 28 yeah that would work if this was a seven these two squares would have to add up to 17 and the way i get that obviously is four sevens are 28 45 minus 28 is 17 that is possible if these are 8 and 9. so this has got to be 7 8 or 9. okay um let me just have a look around again this one this one's this oh yeah this one's this this one's the same as this one it's got a single cell cage and then three dominoes so this must also be seven eight or nine the remainder is going to have to be either 17 13 or 9. uh okay so so i've now i've looked at these i've looked at this one i've looked at these two so i've only got this one i simply refuse to believe is of any use at all it's got one cage in it of size and it's a domino so i don't know anything about that this one actually this one might be interesting this one looks less interesting than this one because at least with this one though i've got a five cell cage ah yeah okay so this one if it's got a five cell cage the minimum i can make five cells that up to if i can't repeat a digit is fifteen i'll use one two three four and five and this also has a domino in it which can't add up to more than 17 so this is uh and it's not 15 because that one was 15. so this this k or box is much more restricted than i thought this either adds up to 16 or 17. now well okay so that means this domino has to contain a 9 because you can't get to 16 and 17 in two cells without a nine in fact we can do better than that not only can we remove the nine from this square but this is either seven nine or eight nine so these three squares together are seven eight nine triple is that useful for this cage that might be useful for this cage you know because this is three six or nine so these these are adding up to 14 13 or 12. so if this is 3 can we make this add up to 14 without using 7 8 and 9 30 oh sorry 15 i know is six five no th that this is very very nice this is impossible because if this is three these have to add up to 14 without using seven eight and nine and you can do that but only like that and that repeats the three in the column uh well in the box the three is repeated so so the three is not right which is progress of a sort so we can remove three from there six words c6 is interesting immediately because that now means the maximum that no six doesn't work because the maximum this could be is three four five which add up to twelve that's incredibly clever so actually this can't be three or six it has to be nine and we get a digit and we get a nine in one of those which ah look at this is beautiful it's a beautiful puzzle look nines here and nines here force and nine into one of those three squares but we know that the total for these dominoes here is either seven or eight so neither of them can possibly could take a nine otherwise immediately we'd have to put a negative number in the other the other cell which is not possible so the nine goes at the bottom removes a nine from that square it's like a trail of breadcrumbs we're following that one's not nine now so okay so this one and this one which have the same sort of topology are now taking yeah this is 8 32 so a 7 and 8 have now gone this either adds up to 13 yeah okay so this square is either eight or four this either adds up to 13 or 17 depending on what we pick for this square which must be the same of course for this one oh in fact look the nine here where does the nine go in this one it's the same as the same as this one the nine can't um can't go in a cage because the cages add up to seven or eight the nine can't go there by so the nine goes here which means this square must also be a four or an eight like this one nine must be in one of those three squares ah this is gorgeous this is just gorgeous okay so nine is in one of these three this is the 15 box everything in this adds up to 15. so how does this domino work now it can't have a 9 in it so it's got to be 7 and 8 to add to 15 that gives a 7 8 pair in row 3 which tells us this one can't be an 8 that's a 4 which of course tells us now what this one is because this this box now has sort of cells outside the cages adding to 13 so this must be an 8 in order to make sure that 4 8 are 32. and if this is eight that can't be eight or we'd be duplicating the cage totals for these two boxes so this must be seven which means this is eight this is eight this is seven by sudoku this cage gets resolved as well doesn't it because now this is this is 17 plus 17 is 34. these have to add up to eleven so without using uh eight or nine so that's five six or four seven look um that can't be seven that can't be four okay sorry that can be four that can be seven that can't be four because that would put a seven here eight by sudoku must go in this square this box um this box is adding up to 36 12 isn't it so with the 8 here this must be one and three to make up this cage is total this ah this this domino needs to add to 12 and it can't use eight or nine so it must be five seven and we can do that as well seven five this slot must be two four and six to complete the box that's not four wow okay so we have actually done quite well here all of a sudden yeah this square is resolved it can't be four or six that's five which tells us that this must be a six because we know those add to thirteen that's not f uh this isn't five or nine this adds to one which means this box is a full of 11 cages don't know how to use that yet this one is full of eight cages right okay we can do something here look because seven is locked into the top row so if seven is locked into the top row we know seven must accompany one so the one must be in one of those three squares the ones align now in row one and row two look so in where do we put the one in row 3 of the grid we know it's not here it's not there so it must be in one of those two squares this box is this box is adding to 15. ah ok so 9 here 9 needs another six and we can't use one five so this is two four nine let's get rid of the the nine two four nine means this is a six this is a two this is a four and we are actually cooking with gas aren't we we're doing quite well um and there's nothing easy about this but there i tell you what there is about it it's just brilliant it's absolutely brilliant six four into those squares because these add up to seven this must be a two five pair therefore we get the value of these which is four and seven these three squares have got to be one two three that's not one uh this one needs one three five and six to complete this 15 cage you can see the five can't go there oh this can't yeah that can't be a one we know that already so this has got to be three or six this has got to be two or five because we know these two add up to eight uh now can we go any further here it's one of these moments when i can feel you all shouting at your screen saying yes stop being an idiot i'm really not trying to be an idiot i promise um okay i shouldn't have said i was cooking with gas the moment i said it i've basically completely stumbled one three five and seven into those squares this this must be the same one three five or seven right so this square has a mirror here i can see that yeah okay so this is not bad actually it resolves this can't possibly be a five because if we look i mean the simple way of seeing that is where's the five going in row row row one of the grid it must be in one of those squares where it must accompany a three so this can never be a three five pair this has got to be two six that becomes a one three pair this becomes a five six pair therefore this must be a five or a seven because we know this is the mirror of that one and there the trail does run cold well except we know that's not a one or a three this has got to be the counterpart to this square [Music] so so let's take stock what have we used we've used 15 we've used 12 so we've used 12 and 15 we've used eight so if you 7 8 11 12 15 and this one was 17 so we've still got quite a lot that we could use what's this one can we resolve this one this one is either 14 or 13 i don't think i've said any of those no this one was 12 wasn't it so i think this one is still entirely unresolved so how do we finish this off then when i say finish it off i appreciate i'm not anywhere near finishing it off but this one ah got it okay this four this four is rather beautiful look at the effect it has on this box we've got to put a 4 7 into this box well neither of those can be 4 7 because that will rule out those two squares straight away and the 4 means that that can't be a 4 7 either so this is a 4 7 we actually know the order that is gorgeous and it appears completely useless oh no it's not useless because the 7 resolves that square 5 3 3 one this ah this is now one seven pair and we have a one here so one seven so four lives on the left hand side of box seven seven lives in one of those two squares this domino is resolved well not resolved but i know i know it's a two nine pair because it adds to eleven and it can't be three eight four seven or five six so that's two nine these squares are one six and eight the bottom one oops one six and eight this one can't be eight six must be ah yeah look the six and the eight here so six must be on the left hand side of box four therefore five must be in one of those two squares and the same goes for eight eight must be here so three must be here so this is a three six pair this is a 5 8 pair um now what does that mean that means that these three square ah yeah look these three squares have got to be three seven and nine but seven and nine can't go here so this is three this is a seven nine pair these squares have got to be four uh two four and five um oh this ah this 3 is pointing at that square so this is a 6 which means this is a 13 box that's a 1. this is 2 4 5 here and this is a 13 box so this this is either four nine or it's eight five because it can't be six seven so we can we can put that in now is there anything going on have we got any pairs or triples we've got a hidden pair look at look at this row where do one and three go in this row well one one cell that can take the one and the three is that one the only other cell i think is that one so that's got to be a one or a three and that makes a pair uh it's very close to something else here but i can't quite get a handle on it well actually look yeah easier where does seven go in this row there's only one position that can be a seven that's very clever that's very clever so this has to be seven that means this is nine that's good because that locks a nine into one of those two squares so that we now know as this adds to thirteen it's four and nine the four helps us out that gives us 4 3 6 1 we need these to add to 7 obviously that gives us 6 and 8 here the 1 fixes this is a 3 that's not four anymore that's not four anymore so four must live here oh and look this domino is the only one in this this box so this this boxes number is either 11 which is impossible that one was 11 or 14 which is possible because this one turned out to be 13. this is just a gorgeous puzzle it is gorgeous um 178 along here well in fact let's tidy up that one first we only one seven eight long here that's got to be a one even my scanning doesn't let me down there this has to add up to 13 so these add up to 10 up we can't never include a 5 in that total that's going to be 2 8 7 5 that's adding up to 13 that's good the three gives us the three and the one so one is in one of those two squares and this row needs two three eight and nine to finish it off let's now have a look at that that's got to be a nine that can't be a three this one can't be an eight so now we've got a two three pair in row four which means this is eight and we've got to presumably work out the parity of this box what are we looking to get here we know we know this has to be at least a 4 but it can't be 4 because 13 has gone hasn't it 13 was this one it can't be 5 14 was that one it can't be 6 because 15 is this one and it can't be 8 because there's an 8 there and also that one's 17. this has to be 7 i think it has to be 16 that gets us a 7 and a 4 if that's right i'm a bit worried about that but it felt like the logic was good um what's that square that can't be that's gotta be a four so this has got to be a five or a six and this box has got to add up to 16 which means ah so 16 if this is an eight these three squares have got to add up to eight as well so they need a one and one can only go there so these two squares are either three and four or two and five so if this was a four this would have to be a three is that possible uh can't immediately see why not let's try let's carry on with some sudoku maybe sudoku will be our friend and help us to finish this off um four nine five six oh this five look that's giving me more stuff at the top there five six you can't put a six oh that's a six that's six there oh that's beautiful that's giving us a three here this one was in eleven so that's the eight five six this three this eight yes the eight keeps us going eight nine this square now can't possibly be a nine so there's only one place a nine can go in this row it's there this must be a two or three that creates a 2-3 pair which finishes off the nine up here which might be useful in terms of the four might knit yes that locks the four out of this eight cage so it must be two and five which means it must be this way round the three goes there the three and the two if i haven't made a mistake the two goes there check yes that's how to solve it brilliant i really enjoyed that it's just a stunning puzzle and there is nothing easy about it it's taking me nearly half an hour and i felt like yeah there was certainly some sticking points i hope you enjoyed it you had half as much as i did let me know in the comments as always and do check out our kickstarter and thanks for watching back for later for another edition of cracking the cryptic [Music] do [Music] you

Channel: Cracking The Cryptic

Views: 490,784

Rating: 4.9620581 out of 5

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Id: M7H0mpeYW00

Length: 28min 48sec (1728 seconds)

Published: Sat Oct 17 2020