The Dancing Grid

[Music] hello and welcome to thursday's edition of cracking the cryptic where today we're going to be taking a look at something i think that's well i think there's a few pleasures in life that can compare to a good killer sudoku and that is apparently what we've got today is called grid dancing and it's by brem stuff and bremster's been on the channel several times before and i well the interesting thing about this is that our testers tell me this is a very very tough puzzle um but my experience of bremster's puzzles as suggests that they're normally sort of about average in terms of difficulty so this might be out of bremster's usual style we shall have to see a very symmetrical grid though uh looking at it at the moment anyway i'll read you the rules of this in just a second or two a few things to mention first let's start with some quite amazing news from the ctc fan discord server which has i think it's something ridiculous like 25 000 members at the moment and yesterday they passed 7 000 puzzles in their archive so that's 7 000 puzzles that have been created by the people on the discord server then tested then archived it's really remarkable anyway um i am told that there is a very special pack that has been created um to basically commemorate that i think bent's joyful has been involved in in producing what is an absolutely beaut i did have a look at this earlier it's a beautiful pack of puzzles i haven't done any of them yet but what i will do is put a link under the video to that puzzle pack do check it out apparently it's really cool uh dying flutchman wrote to us and said that it's really worth looking at so i think there may even be a puzzle hunt in there so uh lots and lots of special stuff um to look at there and congratulations to to all of the mods on the discord server for making such a you know it's such an extraordinary thing it must be the biggest puzzle community on earth um and that is something to cherish um now birthday nathan gilbert um who is an absolutely uh stalwart solver very good solver as well always manages to finish our monthly rewards over on patreon uh nathan i think you turned 40 today so congratulations my friend i'm told that it's brownies that you prefer to cake so i hope that your day is replete with lots and lots of brownies now next the guardian newspaper if you if you're in the uk and you're near a news agent on saturday you might want to buy the guardian because there is a puzzle supplement in in in that newspaper that's been prepared by alex bellos who many of you will recognize a very famous author of puzzle puzzle stuff um and alex has asked us to contribute some puzzles from the from ctc to that so we were very happy to do that i think there are three sudoku's um that we made specially um so they are in that puzzle supplement um and i think the supplements got some cryptic crosswords in it all sorts of things japanese logic problems so definitely worth checking out i'm certainly going to be buying a copy um now next bit of news well more of you have managed to solve the um uh the well our sudoku hunt which is uh of course by joseph neymar over on patreon that's this month's monthly reward i've been reading out the names of correct solvers i will continue to do that until uh until we get to the 20th of the month when the competition closes um but very well done to straw python to rob uh andre uh emily tinney the sudoku bear from germany uh philip nitchko uh jayco driesha uh callum mailer mark dumont volker plassman dr b and d's puzzle consortium that sounds intriguing uh jeff and emmy nicholson and olleh magnus buckholm i'm saying your names correctly i always worry about that but i did my best and very well done to all of you you are all correct um now let me read the rules of grid dancing i wonder why it's called grid dancing there's no dancer in the grid i can see but anyway these are the rules very standard today so we've got normal sudoku rules apply digits in cages must sum to the small clue in the top left corner of the cage and digits cannot repeat within a cage so what that's telling us is i'm just looking that i think mainly probably affects the 28 cage the thing about digits can't repeat within a cage so in this cage here which is a seven cell cage we've got to make sure those seven digits sum to 28 without including a repeated digit and in fact there's something quite interesting we could say about that cage immediately but we'll get to that in a moment or two do have a go at the puzzle the way to play is to click the link under the video now i get to play let's get cracking i've had no there's been no maverick today it's been absolutely joyfully quiet and that's great um no doubt he will now take off and buzz past my window which is open because it's absolutely boiling anyway did i say let's get cracking i think i did right let's start with the 28 cage that is a seven cell cage now given that every digit in this cage has to be different we might ask ourselves what is the triangular number for seven i what is one plus two plus three plus four plus five plus six plus seven well it is twenty-eight so this cage is uh is it one two three four five six seven cage if we if we put any higher number into it we will break this total um so that means that we've got oh uh no i was about to get excited about eights and nines in box five because there can't be an eight or a nine in this cross the question i was thinking about was where do eight and nine go in box five and you can't put an eight or nine in a seven cage so eights and nines are in two of those three cells okay um [Music] no i was about to get excited about central row and realized that that was going to be nonsense so well the next thing i can see here is the opportunity to use the secret in fact i think it looks like we can use the secret over and over again because of the geometry of this grid now the secret i think i've talked about the secret a lot in recent videos but i'm going to do it again today the secret is something i only tell my very favorite people and if you're watching this video and you've got to six minutes 49 seconds into it you're definitely among those people the secret is that in any sudoku any complete row any complete column or indeed any complete box because of the rules of sudoku will contain the digits one to nine once each and if you sum the digits one to nine you get forty five so i know that these two rows of the puzzle sum to two lots of forty five but you can see i also know quite a lot about those cells in that in those two rows because they they they sum to a very specific number they sum to 35 plus 33 which is 68. so if the if the cage sells some to 68 then the uncaged cells must sum to 22 and that is as useful as a chocolate teapot let me tell you 22 in four cells where the digits don't even see each other very cleanly is not going to help us right but the but the thing we can see hopefully hopefully it's fairly obvious about this puzzle is look how this geometry it sort of repeats in in rows one and two rows eight and nine columns one and two columns eight and nine the cages that we have in those columns and rows just sit entirely within those columns and rows so we can we can try the maths again down here down there it looks like we've got 48 60 75 which means the uncaged cells sum to 15 again unusefully um [Music] okay let's try columns one and two then instead there we've got 30 uh what have we got we've got 23 34 46 58. so the uncaged cells sum to 32 in order to get us up to 90. again not this is not going very well actually i'm not terribly surprised if this is a very difficult puzzle this is unlikely to be the trick to get us in but we have to do our due diligence now there we've got 30 39 56 which means we've got those cells adding up to 34. that's still absolutely no there's no use is it and i can hear maverick he has taken off i don't believe it right okay so we're not hm what on earth are we doing then are we doing fistum fistomaphele or something like that i don't think we're doing fistemphel fistomophel for those of you who are not aware is a theorem that tells us that these 16 blue cells are the identical digits in any sudoku to those 16 um orange cells mavericks in a helicopter today um which is well it's actually nearly interesting isn't it because we almost therefore know the total of the blue ring because we almost know the total of the orange squares we know them apart from the four uncaged cells but i don't think that these cages are big enough or small enough to make that particularly interesting so i'm reluctant to think it's vista mobile i'm more interested actually in sort of mutated fistomafels i'm always suspicious when you get two by two boxes and killer sudokus you know that are in or around the perimeter but this or this configuration is not one i know about i don't think although i do lose track of the various the variants of vistamavel that i have come across before um how could we do something with those we would probably be probably be looking at these would we and then offsetting let's make those blue we'll offset nothing terribly nothing terribly look it doesn't look very interesting that row and that row look a little bit interesting in the sense that if i if i um [Music] if i was to include these in other sets you can see i'm getting some quite nice offsets there and i know most of the orange total but what i don't know is those two cells ah ah no i've got it well i've got something that's very interesting right what about those two orange cells so what that got me thinking about is when if you look at those two orange cells obviously i would know the total of those if i if i could get these into the orange set i would know the total of those and i think i can so right so we are going to look at this we are going to look at this i'm just going to un-orangify some cells and talk about what i'm doing here just so that if you're new to set theory in sudoku you don't say what on earth is he doing right i haven't done scrabble tiles for a few days actually so let's do scrabble tiles um these cells that i've just highlighted we don't know what the disposition of the digits is within these blue cells but we can say something very precise about the contents of the blue cells because each column of course contains all of the digits one to nine once each in other words the blue cells contain four sets of the digits one to nine now i want to imagine that i give you 36 strap scrabble tiles and ask you to write down on those scrabble tiles the the these the digits we're going to find in blue and of course we can do that very easily there's going to be four digit ones because there's going to be a digit one in this column a digit one in this column the digit one in this column and digit one in this column it's there's going to be four digit twos four digit threes four digit fours all the way through to four digit nines so it's a very easy task and we're going to put those blue scrabble tiles in a bag now watch this now i'm going to create an equivalent bag of scrabble tiles containing orange scrabble tiles and i'm going to do this row so that's enough that's one set of the digits one to nine i'm going to do this row now here's the thing i noticed what about if i do that row and i do this whole box now this is where it gets interesting this is where it gets interesting because when i do this box the eagle eyed among you will know that this cell here in the center was in this row and in this box so in other words this is sort of twice in orange so i'm going to just give that a little flash for a moment but look look well in fact let's let's do this more slowly actually because i appreciate if you're new to this i'm not going to be making it easy by doing this let me let me do it more slowly and apologies for those of you can see what i'm doing here but i want to make sure that everything is accessible to people who haven't seen set before so i want to let's start off by putting 27 scrabble tiles in our orange bag of scrabble tiles so at the moment we've got 36 scrabble tiles in our blue bag and we're going to be able to fill our orange bag with 27 tiles very easily because i'm going to include the contents of these three rows and i know these three rows are three sets of the digits one to nine so in my orange bag i've now got 27 scrabble tiles three digit ones three digit twos three digits threes all the way through to three digit nines and in my blue bag i've got 36 scrabble tiles so at the moment the bags are unequal they don't have the same things in them but let's let's think about this digit let's make that digit one i don't know what this digit is but imagine we looked at the correct solution to this puzzle and we found this digit was a one what would happen if we went into our orange bag of scrabble tiles and threw away the digit one and we went into our blue bag of scrabble tiles and threw away one of the digit ones well then we could say that there would be 26 scrabble tiles in our orange bag and 35 scrabble tiles in our blue bag but the difference between those two bags would still be the same thing because before we did anything they were the difference between the blue bag and the orange bag was one set of the digits one to nine because i haven't i haven't put a fourth set into orange yet so what that tells us is that i can go through both bags and i can find all of these tiles and throw them away i don't have to know what's in them i can simply say whatever is it whatever happens to be in that in the finished grid i'm going to get rid of it so we arrive at this point and this is where it gets really interesting because at the moment the difference between the orange cells i've got highlighted and the blue cells i've got highlighted is one set of the digits one to nine and now what i want to do is to fill in i'm going to give you nine more orange scrabble tiles this box and i'm going to ask you to fill in those with the digits one to nine and put them in the orange bag now hopefully you can see that when i do that whatever's in this cell in the finished grid i'm going to have to write it on a nut it's already in the orange bag i'm going to have to write it again and put it in the orange bag again because i'm putting all of the digits in that box in again so this cell is now in the orange bag twice now i can find this one now this one this one and this one that's they all of these digits are going to be in both bags i'm going to throw them out of both bags and now look what i've done i've now managed to get my orange my orange scrabble tiles to include this entire box and also we have equalized the bags if you like we should have the same number of tiles in both bags so let's check that in this column we've got well that's that's 10 so we've got 20 blue tiles and we've got hopefully this is right oh yes because i've got to double count okay i was thinking for a moment what on earth has gone wrong here but no it's it's right isn't it so i've got 6 12 i've got 12 in the outline cells i've got 7 in here that's 19 but i've got to count this cell twice so it's 20. so we're still in a position where where our scrabble bags are absolutely identical now now i can do maths because almost everything in my in my bags i can actually quantify yes okay and what we're going to end up with is the difference in value between this cell and these um the these cells here because i don't know what these four add up to and i don't know what this cell actually is in the finished grid but everything else i know so if we add up all of the which way should we do this let's add up all the orange cells all the orange cells add up to uh what's that 22 34 43 50 58 86 right so the orange cells add up to 86 except for this one we don't know what this one is so it's 80 so the total for orange if we include this cell twice is 86 plus this cell's value which we don't know now the total for blue on the other hand is going to be a little bit more opaque we've got um how should we do this we've got 39 up there 44 64 87 right is this gonna go wrong no it's not it's fine it's fine it's gorgeous right okay so so the blue cells yeah so okay so now what we're going to do is we're going to um we're going to start removing so so it the summary of what we've got now is that the orange cells which are so 86 plus this cell are equal because they're the same digits are equal to 87 plus these cells that's just a mathematical equation if i deduct 86 from both sides of that equation i'm going to get this cell whatever it is is equal to one plus these cells and that's interesting because this cell cannot be that high we said at the beginning we can't put eight or nine into the 28 cage so that cell can be a maximum of seven and these cells therefore have to add up to six or less so well they have to add up to exactly what six or less because this could be less than seven but how do i make these cells add up to six or less well if i minimize them they're going to be one two pairs so they have to be minimized in order to allow this to be a valid entry into the orange cage and that is the beginning we get a digit we get one two pairs in in and we get now we know this cell that that is a very hard beginning actually that is a very hard beginning but it's also very pretty isn't it it's very pretty ah now look one two pairs so where am i putting ones and twos in the middle box into those cells which means these cells have got to be the other low digits so they've got to be three four five and six the rest of this column's got to be one two eight and nine this seven cage has now not got a one or a two in it so that's a three four cage one two three four that's a five six cage by um the fact it can't have a one two three or a four in it and we get an eight nine pair in the row so where all of a sudden we're getting all of the digits well not actual digits but we're getting we're getting stuff in the grid aren't we um [Music] now what do we do oh come on i'm sure that this is i feel like this is the sort of thing that's going to now make the puzzle collapse and i just got to see what the next step is come on come on brain tell me um goodness me come on what is it i meant to see off the back of this it is that oh i know what it'll be it'll be the fact that now i can know that yeah so maybe i've now got to redo the maths on these rows now i know that these oh or it could be that's an interesting thought i can't remember what the totals were but now i do know exactly what the value of those cells is these cells here that's a terrible color to have chosen sorry let's try yellow um these cells add up to 20. so what were the gaps in in rows one and two and rows eight and nine adding up two i can't remember i think this was 75 that felt like a nice total when i was doing it yes these so these are adding up to 15 so we can't make that a nine and an eight but anyway 15 was what we had down here now at the top we had 35 51 68 so we've got 22 so so these cells here that i'm highlighting add up to 22 plus 15 which is 37 yet these add up to 20 which means these and these add up to 17. oh poppies that's totally that is utterly useless sorry i thought that was going to be it but it's not it's very much not okay i thought that was an intelligent thought brain you've let me down um right maybe i've got to do sudoku with ones and twos then so ones and twos ah you can't put a one or a two and a twelve cage but you could put one and two in that twelve cage one two nine would be possible so i can't even lock one and two into the corner uh sorry about this i feel like i'm letting everybody down here i think that there's likely to be something very obvious i can't see for the life of me what it is um [Music] okay so maybe what we've got to do i don't actually know i'm doing terribly here um no i've got nothing going on do you have you've got to put a low digit in 16 cage three four five six adds up to 18 yes you do right right okay so there is one low digit in the 16 cage a one or a two there is not there is not two low digits because if they would if they were trying to try and put one and two in the 16 cage they would have to go there like that and that's gonna break that cell so there is a one or a two in here we've now got a virtual one two pair in this column which means the 23 cage at the bottom has not got one or two in it well that's not that interesting three four five six adds up to 18 so there's quite a lot of latitude um [Music] no um [Music] what could it be am i missing here it's such a beautiful break-in this must be but it must be by design it must be this that you have to find but what i'm what i think is very peculiar is that it's such a restricted relationship so i sort of just expected it to cause you know mammoth deductions to flow through the puzzle whereas i've really got very little out of it and then i thought i had a good idea about these two rows and that turned out to be total nonsense this is definitely harder than bremster normally is actually this is very it's very clever but very tricky oh goodness i'm now now getting to this point where i start to stop speaking which is terrible in videos um right okay so maybe what i've got to do oh yeah okay that's interesting golly golly gosh right so let's i got i think i got a bit fixated on the fact that i had these equivalences but let's keep thinking about our scrabble bags here because i've got an awful lot of low digits in blue an awful lot but i've only got two low digits so far in orange yet remember yeah yet remember that we know that the blue set of digits and the orange set of digits are identical they've got the same tiles in them so i've got to make sure that when i'm when i'm filling in all my orange digits and all my blue digits we're going to find at the end of the puzzle that the orange digits and the blue digits are the same well that's actually quite difficult here it's with regard to the low numbers because i've got so many of them ah i've got another one here yes yes okay so i've actually got three at the moment i've got at least three more low digits in blue than i have in orange so i've got to correct that i've got to put low digits into the orange set and i can't put ones and twos into a 12 cage because the other digits will have to be 11 or 12 11 or 10 if i do that so that's that's perfect in fact in fact it's forced so there are no there are no more low digits in blue because how am i going to put five ones and twos well minus these two so three ones and twos into these empty orange cells well i can't put them in the 12 i'm gonna have to put one of them in here because one plus two does not equal eight or nine so this has got to be two nine which means that's got to be one 7 because it's got to have a low digit in it and it's not a 2 which means that is so that could have one could have one or two in it yes it depends it's got it it's got whatever this has got in it hasn't it because at the moment we've got a quality we've got a one and a two and a two and a one so that's two of each and in blue here we've got two of each so whatever this is has to go in here right oh that's beautiful that is beautiful right this has not got a two in it because if it's got a two in it what other digit has it got in it a seven and seven seven i'd have to put a seven in one of those cells by sudoku because in this column you wouldn't have a 7 here and you wouldn't have a 7 here and there would be no in fact there's nowhere to put a 7 in the column so this is 1 8 which means there's a 1 in here using the logic we just discussed which means that this is a two here we go here we go right so now we're off and running again we've got a two and a one um or not um [Music] so this this is now either three nine or five seven now if that's got nine in it oh you can put nine here okay uh if that's got five seven in it there's a five down there that might be all right um this is one eight i don't think that's putting enough pressure on the 17 cage i really don't oh one can't be in there anymore so there is definitely a one at the bottom of the grid because we know that this is the yellow cells are one two eight nine quadruple and okay let me just revisit the fact that in blue yes so in fact we now know exactly what the digits are in blue don't we if we we oh no we don't because we don't know what this is we know very nearly what the digits in blue are because they've got to be made up of all of these digits and then whatever we finally decide to put into this cage that feels like it matters actually doesn't it because how could you not have 7654 only adds up to 22. hang on hang on right that's beautiful that is so beautiful right okay so i was thinking about this cage and i was wondering if i had to put an eight or a nine in it or both and i definitely do because if i don't i can't make the total work seven six five four and he has up to 22 so it's got to have at least one high digit in it but that that's a 23 cage that's even more and that's a 23 cage so i've got to have at least one very high digit in these two by twos but look in orange i've got one possible nine here i've got one nine there and i've got one eight there and other than that i've just got sevens which are not eights and nines so given that these three cages need to have high digits in them that must be not five seven it must be it must be three nine in order to allow me to put a high digit into each of these three cages now that tells us that i don't have more than one high digit in these three cages either because if i was to try and put eight and nine in here for example i wouldn't have enough eights and nine left to fill in the other two by twos so now now by sudoku this is a nine there we go because where does nine go in this column can't go here can't go here so this has got to be eight that's not three whoops by sudoku um [Music] come on what's that done that's okay so now now i must have to i have to put one high digit into each of these cages i have a feeling that's going to interact somehow with this 2 1 2 8 9 quadruple i've got to put so in blue i've got to put three threes there are three threes two fours oh two fives two sixes two sevens okay oh is it two sevens or three sevens hang on because isn't this counted twice i think it's three sevens then because i've got to put that so i've got to put quite a lot of sevens in because this is in this is twice in orange um oh only one eight so eight is the most restricted digit i'm only allowed to put eight into one blue cell or one one yes one of the blue cages which probably probably matters but i'm not quite sure how um [Music] this is tricky this is really really difficult um let me i'm far from sure what i should be focusing on i've got a feeling it's going to be allocating these digits cleverly around these two by two somehow um where does okay let's do sudoku where does two go in row three because it can't go in very many places it can't go there look it can't go there and it can't go there that goes there grief right so that's not got two in it so that's not got eight or nine in it that's interesting ah now i bet you now now we can do the maths can we on these rows i can't remember what this one was this was 35 plus 33 it was so 22 we needed these four squares to add 22. these two add up to 17 so these two add up to five so the ones twos threes and fours that's not one so that's not four that's not three so that's not two so suddenly we've got a three four pair in column eight ah probably does something but i'm quite excited to check the bottom of the grid as well where oh no that's not going to work i'll just remember well because this is these were 75 weren't they so these add up to 15 1 plus 2 is 3 so those two add up to 12 and that's far too well it's far too middly to be interesting and they and they could be double six as well which would be very irritating so these cells have to be either double six or five seven now if it's five seven you'd have to do it this way round if it's four eight you can do it either way round i think yes maybe that's true i think that's true and if it's three nine that's got to be three and that's got to be nine so these cells are very well they're not very restricted although having said that i now can say there's a 2 in my 15 cage look because there's a 1 and a 2 here and i can't put 2 in this cell so this is oh so this is now a 2 and then two cells add up to thirteen that are not six seven so this is either two five eight or two four nine if it's two f four nine the four would have to go here this would be a two nine pair which might be possible actually ah oh no i was about to get excited about where two went in row seven but that's silly oh one same logic we did with twos here where does one go in this box it's got to go in the 12 cage so there's two more digits in there that have to add up to 11 that are not two nine but they could be three eight four seven or f can they be five six would that put an undue number of fives and sixes at the top of column three perhaps not wow ah ah this is a three or a four so there's a two oh this is important yes so there's a two in my 17 cage at the top and therefore the other two digits add up to 15 and they don't include an 8 so that is 2 6 9 exactly that must do something that must do something come on what's that done i don't know i'm sure it's done something i can't work out what it is all right what are these digits then these are three spores fives and sevens and we know that there's a five and a seven in this string of digits which is almost really good but not quite good enough the fact is i could make this sell a five if i couldn't make this sell a five that would have to be a five in my fifteen cage hmm so so the challenge here might be to restrict these digits somehow fortunately i don't have any good ideas about how to do that oh that's not a three by sudoku ones so in that row we've got four five six and no must be there must be another thing in there as well unless i've miscounted the row four five six and seven oh yeah okay four five six and seven i'll put those i'll actually label these up i think four five six and seven just in case something emerges i know oh okay i know there's a one in my 16 cage so the other digits add up to 15. so that count oh no that could be seven five with one three i am bamboozled by this oh here so here is a a weird point yeah oh good grief there's a hornet in the room whoa i'm gonna have to get rid of that that's that's too big to be uh allowed to float around in here and let me just see if it flies out of the window i've just spotted something good as well around a three go away um three here i'm trying i'm trying to say go out there's a three um so if if if there is a three in here you'd have to put a 3 in the 15 cage oh it's gone out it has gone out and three plus two is um uh five so then i'd have to put a ten in as the third digit so there's no three up here so that means this is a three which means this is a 4 and this is a 3. and now this is 4-5-7 and that's interesting is it yes it is yes it really is because well for many reasons in fact because i suppose i now know these digits they've got to be three six nine and i'm starting to get rid of digits in this corner now um and i think that corner digit has to be a four or a five because you can see from by sudoku we've got to put four and five into these cells here and if i put four and five into the 15 cage along with the two it won't add up to 15. so cell in the corner has got to be a four or a five which means there is definitely an eight now in this cage here which means that we now know what this is this has got to be two eight five and that's a four in the corner so that feels like progress doesn't it so that means that that's not nine because there's a 9 looking at it so this is just 3 or 6 which means there is a 9 in my 23 cage so this is if this is 9 6 that's 15 these two cells have to add up to eight without using one and two they'd have to be three five which would put a five here um [Music] i can't see what's wrong with that immediately but if this was 9 3 adding up to 12 these two would have to add up to 11 without being three eight or two nine so they would have oh four seven or five six oh okay sorry that doesn't seem to tell me what's going on in the world does it ah but now this 16 cage right we might be able to do better now with these two digits we know one of them is a one if this was seven five that would be twelve thirteen we'd have to put a three here so we'd have to do that what's wrong with that not sure maybe nothing okay what about seven four that's 11 12 we'd have no we'd have to repeat the four it's not seven four so so there must be a five in one of those two cells now the five is going to match off over here so we've now oh no we've got one more five to place in blue okay uh and we've also got to think about four or five up here so four five plus one oh this would be one six oh that would put a six here don't know i'm not sure if that's possible or not i can't immediately see why not so three is in one of those two cells um [Music] oh here's an interesting point here's an interesting point remember when we worked out that each of these two by twos has to have a high digit in it where does the high digit go in that one and what is the high digit in that one well it's got an eight nine here ruling eight and nine out of those two cells and i can't put nine in here because of this three nine pair so that one's got an eight in it ah ah and that's the only eight that's the eight that matches the eight over there in orange so now every other large cat oh we've already got the nine down here but this one's got to have a nine in it now i think by that logic because if you look at the comp the um all of the orange squares we only had one eight to use we've used it here we know that this is adding up to 25 so if it doesn't have an eight or a nine and it's broken it can't have an eight in it must have a nine in it the nine must go there which means that's not a nine i don't know if that can be an eight still um ah bobbins um sorry i'm stuck again i thought i was on a good path there but it appears that i'm not um but okay how about that though if there's an eight in one of those squares where does eight go in this box can you put it in there the answer is no the answer is no if you put 8 in this 12 cage it's got to be 8 1 3 and that 3 those 3's are matching off and you can't put a 3 in this column anymore 3 couldn't go there there'd be a three in there can't go there there's a three in there and those squares are not three so so this is eight there we go so we've got an eight here we've got an eight in one of these two cells we've got an eight here this is important so i've got a 2-5 pair here i've got oh look i've got more eight one one seven right come on crack you little naughty thing um [Music] i don't know what oh there's two fives differently the one and the two oh i've just realized something i could have got this eight when i got this four i could have got the eight then couldn't i because i worked out those two added up to twelve oh simon you're such a nutty oh well i proved it a different way in a far more complicated way sorry um oh yeah okay well that at least has allowed me to remember that i worked out those two squares added up to five so that being a three gives me a two here which presumably that's going to flow around the grid yes of course these um okay so there were definitely easier ways of solving this part of the puzzle but i still haven't done it all right okay this is this 12 cage has oh two cells that sum to 11 that are not two nine or three eight uh if they're four seven that would be a four this would be a one seven pair but it could be one five six could it maybe maybe what about this 12 cage that must have a one in it now because it hasn't got a two or a three in it so if it didn't have a one in it it would be a minimum of four five six which is fifteen so there is a one in there okay that's still not quite done it has it um whatever you put in this 12 cage has to be different to whatever you put in that 12 cage because well because because if these are the same so imagine that was one four seven and that was one four seven then those squares in column three would have to be one four seven and they're not so the fact you come we can't make these one two nine both of them means this these digits restrict these twelve cages ability to be the same numbers so one of these is one four seven one of these is one five six right okay i think what we have to do here is to think about how we're going to allocate digits from orange into blue because we're starting to learn quite a lot about this aren't we so we've done all of the low digits we've done the eight we've done the two nines we know there's a nine in here and there's a nine in here so what we haven't done is all of these sevens they've got to be a lot of sevens now do we know that one of these is a seven do we know there's a seven in there no we don't that could have been four or five couldn't it okay so i don't know if there's a seven in there which is annoying because if i in fact if i knew there wasn't a seven i'd know all of these have to have seven can that one have seven in it nine seven would be 16 oh that's horrible then we'd have two cells added up to nine and there are four ways of doing that although one and two would be tricky um [Music] three sixes four fives what about this one's got seven in it oh yeah because this one's got nine in it so that would be sixteen and then we'd need two digits that added up to seven that couldn't be ones and two so it would have to be a three four pair so this would have to be three this would have to be four and this would have to be seven not sure that seems possible as well doesn't it this one's got eight in it so can this one have seven in it that would make it fifteen it would need again that would have to be with three five because it can't have ones and twos in it i think that's okay um [Music] wow wow okay so how do we do this then oh is that five correct pencil mark yes because i couldn't have this being yes i worked out tonight this was not a four seven pair so that's not a five doesn't do anything um so there's a five in there that maps to this five i've got a five in here so there's got to be there's exactly one more five in here sixes there are two sixes we don't know where they go oh this is tricky this is very difficult there's got to be something i think we can do to allocate these digits in an efficient way i'm just going to check this one again because i know there's a 9 in here this is 9 6 9 6 these these have to add up to 8 and they have to be 3 5 is there something wrong with that in fact they would have to be in a better order than that they would have to be five here three here that would have to be a five but if this is 9 3 these have to add up to 11 without using 3 8 or 2 9. so they're either 4 7 which would have to be this way round or 5 6 which would have to be this way around so this cell is more restricted than i thought but this cell it really isn't under that much pressure wow okay gosh it's another very long video tonight i'm sorry this is tricky though this is definitely not an easy puzzle um hmm so where is it that i meant to look for an epiphany i think it's going to be under the sea in an octopuses garden in the shade we could argue about um i don't know i really don't know do i have to use this one's got an eight in it so i've got three cells that add up to 15 that don't use ones and twos at all so if they don't have three in them they have to be four five six and what's wrong with that maybe i can prove there's a three in this cage that would actually be helpful because it would have to go here right so why is 456 impossible i'm not sure it is is the truth um [Music] if it has got three in it ah it's got a five in it then okay that's interesting if if this cage does not have a three in it it's got to be four five six because it's not got ones and twos in it and i need 15. so if it's not got three in it it's got um four five six plus the eight that we know is in it now if it does have three in it then then the eight and the three sum to eleven are only two cells that sum to twelve that don't include a repeated eight and don't repeat the three so they're not three nine so it's five seven ah this is good right okay so there's a five in this cage there's a five in that cage which means there's no five in my twelve cage here now that means that this is not one five six and i think that means it's got to be one four seven doesn't it because it can't be one three eight and it can't be one two nine right so that's one four seven which means that that is not four or seven oh i don't know whether i don't know which side the five is on do i so i don't think i know what this is um [Music] i'm not sure about that but okay what are these digits then these are five six and eight so now i know what these three digits are these three digits are three four and seven which and that's not seven and that's not four so these digits have got to be one five and six and that's not five oh there's a what there's a one five six triple in column one look so so this can't be a one uh this cell here because the one in this one five six triple is definitely at the bottom that can't be a one now has that done anything for us oh hang on there's a there's a one looking at this hang on have i made a mistake here one five six triple i think i've got i think i've gone doolally hang on let me just unwind this a minute one five six triple i think i i think when i pressed the button on this i took the wrong digit out i think i was intending to take out five because i saw this i ended up taking out six and that's got me totally discombobulated but actually if we come back here i can do better and that's what was confusing me when i was just looking at it i was seeing a one and a five in the row that's got to be a six which means that's six that's five that's five that's one here we go here we go maybe um this is not six anymore i can't remember what the combination was that that was affecting this five is looking at that square making it a seven so now in this cage i've got a nine and i've got a seven which is sixteen i need seven more in the other two cells and we know you can't put ones and twos into any of this box so this has got a three four pair in it so i can't have 6 in it which means that square's a 6. there's a 3 9 here so this square is a 4 this could be it you know we could have just cracked this i think let's hope i'm not speaking i'm counting my chickens here now that seems to have to be a four so this is not four or six anymore so this is three five and eight which means i now know what these digits are i suppose i've got 10 19 this has got to be a six nine pair and there's a six here so this is all good six nine nine three three seven okay so now oh we don't know what these are yet can we do can we do something else two that's a two here by sudoku has that been there for a while i think it oh no i think it has does it do anything it does a little bit just this two at the bottom does the five here um doesn't do the six and the nine um these squares have got to be five six and nine and these squares have got to be six seven and nine i think okay so we can't do that we can how am i going gonna resolve these ones and twos is that oh i know how to do that there's a six here five therefore that's two that's one that's two that's one that one must go with a nine to add up to ten which means nine these are not nines and this is now a six and this is a seven by sudoku so that's lovely that gives me the nine here and the five which gives me the six and the nine at the top i think this is gradually slowly but surely coming together isn't it this is this can't be six anymore that can't be six anymore oh try not to disregard the eights and nines as well so that's nine that's eight that's five whoops ah no i just want to remove five from this square oh can't do it um that seems to have to be five because there's a four seven pair okay so that's going to be a six then if we trust our pencil marking that's going to be an eight six comes out of these squares we're left with fours fives and sevens which is probably oh it is resolved that's a five by sudoku so that's four that's seven that's four so now okay so now i've got nine in here so these have to add up to seven so we can do that that's got to be six that's got to be one that's a seven that's a four that's a one all by sudoku this box needs three and seven which we can just fill in and we'll check whether this adds up which it does to 23 yes okay so i'm now fairly convinced we're on the right track here 5 comes out of those two squares so that's a 3 6 pair making this a 5 and we can do the 3 and the 8 by sudoku as well plonking an 8 here telling us that digits are four that digit's a four by sudoku that's an eight by sudoku this is a three seven pair so seven and three go in and suddenly the puzzle's finished in a flurry and we can click tick yay that's really clever my goodness me that's one of the hardest killer sudoku's i can remember trying on the channel i mean i know i spent a long time uh laboring the point about scrabble tiles at the start but hopefully if you've not seen that before it will have at least made some sense it was a tricky set to find and i only found it because i noticed that those were hanging in the set and i suddenly thought how do i get the rest of that 28 cage into orange but even once you find that it's not easy you get those digits um but after that yeah no that's it i had to do the count didn't i have low digits in blue and then allocate the low digits to orange which is very in it's a very interesting but difficult idea um [Music] i can't remember what i did after that i think i messed about a bit i think i could have got some more stuff like when i got the two and the three and the four and the eight i could have made better use of those but some of these puzzles they are meant to discombobulate you and this one certainly did so apologies it's another long video um maybe tomorrow i'll be given a slightly lighter workload we shall see um but uh do let me know in the comments how you got on with the puzzle it's a great puzzle grid dancing bremster take a bow and i do enjoy those comments especially when they're kind i will be back later with another edition cracking the cryptic [Music]

Channel: Cracking The Cryptic

Views: 37,748

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Id: Oz3W9ogZ9N0

Length: 68min 54sec (4134 seconds)

Published: Thu Jul 14 2022