A Tribute To Numberphile!

[Music] hello and welcome to Saturday's edition of cracking the cryptic where today we're going to be doing something um as a little tribute to a YouTube channel that we admire very much and that is of course number file um many of you have already seen that somehow or other um Brady Haron who runs the channel decided to um to do a s a couple of sidoku videos um and featured us um so if you if you haven't heard my explanation of the fist in Mell ring before or you haven't seen my sideways profile which seems to be attracting a lot of a lot of comments you can you can you can see those things in in number files most recent video so um massive thanks to Brady um it was um he is exactly as you might expect Charming Charming bloke uh and a lot of fun to talk to so um yeah we we we achieved one of our small Ambitions of this little Channel about sodoku variants um yeah somehow somehow made its way onto number five is fantastic anyway we thought therefore we should do something that had a mathsy flavor today and we've been recommended the puzzle on the screen by none other than codec um and Marx had a look at it and says that it has it has maths behind it it's called reindeer and it's by ket's dad and it was made apparently as part of the secret santa um uh which which happened on the Discord server over Christmas time and it was made as a present for Rocky rower um and um yeah apparently it's absolutely brilliant and and the basic idea I will explain the rules properly in a moment or two's time but the basic idea is that each of these lines operates as both a zipper line and a region sum line so if you know what the rules are behind zippers and region sums you'll be good to go um but anyway I will read you the rules in a moment or two there are other things I'd like to tell you about first I'm going to start by mentioning something quite incred rible uh which is that our book uh well cracking The cryptic's Greatest Hits Volume 2 has been arriving lots and lots of you have been tweeting this to us um do I have I do have a picture I do have a picture here you go here's one such tweet there you can see there's the original book there's the new book there's some of the acut tramont that accompanies the new book we've had bobin's cushion covers tweeted at us um and this is great obviously we are at the whims of global Shipping when it comes to I mean the book's been ready um uh for ages um but we have to we have to allow the ships to the ships to sail and the and the airplanes to deliver etc etc but they are now arriving on mass so this is great news we hope you enjoy the book um it's been an absolute treat for us to create it and there's lots and lots of interesting new stuff in there including lots and lots of bonus puzzles the book's still available obviously you'll have to wait for delivery um but I'll try and remember to put a link on the screen in case anybody is new to the channel and doesn't know about the book and thinks they might like to get a copy um other than that the only other thing to mention is what's going on over on patreon at the moment where we've got all the fun of the fair our brand new sidoku competition runs until the 20th um and to oh yes and in fact tonight it is tonight yes it's tonight so if you if if if you watch this video and you want more cracking the cryptic then um I am releasing this evening my Sol of this puzzle over on patreon Roller Coaster newari by the Kito this is this is a brilliant puzzle but as you can probably see from from the question marks um there's not a lot to go on it's a 2 and a half hour video um of me doing battle with a beasty um and yeah it's um that's something that we we we've started to do as an extra present every month um for you guys who support us over on patreon Long solves of very very very hard puzzles so that's coming out tonight um other than that no oh yeah no birthday I mustn't forget um let me look and it is the birthday today of sigan over there in Norway and sigan how do I know this is because your friend Clara wrote to us and I think the two of you met on a student exchange and she wanted to wish you a very happy birthday and I do too so happy birthday I hope you have chocolate cake today and have a wonderful celebration now let me read you the rules of kennett's Dad's puzzle reindeer they are as follows we've got normal Sudoku rules apply so the digits 1 to 9 once each in every Row in every column and in every 3x3 box along any individual line each line segment within a different 3x3 box must sum to the same total different lines may have different totals so let's stop there and check we understand that um so this is the sort of region sum line rule what that's saying is that that digit I'll explain why this this is all the case in a moment but let's look at this this line here now you can see this red line has a has a bit of its itself within box two just this cell here so let's say that this was eight if this if this was eight then we would know that the blue digits had to add up to eight because they are the two they are the they are line segment within box one for this line and the line segment within box four for this line is those two yellow digits so the blue digits would add up to the same as the yellow digits would add up to the green digit so that's how let's let's do another line just to make sure we understand let's do this line so those three add up to those two add up to those two something like that is how it would work um a funny squeaky noise I can hear hopefully that won't come out on the microphone anyway um and different lines may have different totals so if if this was eight that doesn't have to be eight oh no not that no if that's eight these two don't have to add up to eight these could add up to don't know 15 or something they could add up to quite a lot couldn't they cuz yeah they I think in fact the maximum I'm going to claim is 15 so those two could add up to 15 um and that's the way I've got that is I've noticed the maximum sum of those digits would be 30 wouldn't it it and if they were 30 but each of these individually has to sum up to the same number then 30 / by two is 15 so I I apologize if that does turn out to be the region sum total for this line it wasn't it wasn't it was just by luck it was serendipitous um okay and that right so now there's the zipper rule so it says additionally along all these same lines digits an equal distance from the center of the line sum to the same total for odd length lines the total is the digit in the center of the line um so how does that work um let's have a look so what we let's use this line again so this is saying that for this line digits and equal distance from this Center add up to the same number so those two add up to the same those two add up to the same those two add up to the same and because this is an odd length line the middle digit is what these purple add up to is what this yellows add up to is what these blue set up to now let's find an even length line um I think maybe this might be the only one I'm not sure so on this line how does it work for this line so these two have the same total as these two I think that's how it must work but you but on the on the even length line you don't know what the total is or at least that that isn't revealed in the grid whereas it would be for this line um and then there's one more rule which says oh no it's no it just says in other words the lines in this puzzle are simultaneously region sum and zipper lines so that's all the rules do have a go the way to play is to click the link under the video as usual but now as the clock Chimes I get to play Let's Get cracking I might start down here actually this looks like it's got the most the most things going on I'm not sure if it is the longest line length seven it is the longest line actually so this is probably where we're meant to start so let's think about it what we know about this line is that the digits on the line are a multiple of four and A all right and a multiple of three right so the digits on this line are a multiple of 12 um that feels like it might be important so so how am I seeing that by by the way that's hopefully that's fairly clear um because of the region sum rule so because these digits add up to the same as those digits add up to the same as those digits obviously all let's call this green section X then the line overall adds up to 3x but because of the zipper totals the line also adds up to four Y where Y is the digit in this cell so simultaneously all of the digits on on because if this is y those two are y those two are Y and those two are y hopefully that's clear but but so simultaneously all of the digits on this line add up to three times a number and four times a number in other words the digits on the line must up add up to 12 times a number now if that digit is 12 what does that mean 12 feels like it no 12 is impossible 12 is impossible because these digits here sorry my phone is buzzing at me um these digits must add up to at least 10 mustn't they if these were 1 2 3 and four they would add up to 10 which is the least they could add up to and then those digits must add up to at least six if they were 1 2 and three um so so it's not possible to keep this this line down to only 12 overall now if it was 24 if it was 24 then each segment on from a region sum perspective would add up to eight yes okay well that's quite interesting so you can actually start to fill this line in um so what I'm seeing now is that if this line adds up to 24 then from a zipper perspective we know we know the line adds up to 4 * Y where Y is the digit in this cell so that's a six so if this line adds up to 24 this is a six but in this box this adds up to eight doesn't it because the line also adds up to three Zed where um where Z would have to be eight so this would be a two and that would be a four um because I'm thinking of zipper logic and now these two squares would have to add up to four as well because this this line segment from a region some line adds up to eight overall so this is a 1 three pair and these two squares add up to eight as well but we've got to zipper eyesee them so these are oh so we're going to get double three on the line if this is right this might not be right by the way but this is just me trying to understand what this is doing [Music] um yeah this is going to be a 35 pair because the one is going to be opposite five in one of these positions so that's very cool so if this line adds up to 254 overall you can almost fill it all in now the problem is I don't well let's just see whether we can we can find another option that works for this line so if we went up to 24 so we need multiples of 12 so if we go up to 36 then we right that's the most we could go up to because the line is we know that the line is four times this number which would have to be nine so we can't go up Beyond 36 cuz we can't put more than 9 in here here now if we're at 36 we know the line three times the line or three times this value is a sort of region sum total so this would be 12 so this would be three this would be six um and then these would add up to uh what would these add up to these would add up to six and these would add up to [Music] 12 um that feels M that feels much more open-ended actually because there are lots of well there are two ways of this these two digits having up to six they could be 1 five or 2 four and I don't think either of those are ruled out from here oh that's that's very distressing then so okay so all I actually know is that this digit is 6 or n ah I do know I do I can get these two down can't I for sure so if that two opposite four was one option three opposite six was the other option so the only deduction I'm seeing as a result of that is that six is in one of these two squares which means that is not a six um that cannot be important can it uh does it matter for this line is this somehow important I think it's not going to be because this line is so much less constrained than this one so this line we know it adds up to a multiple of two because it's got two line it's got one line segment in box eight and one line segment that must add up to the same number in box seven so it's a multiple of two and it's a m and it's a multiple of three because it's an odd length zipper and what we're also I suppose supposed to appreciate is that those each of these colors adds up to the same number by zipper logic so this line adds up to a multiple of six Al together um now but that's got that's got a lot more flexibility than a line that adds up to 12 cuz it could add up to 6 12 18 24 30 you could easily get up Beyond 30 ah no you can't no actually I'm wrong aren't I because the line adds up to three times this number and this number can't be greater than nine ah hang on three times yeah no okay this is even right that's that's so straightforward why can't I see that immediately don't know brain brain failure yeah this is even because if it's odd the line overall is adding up to three times three is an odd number it's adding up to three times an odd number which is an odd number but we know because um because the line could be expressed algebraically as 2 * x with this being X and that being X that it should add up to an even number so this is even it can't be two can it no there's no way it could be two because we can't we can put double one there but then we can't put double one again there so it's at least four um it's four six or eight now if it's four the line overall adds up to three lots of four which is 12 and he right that doesn't work that's beautiful right this is this is very clever by the way um this can't work because if if this is a four and the line therefore adds up to 12 overall by zipper logic each region Su piece has to add up to 12 / 2 which which is six now I can't make those three digits add up to six because these can't be the same number so this is not four this is six or eight oh for goodness sake okay and that's it that's be it's beautiful it's far more it's far more brilliant than I'd I'd appreciated somehow when I looked I I saw the one of those two squares was a six and I said that digit can't be a six which is totally right but but that logic equally applies to that square that is gorgeous so because one of these is a six this can't be a six because it would wipe six out of these two squares this would be a four this would be a nine and now this Square would need to be a five and the it would add up to 14 here and we can't make that work um I can't remember why that doesn't work work but it definitely doesn't 14 42 overall for the line 42 is not a multiple of four yeah that's why so so this is total nonsense we've got to go back we've got to say this can't be six so this is eight which doesn't do any immediate damage to this but now presumably we can work things out what does that mean so this line adds up to 24 3 * 8 because these add up to eight and these add up to eight but each region sum strand is therefore 24 ID by two which is 12 and to make those three out up to 12 this has got to be a 1 three pair and they must be opposite a 5 S pair because each individual sort of pairing has to add up to eight now we can't put one or three in these cells now which does that affect anything if this was six that was going to be 2 4 8 24 12 um 8 four yeah that doesn't work I don't think so if this was six and this was two and this was four then the region sums total for this line is eight so these have to add up to eight they'd have to be 1 3 4 and they can't be right this is great so now this this is nine this is three this is six these two squares add up to six and then don't involve a one so there are two four pair which must be opposite 57 so each individual bit adds up to nine five and seven add up to 12 which is right that's perfect that's perfect because we wanted each bit to add up to 12 so therefore well therefore what are we saying next here is a funny point about this circle this this circle's mathemat or this Line's mathematics are the same as this Line's mathematics so there's a subtle difference in the shape of the line that this two cell sequence here is straight whereas this two cell sequence is on a diagonal but when we did the mathematics of this line we didn't care about the exact shape of this within box s we just cared about the fact that the line added up to a multiple of two and a multiple of three and that is the same for this line and that meant that that had to be even and and it had to be and we worked out it couldn't be four because that would that would cause both of these to be one so that is six or eight now if it was six what did that mean the line added up to 18 uh see that would work I think because if this is a six I think the line adds up to 18 which means each strand on the line adds up to nine which would mean these could be a one two pair so that's option one if this is eight oh if this well if this is eight we're in this world aren't we so this is a 1 three pair so this is either 1 two 3 it's either one two or it's 13 there's definitely a one in one of these squares now what's what happens on the other end of the line so if this is eight this is going to be 57 again because this will be 13 if this is six [Music] um these two digits add up to nine this is a one two pair so these are 54 pair I think so this is either sorry this is either a 54 pair or what was the other option it's a 5 5 S pair so it's definitely got five in it so oh no that I thought that was going to do something sodoku for me but it doesn't seem to want to um okay may maybe it is soku actually I'm just seeing I can do some pencil Mark nines um I don't know what am I meant to do now what was this this was either oh 57 5757 what is that doing something clever it's putting fives and sevens down here or this was four five there's definitely a five in one of these squares h not sure or is it going to be is it going to be this line or this line this line this line is the same trick again I think that's three cells in one box two in the other and it's a length five Lin so it adds up to a multiple of three and a multiple of two so it adds up to a multiple of six and the dot is in the same place so this must must be six or eight we've got a 68 pair in row four now and we can we must have the same pencil oh that yeah we have got the same pencil marks but they don't I thought for a moment they might align but they don't actually seem to so we must have a one in one of these and this is either 57 or 4 five and it's definitely got five in it so five in row row one has to be in one of these three squares now I mean the the thought I'm having at this point is how does this possibly how does this possibly resolve itself uniquely at this stage or not at this stage but in the end there must be some absolute magic that we can do with this line or this line I don't like the look of this line line at all this sort of I don't know what would you call it pedy line um what are the digits I've not put in there they are uh 5 S and nine aren't they 579 right so there's a 579 triple that's not a five in row nine that's not a nine 5 seven oh hang on hang on what's going on is that right does seem to be doesn't it it's a straightforward sidoku get a 5 seven pair here so I can place five in box box nine I don't think it's going to do me any good mind you but it is at least a digit now these squares so we need 1 7 8 n oh where's seven where's seven in oh this is huge sorry it's soku I shouldn't be surprised should I it's soku I was all all prepped for my math today and it's soku that's a seven so these so these squares are now a four five pair now that went with six on the line didn't it so these are a one two pair let's I'm I'm just going to check the mathematics of this line now uh they add up to nine they add up to nine so that looks great and each individual sort of pairing can be made to add up to six so that feels right and seven is in one of these squares oh this being six means this must be eight now that means we've got we haven't got four involved here so we've got a 5 S pair which must be opposite a 13 pair and these squares are 1 8 and 9 that's not eight this isn't one and not sure not now now very unsure about whether to focus on sidoku or to focus on eight is in one of these two squares uh or whether to focus on line logic four is in one of those two squares by by the fact there's a four in this this Domino can we do any better with this line or do we have to think about this line let's well let's color let's color this line in so those that adds up to the same as these adds up to the same as those so this line is a multiple of three overall but from a region sum perspective it is in three different boxes so we don't improve upon that in this case so this this is weird although this line goes into more boxes than this one and this one its mathematical proposes are less restrictive I suppose apart from that digit has to be a single digit total um what does that matter really these two digits these add up to the same oh hang on let's do my head in is it if that whatever that is I see oh dear okay okay this is very very interesting I love the fact that kennet dat has obviously given these lines quite a lot of thought because this one it is it's less restrictive in one way but it has got an interesting property and that property is that the sum of these digits is the same as the sum of these digits is obviously the same as whatever this digit is so and we know this line is a multiple of three imagine this line added up to 18 maybe it's better if I do this with an example if it if it adds up to 18 overall then this would be a six the these this line would add up to six and this line would add up to six but simultaneously because the zipper properties are the same these two have to add up to six and these two have to add up to six in other words um this those two cells add up to the same as these two cells and they have a common digit here which is that cell when that means these two cells have to be the same number to make that work and surely that must not work the other way around which is to say these two cells add up to the same as this cell um or these two cells together the common digit being this one so these two cells are the same so actually so by sodoku A and B go down here can a and b oh can you can you well you can't make you can't make a or B9 definitely not ah ah this is oh this is superb right this is this absolutely huge right so the question because because A and B are going down here the question we now need to ask is is this A or B and I think the answer is no clearly nine can't be in any Can't Be A or B can it because if nine was here once we added on one another digit to it this digit would be a double digigit number which it cannot be so so A or B is not n could A or B be eight no because if one of these is well actually straightforward how do I do it this way in my brain I was I I was in love with the fact there was a one here so so one of these the lowest one of these digits could be would be two and 2 + 8 is 10 I didn't just see there was an eight there and Rule it out that way which is completely Bonkers it's completely Bonkers anyway there are many ways therefore to prove this is not a or b so this is an AB pair right isn't that going to tell me where nine is then down here because if this was nine we've got the same problem all over again which we're not allowed to have so we can get rid of nine from here which seems to mean oh hang on why have I got nine why did I have nine pencil marked into those squares I've got no idea that must be an an oh well what digits are they from they're not very many different things actually I want to say I appreciated this but I want to say that they're from they've definitely got twos and fours in them as possibility six oh bother okay B sokio is how I'm seeing that I've got 1 3 5 7 and nine so they're not odd they can't be eight so they're from 2 4 and six so they're they're very even in their nature 2 4 6 are the options which means this digit is even now this digit can't be eight so the maximum size of this is six well it is six then yes that's beautiful as well isn't it because we're because we're adding up even numbers to generate this total double green is even double blue is even so this is even but it's we're adding up at least 2 + 4 to get six we can't use eight so it must be six and now we can't put six on the lines so we've got twos and fours which means this is a two four pair right we can get rid of our AB um pencil Mar now now three is in one of those squares along with six by the looks of things so let's put that in pregnant Paws will I try and work out if I can do better than that this column now has got lots of digits in it hasn't it six 8 and six again 6 8 and N so that square is 6 or n and that top digit is 6 eight or nine six is in one of two places in column five four is common between the the these two squares and this Domino so four in row one has to be in one of those three squares um now what does that mean that digit where does that digit go in box four well it's got to go there that gives me a 57 pair in column three we might color our fives and sevens if we get very stuck actually because there are we have got a lot of those pairs in the grid now probably I'm also meant to think about this one aren't I I've got a horrible feeling that there's some sodoku staring me in the face as well let's Oh I thought I was going to get a two four pair there no I'm definitely not actually but that digit is there four in this box no I'm not sure okay what's this line telling us this line is telling us that um the digits on it all together are a multiple of two and we can see that in two different ways we can see it because those two must add up to the same number and those two must add up to the same number so if that number's X the line overall is 2x but we've also got the situation where these two must add up to those two by region sum logic so these two so yes okay so so again it's a bit it's a bit like this line isn't it oh it's a bit like this aspect that's so weird I feel and this might I might be about to totally disprove what my brain is sort of implying to me but I feel like the logic we did there transposes to to this pedal shaped line now let me see if I let me see if we can just prove that so what I'm thinking is that this digit whatever this digit is it has a partner here so the two purples add up to a number let's call that number X therefore these two digits add up to a number which is also X so the line total for this line is 2x where X is the is the sum of the two purple digits but the line is also from a region sum line perspective the sum of these two digits well the sum of these two digits is the same as the sum of those two digits so if this is y this is y so the line is also 2 Y where where Y is the sum of of these so whatever this digit is those two digits must be the same because we need to make sure that 2x equal 2 y if you see what I mean x equals y so where we said X was the purple y was was the vertical for those two things to be the same when this digit is common to both sums these two digits have to be the same and that that must work the other way around by Sy so these two digits are the same number um a and we'll call those B now and we'll get rid of the A's and the B's that we had over here now let's in fact let's just prove that to ourselves using numbers cuz that could be helpful couldn't it just to absolutely make sure that we understand that let's imagine this line added up to seven uh in other words purple adds up to seven and let's make this square a oh well let's ignore all pencil marks in the grid okay I'm just going to make this a four and let's think about how the line would work if we if this line was adding up to seven this would be a three the line that's adding up to seven so the line overall adds up to 14 um which means each region sum segment adds up to seven yeah so it is very clear isn't it once you think about it like that um the only way it could work is like that and these two are the same and these two are the same so our logic is correct now that means that b look is in one of those squares by sodoku let's actually put that in B is in one of these now can we can we rule out any options for these squares okay I can B is not that one because that's a five or a seven and five and seven look at B in column seven so B is not that one can we get rid of this one don't think so it's quite close actually I'm not sure I don't think I can get rid of that one isn't yeah I'm not sure I'm not sure I'm going to come back and think about that I'm just I'm just going to ask the question what this digit is that digit by sodoku is one 3 6 N I think but three and nine wouldn't oh actually no it's not six by sedu either this is interesting I think because I can see that three and N are ruled out out of being this couldn't if this was if this was a three or a 9 it couldn't be B Because b c is three and N in this column so I think B which is those two digits is now either 1 two or four now can we do any better oh it's not full four actually Four is here okay B has come B is one or two now but it still doesn't tell us which of these cells it goes in so these two right maybe I maybe I need to change my coloring actually because I when I'm looking at this I'm not sort of appreciating that those two are the same and these two are the same that feels a bit better so one of these two is the light green digit um so if B was how are we going to do this then a has to go up there but is a is a under some sort of pressure that I can't foresee um not sure not sure um let me think let me think or is there a reason that this two doesn't work so if this was two this was two and this was two then we know that's two don't we from our yeah see all my shading is all a bit up the swanny here I think I'm going to change it because because what we actually learned before was that these two digits were the same didn't we so they need to have their own color and these two are the same so they need to have their own color let's make those red [Music] um that's what generates these two as being a red blue pair and if that digit is the same as B so if these are twos that's a two and that's a two two is in one of those cells there an awful lot follows from that that might be fine um bobbins I think that's the technical term but what we need to do now um there's no neither of these digits neither of the oh if we could resolve this if this turned out to be a one that would give us B maybe maybe I've got some sidoku that will help me um let's think about that for a second or two come on sidoku be kind what does that mean um I don't know and these are such low well does it matter they low I don't think it does really these two digits Under Pressure one from a straightforward soku perspective let's look at a a could be 1 2 4 it can't be three can't be five six it sees this six sees sees the bottom a it could be eight I think unless there's some eight looking at this that I can't can't see now 1 2 4 or eight but a oh it's not four is it because four has evaporated in the in we've used up the two fours in rows two and three already so it's one two or eight and if it's two then you've got to put two up there that doesn't work by sodoku because this is a two four pair so it's not two so it's one or eight oh this is so restricted now surely we can do this come on how do we do this surely we can do it um if so we know ah I see so we know that there's always a one don't we is that right actually that might be wrong no that's wrong you could have a 28 pair with it adding up to 10 28 28 yeah that might be possible I'm not sure um okay so we might have to do some coloring some other way or I mean there's no there I don't think there is any parity trick with this I was wondering if I could if I knew the parity of this do I know the parity of that I don't think I do might be wrong but I I I can't my brain isn't telling me that I know that what could we do let's think about um let's see I don't know where to look if we could get yeah I mean if we did know that this was a one everything would flow over here it would do a disambiguation of our twos and fours if that's one that's two that's three so sorry if this is obvious to everybody I apologize I'm not quite seeing it six okay oh right so now I can do six in this box because it can't go on the line which gives me a six down here come on which gives me a six here and a three here no it's still not right it's not quite going to see the right places oh look three is now in one of two places in box one it's close to cracking isn't it it's really close to cracking this three no no that's not the right way round I thought that was going to be the right way round I thought this three was going to look up what I thought this was going to be a one and look up there but it doesn't bother um okay but but we can use the zipper property can't we so that's seven and that's five now because each each sort of thing has to add up to eight around the line that seven does a five here okay which does a five here and a seven here that's all fine that does a five in box um in box eight now so we get a 79 pair we've got a lot of digits worked out in this Row one two and four to place that can't be four so there's now one two pair in column nine and we haven't placed three eight and nine so that's a naked single that's an eight and these two squares are a 39 pair please pleas well they're not they don't include eight anymore so sidoku is starting to help us here that's eight that's four that's four that's two that's two that's four and that's done it that's beautiful because now two is looking at this digit so that is a one and that means these are eight good grief that's a one by soku so that's a nine that's an eight that's a one this this is a nine c six and eight in these positions so that's a six so that's a six that's an eight by sidoku so there four eights looking at the central box okay now now I'm hopeful eight eight in box one can be placed three looks like it wants to be placed in box one six can be placed in box one that must be all the sixes I feel like I've written in a whole host of sixes um okay so these squares are now seven and nine which is resolved which gives us a nine and a three okay and oh because these are resolved we can do the zipper tactics on this line at the bottom um seven that must be with two that must be with four okay so four in one of those squares and right what else can we do with this this square is a two or a four apparently so there's a 1 12 4 triple in column 8 so we need to place threes sevens and Nines in which means that digit is now obviously known that's a two so we just need just need this zipper line this ambigu okay we we've got a seven at the top here because it sees 39 so now those digits are known they're 2 45 and that's a two in the middle CU it sees a four five pair so these digits are 379 that's that seems not resolved not sure this digit is a three or a seven so that digit is that these two digits are the same aren't they um okay and for our next deduction we will say what [Music] um oh I don't know we might have to color um I don't know twos and fours or something I would be very prepared to believe that is necessary around now [Music] um what about well let's let's label up row six I mean I can see that's this is two or four now or maybe row five 1 2 3 and nine that's a two or a nine only 13 n so two is in one of those squares these two digits are the same ah um have we we used up all the lines or everything we know about some of the lines already I think we have actually I think we have can I get a three to look into this box that would be useful wouldn't it or okay I'm going to look at these digits Now 1 3 uh what is it 137 obviously but it's got to be something else as well five okay so this square is not three or one that's five or seven apparently that feels like it might matter I feel it's surprising because we've done so much work with fives and sevens okay so we arrive at this juncture and for our next trick we will ask where oh where's four oh there's this four that's it we've done it four five 1 2 1 3 this is now nine that's therefore two that does the nine and the Seven at the bottom and okay let's do that's now three so that's three that's nine these are that's three in the column this is now nine this is seven that's seven that's five now let's check yeah that's great isn't it eight is the sum of 1 and seven it's the sum of five and three um we can get this is a five naked single that's a seven that's a five that's a four and we've got we've got to put four in here one in here and don't tell me this is no it's is fine isn't it it's going to resolve 2 441 beautiful beautiful that is brilliant one person I suppose if it's secret Center maybe not many people have looked at it um that was that was really really interesting um each of the lines well apart from no it was odd wasn't it the I was about to say they all did different things they all had these three had quite similar properties these three uh oh hang on I didn't mean to do that let's go back I was going to label them gray those three had a similar property which is that their Central digit had to be even and had to be six or eight and then had sort of certain pairings that could go on either side of it but the this one was really interesting the way those digits were forced to be the same same this one had that same property which was weird and this one I loved the fact that this had one of those had to be six and that that could see that once once I appreciated the importance of that it was a very beautiful thing to notice that's a quality puzzle Kenneth's dad take Take a Bow kennet you should be very far proud of your father that is a um a really really interesting puzzle codec thank you for recommending that Rocky rower what a lovely Christmas present let let me know in the comments how you got on with this one I enjoy the comments especially when they're kind and we'll be back later with another edition of cracking the cryptic

Channel: Cracking The Cryptic

Views: 49,623

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Id: y18YGirVpIQ

Length: 57min 39sec (3459 seconds)

Published: Sat Jan 06 2024