You Won't Believe How This Puzzle Ends

[Music] [Applause] [Music] hello and welcome to friday's edition of cracking the cryptic and we have a puzzle today with the very rare quality of having a 100 approval rating on logic masters germany this is another puzzle by joseph neme who we've well he's been wowing us in recent weeks with just a series of superb sudoku puzzles and the testing reports on this one confirmed that it's 100 rating is completely justified so we're in for an absolute treat and i mean before we start just look at the structure of this grid it is so beautiful it's sort of a sort of i don't know a swiss flag in the middle the sort of almost symmetrically disposed arrows these arrows are all um all symmetrically placed and nine in the middle the puzzle is called encaged nine presumably because look the nine has been encaged um so our job is to well fill in more nines etc we'll do that in a minute um few announcements first uh we've got there's some quite big puzzle competitions on the horizon this weekend i think is the first round of the world sudoku grand prix for 2021 i think it's bulgaria's turn to create the puzzles so if you're interested in competitive solving do check that out i'm sure google will help you and point you in the direction of the competition um also next weekend it's the um german sudoku qualifier which i think is hosted on logic masters germany and that's open internationally although i don't think international competitors can qualify for the um the finals in april but definitely that's going to be worth doing because the i well the puzzle uh creators are richard stolk uh philip bloomer who you may know as glum hippo um from the channel and also christoph seliger so a phenomenal lineup of puzzle constructors um for next weekend's contest i definitely recommend that one um anything else yeah on our own patreon pages you'll well i know a number of you have been trying the reverend puzzle hunts that we released earlier on in the week that has been going great guns but today we put some new content up there if you enjoy your cryptic crosswords then you may well enjoy mark solve of the times monthly special for january i always enjoy that video because you never see a mark struggle with a cryptic crossword like he struggles on this one it is always very amusing um oh well and now i should read out the names actually of the new solvers that we've had to reverence uh to reverence puzzle of course we have had and well done to daniel curtis jonathan lahav lucy stewart peter zuger uh i'm not sure if it's abdi or abday but abdi or abday is only nine years old and he's been doing it with his father moise so fantastic and just a quick word to say i mean if you do have very clever kids that is wonderful that they are getting through this hunt that really is impressive and um that uh i'm sure abdi will be a very very good um solver in in years to come if he's already able to reference puzzle hunt at the age of nine uh kenny palmer jeffrey beggan and oppo from finland um well done to you guys as well fantastic um now let's with that let's get on to joseph's rules what have we got we've got normal rules by the looks of it got normal sudoku rules apply in cages digits must sum to the small clue given in the top left corner of the cage and digits cannot repeat within a cage so normal killer sudoku the digits in the circles are equal to the sum of the cells along their respective arrows so normal arrows as well um so do have a go at this um the way to play of course is to click the link under the video with that i get to play let's get cracking and the first thing that sort of shouts at me in this grid are these arrows because these circled cells each see three well the arrows that emanate from them each see three cells in a box so these yellow cells these can't be the same digit so the minimum we could put into any of these trios is one two and three which means the circles must be at least equal to six so let's put that in that's a six seven eight or nine straight away [Music] now none of the killer cages seem to me anyway to be i was about to say they don't seem to be useful but actually the 10 cage well the 10 cage isn't in and of itself i mean i don't know what what's in this 10 cage but i do know what's not in the 10 cage a 10 cage in three cells can't have an eight or a nine in it and that's just got me wondering about this column because could never put an eight or a nine on the arrow because obviously if i put eight there for example the minimum those two squares could be would be one and two and that lot adds up to 11 which is most certainly not a single digit total so okay yeah so it's not quite perfect but where does eight nine go in column two well one positions here and there's two more at the bottom so there must be two of these three cells contain the digits eight and nine which is very nearly useful but actually may not be useful i've got yeah we've got the same thing in column eight as well but here that's slightly different digits look they're not quite aligned in the rows they're nearly aligned in the rows but not quite i'm actually going to highlight this this is quite interesting um so green cells two of the three green cells in each column has an eight and a nine so i'm now wondering whether we can ask questions of these ten cages or maybe it's just a better question is can you have a seven because you yeah you can't put seven on the arrows so if seven doesn't go in the ten cage you'd have a seven eight nine triple in the column so if seven is in the ten cage you'd have it would have to be one two seven which would lock one and two off these squares which would make these squares a minimum of three and four but that could still be one or two bobbins ah there's something here isn't there that this feels too too cleverly set up to not be important unfortunately i obviously haven't plugged in my clever brain today because i can't see i don't quite see how to do it it's the same on this side presumably it's just symmetrical yeah we just locked the one and the two out of the if there was a seven in there you these would be three and four this could still be one or two ah i don't think this is quite right so how do we do this then this is so peculiar it must be the other actually the other theater thought i'm having now is what if that's not the right question to ask about the 10 cage maybe the right question to ask is does the 10 cage have a 1 in it because if it doesn't the only way of making 10 in three cells is with two um two three and five gosh i had a complete brain freeze two three and five now that puts incredible pressure on the arrows because if this is two three and five those squares would have to be one four and six because you can't put a seven on the arrow and if they're one four and six the two in the same box would have to be the one the four because you can't put it i know you could go six one couldn't you could go six one and two you just know that the one is definitely up here that's putting pressure on this square so if you had four one or six one this has to be relatively loath so maybe it's maybe it's something to do with oh no i know what it's going to be i know what it's going to be i think it's i think it's i think it's the rows and the columns isn't it because if these two rows columns are going mad if these two columns are restricted and they definitely are especially regarding what has to go on the arrows given whatever i put in the 10 cages then that is having an effect in both instances on what can go into these squares and the 16 and 14 are not that well they're not that low but maybe they are low once you take into account what can go into those cells so i'm actually tempted now to look at well look at all of those cells together so let's let's just do the maths that's the best thing to do so if we look so that well each each column of the sudoku will contain the digits one to nine add up the digits one to nine you get 45. so this column adds to 45 that's another 45 that's another 45 and that's another 45 except obviously i'm double counting these sort of intersections in those sums so the sum of the sort of cross hatch pattern that we're we're creating here is 180 minus these intersection points now yeah this is interesting this is interesting so it feels like yeah i just wonder is it do i have to max this out in order to make it work if i have to get to 180 let's how could we do that how can i make this how can i make well i can make all of these nine can't i let's just make them all nine and see what that means because that makes the sum easy if these are all nines then along the arrows we know that these are all nines as well whoops miss click down here but ah new software helps me out so we know that the yellow cells are also equal to nine so in each box we've got nine plus nine so we've got eighteen from each box four eighteens are seventy two so i've got seventy 72 from these cells i've got to put the these in so i've got oh that's easy that's 50 look so i've got 72 plus 50 which is 122 and i've got to get to 180 ah but i get to double count each of these squares so 180 minus 122 is 58 and i'm double counting the squares so 58 divided by 2 is 29 that is oh that is very close to being perfect isn't it that is so close to being perfect because if i have to make these intersections add to 29 and that's that you know i can't make these these sums add to any more so they have to add up to at least 29 but i can't use nine in any of the any of these positions because the nine is is ruled out so if i have to make 29 i can repeat the eight of course right so i have i must have to repeat the eight so i've got two eights a seven and a six is what that would imply but i could have two eights i could have two eights and two sevens couldn't i so this is why i feel like this is close but maybe no cigar because each of these would then get doubled so this time i've got 30 30 doubled is 60 60 plus 122 is 182 which is too high so there there are there is a tiny degree of freedom about this if these are all nines but that that does worry me a little bit does that mean i can switch it if one of these is not nine if we say for example if i switch this nine in here and then make this eight does it still work or not because the eight gets double whammied as whereas beforehand this added up to nine plus nine is eighteen this now adds only adds to sixteen eight plus eight so i lose two there i gain one here so that still works bobbins ah i thought at least we might get the positions of the nines oh no but maybe having a nine here affects that one oh that's very clever that is very clever wow that this is going to break now oh this is lovely right so the question i'm i'm asking hopefully it's clear but let me go through it again i'm asking whether it's necessary in order to get this crotch crosshatch pattern to add to 180 i'm asking whether it's absolutely necessary that the circle cells contain nines and i was concerned that it isn't necessary because if they are all nines i can reach 182 by fiddling around with these digits rather than 180 so it feels like there's some latitude but if we switch one of these cells into the middle of its box rather than the arrow although we only lose one degree of freedom from the box itself this nine look it's having an effect over here which is massive because now this cell and whichever nine is in the middle is going to have this effect because of the beautiful geometry of the pat yes it always works it always works whichever one of these you decide is going to be the nine it's always going to hit another an arrow circle so let's look at this arrow circle anyway this would become an eight these squares therefore add to eight so all of a sudden from this adding up to 18 it now only adds up to 16. moreover this can't be a nine in this case either and it can't be an eight so this would come down to seven as a maximum so you're losing one two well you're losing at least three degrees of freedom in this box and you've lost one degree of freedom by by putting the nine in the middle in the first place and that definitely takes you below the 180 threshold so this is all an incredibly long-winded way of saying that you've got to have nines in the edges you have got to have nines in the arrow cells but the problem we've got still to wrestle with is although that feels like it's true we don't i've just got now i've got to make these squares or twice these squares add up to 58. so we don't really know how to do that we know what the digits are that are involved there must be two eights involved if there aren't two eights i can't get there because because the thing about these four squares is that you can't include three of one digit however you put three of one digit into these squares you will break the rules of sudoku so we can only repeat we can repeat a digit twice so if we go eight two sevens and a six for example that is not enough we need to get to 29 at least in fact exactly so we've got to go double eight seven and six but we don't know which way round the eights go so one way of thinking about this is that there is an x-wing on eight that is one way we can think about it so there's either an eight here in these two cells in the finished solution or here now that puts pressure on the 16 cage yeah that's lovely oh that's absolutely lovely the x-wing on eights so we know that the eights are either here and here or here and here so there cannot be an 8 in this 16 cage now if there can't be an 8 in the 16 cage and there can't be a 9 in the 16 cage can there not be a 7 if there's no seven this would be four five six which only adds up to fifteen so this doesn't work so there is a seven in here now once there's a seven in the sixteen cage it sees those two possible sevens there and makes these an eight six pair which means i now need these two to be a seven eight pair in order to get up to twenty nine and now i still don't know which way around the eights go but we feel that that feels like enormous progress sev oh you can't put six in here now either so this the 16 cage now is seven it is that's the only way you can do it which means the remaining cells are one two and three in row two and that's nah it doesn't seem to that doesn't seem to help oh but look yeah look the 14 cage down here now can't contain seven eight or nine so it must have a six in it otherwise you can't get up to fourteen it must be six five three that's the only way you can make the total work so now we get some more numbers on arrows one two and four this time um okay i don't quite know how to do this in terms of what are we learning from these so if we restricted the values of some of the arrow cells oh i ah this is beautiful i mean this is just a beautiful beautiful puzzle let's come back to the question i asked about 20 minutes ago which is where is the seven in these columns and the answer is i still haven't got a clue i do not know but i do know that one of these cells here in row eight is not a seven and whichever one of these is not a seven i've then got incredible problems putting the seven in that column so imagine this was an eight where do i put the seven in the column i can't put it on an arrow so in the column where the eight lives the ten cage is a one two seven so one of these is a one two seven triple now there might be a way we can tell which one of those is there a way we can tell which of these is one two seven the answer uh feels like it's blowing in the wind i do not see immediately how to tell that one two seven yeah no although i say that two eight two seven this is extraordinary isn't it i think i think it's going to be these digits is it the fact there's a four in here that matters well there may there could be a four in here and there's only a three in there not sure let's just have a look at the nine totals so in this tote given this can be one two or three this square here can be four five or six in fact it must be in order to get up to nine now this square down here that can be six still that can't be four because that would be imply these were a 1 4 pair and it can't be 5 because you can't put 1 3 here so this is either 3 or 6. that's so strange that there's such a discrepancy between these two digits as a result of the one switch in the the options being one two three or one two four six one two seven two seven eight six three yeah got it got it the um look at column two now if this triple we know remember we know one of these ten cages contains one two and seven if it's this one where do you put the four and the five in the column everything we've got here is not four and five if these are one two and seven the four and the five have to go on the arrow which means this square would have to be a zero well it can't be a zero so this can't be a one two seven so this is a one two seven which means this square is an eight this square is a seven that's a six that's an eight that's not six anymore [Music] now surely that is very useful he says he tries to work out why it's useful um yeah okay these are three four and five so this can't be four anymore look because given the option if we go three five there that would add to 12 which most certainly is not nine so the four must be over there lovely because that means if one of these two squares is a four this cannot be a six so this is a three that's not three anymore this must be a three two four pair in order to equal nine that results that this one is a one that's not one anymore three um [Music] three in this column can only go there that means in order for this nine to work this has got to be five four this must be a two three pair to make nine it's going around the grid isn't it it is this is now a one we can't make this three and five because of the three here so this is two and six okay well we don't know which order that's in but look this column is now done apart from one four and five which must go in the ten cage let's get rid of the corner pencil marks here let's uh pause for a moment nines by sudoku actually look at oh a c ah i could have seen this earlier as well but that's very well it's very beautiful again i don't quite know how to use it but nines are locked into one of those two squares in box four but you can see exactly the same happens in box two but if this was a nine you can't repeat the nine in the cage so if this is a nine that would be a nine and this goes right round the grid it's very much actually in line with the theme isn't it the nkh9 there are there is definitely yeah there is definitely an encaged nine not only here but in each of these cages there is one nine and it's either disposed like this or they're disposed like that can't read some of these totals let's just check what they are 16 there 20 there 18 there so this is the lowest so this square has to be six or lower so this square has to be six or lower let's look at that so this is six or lower now it could be six if it's not six well well it is six because this square here sees one it sees two it sees three it sees four it sees five so this is only six this is now one six nine there's a one there so we get some digits there the nine we know where the nine goes so we now can send this round the grid scuttling around there we go all of the nines get fixed uh that's not six anymore six is in one of these two cells and probably we now need to focus on these more of these arrows coming into the cages let's look at well we can look at this one or this one i think let's look at this one two four six seven two four seven because six is impossible so this is two four or seven so this is two four or seven it's in an 18 cage so these two add up to ah so these two add up to nine now look if this is two or seven this is two or seven which it can't be because of the ten cage so this is four this is five that's four it's stunning isn't it it's just it is really really stunning setting this ah this square's a one by sudoku that one there because of the four five looking at it that's not one anymore let's carry on right oh the 20 cage is unlikely to be as restricted as the 18 but let's just check this one because we've got more digits in the column we've got uh one five seven and eight this ah so this is just seven or eight is it is that right let's just double check that one five seven eight yeah i think it is so this is only seven or eight but we know this domino has to add to eleven given the nine in the twenty cage and you can't so this can't be seven or this would be four and the four would clash so this is eight this is eight this is three that's not three anymore uh okay can't quite see what we can do with that but we know these two add up to sev at a nine three four five seven so this square by sudoku is five or seven so this is five or seven if it's five that would become a four and that four would clash so this is seven this time so each of these well each of these totals has been selected in conjunction with these short arrows to resolve it's absolutely beautiful um now the two fixes the two and the four does that do something yeah that places a four in the top of the grid by sudoku this 2-7 pair sees that cell so that's got to be a one one goes here by sudoku now probably we've done all the ones have we no we oh we get a one here uh which ones have we not done i've not done a one in this box must be in one of those two cells and there as well probably means i can't resolve the ones yet this can't be a four this can't be a seven this row has already got lots of digits in it we need 2 7 and 8 to finish it that's got to be an 8 therefore that means this is an 8 by sudoku this is an 8 by sudoku we must be nearly able to do all the eights near oh nearly ah not quite eights in one of those squares and eights in one of these squares i think these squares were two and seven which doesn't seem to be resolved um [Music] adjust glasses think again um [Music] three four five six into this row so this is a three or a five that's a three or a six and that is three four or six i'm not sure if that's useful doesn't maybe appear useful sudoku on four is useful because it's yeah look there's a four eight pair here i think four seems to be locked into the same cells as the eight which means this square must be two ah bother it must be two or seven it doesn't resolve two five six seven in the column but this square can't be five or seven so this is two or six that gives us a two six pair there which might mean this square's restricted actually let's check this one um so what can if we look at the column this could be two three four five or eight so let's fully pencil mark it so we don't make a mistake now it can't be four or five because of the four and the five there uh it can't be three there's a three in the box now why can't and it can't be two because of the two six pairs so this is eight that gives us an eight here gives me a four here that fixes the five the seven oops the five the seven and the four that fixes the two and the seven into those two squares that makes that one a six that's a six that's a two still gonna put two and a one in that box which we can now do these squares now are five and seven which we can do nice just sudoku that's gotta be a three by sudoku that's got to be a something a five and seven look this seven seeing that square i've still got to put a seven in this box so it goes there that's not a four don't scan like that simon it is not the path to success that's a five this column still needs two and three into this square there's a two seven pair in the box though so we can go three two three this should be a four six pair of course that's not resolved no it's not is it okay um two three and seven into this line so this is a three that fixes the five that fixes the five and the four the four and the six gives me a three here so in this box over here we you can see we need six and seven but there's a six there so we go six seven seven two and this square looks like it should be a two three six five i think looks like i filled in all the digits i click tick yes that's how to solve another gem of a sudoku from joseph loved it that one is elegance personified isn't it it really is the whole trick with the uh the arrows interacting with the cages is extremely clever there may have been a better way of me explaining the beginning there um i'm not sure be interested i always enjoy the comments so do leave me a comment especially if it's a nice one and we'll be back later with another edition of cracking the cryptic

Channel: Cracking The Cryptic

Views: 116,222

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Id: 8kNGunKUGi0

Length: 36min 54sec (2214 seconds)

Published: Fri Jan 15 2021