Sudoku In 2022: It's Not What You Thought It Was

[Music] hello and welcome to monday's edition of cracking the cryptic where we're going to be looking at a puzzle called silent fletching today by oddly even now fletching is a word which means to make arrows and i guess that's explaining why we've got some arrows in the grid and also i think these are german whisper lines um and apparently this is a beautiful puzzle we've had three recommendations for this just in the last couple of days so it should be something very special indeed um do i have any news for you oh well we hadn't i tweeted this earlier it's been getting quite a lot of traction a friend of mine uh sent this to me on whatsapp this morning and it tickled me pink so i thought i'd share it so have you noticed the best formula one drivers are named after scottish towns i'll let you read out the names and figure out what's going on but let's just say that one in the bottom right amused me greatly and i hope some of you will find a smile from that one um other than that i need to say very well done to matt boss and to alfredo gliotti um because both of you have correctly solved the star wars puzzle hunt which is now available for our patrons over on patreon that is some mean solving we only release that on the first of january so to get through all those puzzles in just a couple of days is very impressive indeed um and a reminder for those of you who either haven't started the hunt or who are stuck on the hunt there is a great channel on our on discord at the moment it's called patreon chat uh if you go there you basically find a lot of people discussing what's going on and you'll even find peter c hayward there and peter c hayward wrote the hunt so a good person to get some tips from um now all that said and done let's get on with silent fletching oh silent because it's for german whispers right now i understand gosh simon speed up here are the rules we've got normal sudoku rules apply digits along an arrow must sum to the digit in that arrow circle and adjacent digits on a green line must differ by at least five so just for those who are new to variant sudoku how do arrows work let's imagine that this square was a two and that square was a six two plus six equals eight so you have to put eight in the circle of the arrow and german whispers basically they were let's make this square a two now this square must be at least five different from two i think we had this rule set yesterday as well so two plus five is seven so this has to either be seven eight or nine obviously we can't go down from two or this will have to be a negative number and we haven't yet got to those levels of madness in sudoku please don't think about it any constructors watching this the software can't handle it i don't want negative numbers in my sudoku at least not at the moment um anyway do have a go at the puzzle the way to play is to click the link under the video as usual now i get to play let's get cracking i'm gonna get rid of the example too because that will confuse me um now what are we seeing here i'm seeing this sort of circle i don't know what that means i'm seeing three arrows that have length three now normally a length three arrow is very interesting this one's interesting and this one's interesting unfortunately this one you wouldn't invite round to a dinner party because it's let itself down by flicking off here into box three all of its potency disappears because basically we can now repeat a digit on this arrow so we could have a one here and a one and a two there and make this circle a four whereas this one must be at least six because if we go one two three on the arrow that will be one plus two plus three equals six and the same is true of that one um [Music] that's a short stubby arrow so probably we need the whispers i think uh to get us started here although i am sort of wondering about set again it wasn't yes it wasn't yesterday's puzzle uh german whispers involving set i i lose track of the days in the sudoku's they all merge into one but i think it might have been let's have a look at this this is obviously the longest whisper line now what do we know about whisper lines we know the two facts which are so important fact one you can never put a five on a whisper line and that's because if you try to do it the next digit you place on the whisper line will be a problem because it either has to be a zero or less or a ten or higher both of which are impossible because of course the digits have to be 5 apart now the the corollary of that or an implication of that is that because you can't put a 5 on a whisper line each digit is either a low digit like a one two three or four or a high digit a six seven eight or nine and and the line must oscillate so a key thing uh when i say oscillate i mean if this is a low digit that will have to be a high digit and then the next digit will have to be low again etc um so the key thing that you normally have to work out with whisper lines is you know what is the parity where where are the high digits on the line are they in whoopsie are they in those four cells or are they in those oh one two three four one two yeah okay so length seven line so that makes sense all those three cells [Music] so let me just have a look at this we seem to have quite a lot going on in terms of row one row five row nine column one maybe certainly ah yeah the wheel this is it this is it this is it yes okay okay what we need to do here i think is to make use of the wheel and what i'm so what i'm thinking in terms of the wheel is if i can put these digits into a different set of to this digit i can cancel them out and i can see how i can do that yeah here we go right so we're going to highlight we're going to be doing scrabble tiles i think again today so i'm going to highlight column 5 and column 9 in orange and i'm going to highlight row 5 and row nine in blue and what am i why am i doing this well let's do some visualization so i want to imagine that i've got nine scrabble tiles nine orange scrabble tiles representing column five and on each scrabble tile i'll just write i know this is a set of the digits one to nine i don't know um [Music] i don't know obviously what the order of those digits is but it's a complete column of the sudoku and every sudoku column contains the digits one tonight so i can write the numbers one to nine on each of my scrabble tiles and put them in an orange bag and then i can do exactly the same for column nine and add those into my orange bag so i've got 18 scrabble tiles in my orange bag and i've got two of them will have a digit one on them two of them will have a digit two two will have a digit three etcetera etcetera two of them i have a digit nine and that's how the 18 are accounted for now i'm going to do exactly the same with a with 18 blue scrabble tiles and put those in a blue bag so i've got an orange bag and a blue bag but look this is where i think this gets rather beautiful this digit whatever it is in the finished grid let's make it a 9 just for the sake of exposition i can go and hunt in my well let's let's establish some facts obviously my scrabble tiles at the start of this exercise are completely the same because they both contain 18 scrabble tiles with two sets of the digits one to nine on them whatever is in this cell i can go and find that in my orange bag and find it in my blue bag and throw it away from both bags i'll be left with 17 scrabble tiles in both bags and i'll still have exactly the same contents because i've thrown away the same thing from both bags so any cell that's now colored in two colors i can do that for if i could find i could just i can just delete or throw away both those both the scrabble tiles or each of the scrabble tiles from both bags and it's still true at this point although i've now got only 14 uh tiles left in each bag that they still are identical they still contain the identical sets of digits now this is what i wanted to do though look look what's going on if we consider these two squares and this square and i want to change slightly what we've been talking about so at the moment i've been trying to ensure that the tiles in both bags are the same and they still are at this point now if we sum the tiles in the orange bag and sum the tiles in the blue bag obviously those sums must be the same because we got the same tiles in both bags but think about the nature of an arrow an arrow is telling us that those two cells there add up to the same as that cell so if i was to remove these two cells whatever they are from the blue bag and this cell whatever that is from the orange bag delete them it's still true to say that the sum of the orange digits and the sum of the blue digits is identical albeit that i've now got a different number of scrabble tiles in my blue bag because i took two out of that to my orange bag and i can keep doing this look this one and this one so i find those in my scrabbled bags remove two from orange one from blue i removed two from blue one from orange down here this one from the blue bag take out those two corresponding orange black tiles and now we get to this point so at this point interestingly we do have um we do have the same number of tiles but we don't know that this exactly the same digits what we do know at this point is that these eight orange scrabble tiles add up to exactly the same as the orange blue tiles and that must be interesting because these are on whisp these are both on whispers lines and these are both on arrows so um okay so the minimum we could put if we made this a six seven pair the orange cells would add up to two times six plus seven which is 26. now that won't work that won't work because if we think about the nature of a whispers line we know that yeah this is this is really lovely it's a bit like what we did yesterday again though let's think about how this line actually oscillates what does that mean well it means it's going to go either high low high low or low high low high in other words this whispers line has exactly two digits from the high set of digits in it so the high set are the six sevens eights and nines of this world and two digits from the low set which are the ones twos threes and fours of this world so if i absolutely minimize the contents of this whispers line i could put a one and a two and a six and a seven on it and 1 plus 2 plus 6 plus 7 is 16. so if i can put 16 on that minimum and 16 on this minimum that's 32. so the orange cells have to add up to at least 32 and that's nearly good but not quite good enough because we could make this an eight nine pair and if it's an eight nine pair then the orange cells would add up to two times 17 which is 34 so we've got freedoms and freedom since freedoms in life are great but freedoms in sudoku are absolutely awful we've got two degrees of freedom we don't have to minimize this or we don't have to maximize these um what did i say this was is 6 16 was it so 32 is the minimum value of blue right so we can get rid of six from the sums here because if we even if we go six plus nine uh or six here nine here then we're doubling 15 to get the total of all of these cells and hopefully that's clear to everyone the reason i'm doubling them is obviously if this is a six and this is a nine because the arrow also adds to six i can view this circle plus arrow combination as two times six and i can view this circle plus arrow combination as two times nine in other words to get the total of all of those cells i simply add these two and multiply them by two but you can see that six plus 9 times 2 is only 30 whereas we said that this was a minimum of 32 so we can get rid of 6 from here um 32 so what we can't have is 7 and 8 here so if there is a 7 in the circle it must be with 9. so [Music] yeah ok so we definitely have a 9 in one of those two cells now and it's either either we're heading towards if this was 9 7 then we would know the contents of these lines they both have to be one two six seven we'd have to think about how they were ordered [Music] actually we would have to think about how they're ordered as well because there are two digits on german whispers lines that are very difficult and that's the sixes and the fours and you can think about that if we put a six here what happens well both of these squares now have to be five away from six so they both have to be a one and that's broken so we do have to be a bit careful oh i see we're going to get a sort of x-wing on sixes um in other words we could have a six here and a six here and then that would work or a six here and six here so we can we can just rearrange the lines um so how do we finish this off then i finish this off i've not got a digit in the grid i've got two cells pencil marked and some colors placed oh deary me um what do we do next we've got eliminated the circle the circle i mean doesn't look very interesting in and of itself there must be something to do with is there a reason you can hang on let me just think about this there might be a reason you can't go si if we go six here go six here that has to be a one now we have to go to a high digit which was saying could be a seven and then that could be a two and that would work and then here we could go we could just reverse that six one seven two nothing wrong with that i don't think that is sixteen plus sixteen so that is thirty-two ah yeah oh that's ah got it right that is absolutely gorgeous this is this this is world-class setting oddly even take a bow this is world-class setting look at row one look at row one look at this whispers line here there are four cells on this whispers line so what do we know about those four cells in terms of high low parity two of them must be high so two of them must be from the digits six seven eight and nine in other words combined with our circles these two digits wherever they live on this line have to form a quadruple in the row but that means there is a six in one of those cells now at first blush we might not say we knew where that six is but we've just talked about sixes down here you have to put a six next to a one on a whispers line so you can never put it in the middle of a whispers line where the two digits on either side see each other so the six simply cannot go in any of those cells and you get a so our first digit is six in row one and now we know the parity of the line so now we know that this is high this is high this is high and this is high so we need colors for that and we'll use purple and we'll make the low digits yellow so we now know this is a one we know that this is a seven eight or nine and we know that that can't be a four uh this can't be a four because if we put four into this square both of those squares have to be nine to be five away and i'm just i'm now having a bit of a panic because what i did want to do was to put sixes into an x-wing shape down here on these two german whispers lines and i can't do that anymore let me just think about this for a second is this what gets rid of my degrees of freedom between the the sum of these and the sum of these i really hope it is because that is if that's right that is staggeringly beautiful to me i now can't yeah well it's certainly true to say you can't put six one seven two onto both of the blue lines because the six always is at the end of a line and i can't put two sixes there so i need to put a six at one one of those where i can't now put it so if i can't put six on one of these lines at all [Music] then the high digits on that line will have to be a minimum of seven plus eight which loses up my two degrees of freedom qed that is absolutely beautiful so now because because we can only put one six in the oh well in fact that's a good way of putting it in those eight cells there can be a maximum of one six now because if there is a six it must go in on an end point and these two end points have been removed and you can't put two sixes there because of sudoku because i can only put one six now the lowest high digits i can put on those eight cells are two seven and then seven eight on the other one and i combine those with ones and twos and i get to 34 and 34 is rather beautiful because that is the absolute maximum i can make those two circles add up to so those two circles are now eight nine this square here is a seven seven can't be next to three because it's not five away from it so that's a two that's a low digit that can't be a four because it would require double nine around it so that's a three and those must be an eight eight nine pair and that this is absolutely brilliant oh this is absolutely brilliant i ca i'm already i'm at a point where i can't wait to read the comments on this puzzle because this is the sort of thing that i think is just it's not what's the right way it's not brutally hard once you see it but once you do see it you just you just feel like everything works and like you know maths works and everything is in order and has a special place [Music] now having said all that now one of these must be a six now that's what we definitely know i don't know which one um hang on a minute let me think about this uh so let's actually i'm just i don't know which one of these is a six i'm just going to try it and fill one of them in so let's say this is six if that line will have to go 6172 now the other line has to have a seven and then an eight on it and a one and a two on it so so is there a problem with the seven going see i can see the seven can't be in a central position because of the sevens that must exist in these two positions and if this was six one seven two that logic would still prevail over this central domino so the seven is definitely at the end so it could go seven i think the ones and the twos are sort of ambiguous as well i suppose that no this will fix that so if this was 7 we'd have to go 2 8 1 but if this was 7 we'd have to go 2 8 1. and this of course could could be absolutely the other way around in the sense that this string of digits could be here and the 6172 could be there that's very annoying um [Music] so maybe what i should do is to put these options in down here so let's do that six one seven two and now i'm just going to copy these up here so that we've actually got a full and complete sort of mapping of the options for these two whispers lines right um [Music] okay maybe row one what do we need to complete row one we need threes fours and fives into those squares and that's quite a high digit ah yeah this circle now which i'm aligned earlier for being boring at dinner parties has now upped its game it's read a few books and it's trying to become more witty because now even if i put one and two into this domino here i get to add a three to that so this also acquires a little bit of i suppose a little bit of grandeur and weight it's got to be at least equal to six now um ah got it right okay and now look at box two because what what you can't put on any of these arrow lines now is a particularly high digit in fact that's really interesting so is this a 789 triple i think so i was actually thinking about seven in the context of these two squares but these squares here can't contain eights or nines either so the only places for the digits seven eight and nine in box two are these three cells so these squares uh have to form a triple and the seven in that triple is in this domino and that fixes seven out of here and that tells us the parity of course right so now i'm going to color these lines of something other than blue because now i know those and these must be yellows because i know that these two cells have to be low digits so we can take eight out of those two squares so these have to be high digits which means they they acquire the level of purple and now we shall can i do this do i know which way around these go um probably i've got a one-two pair here looking at that square that's got to be at least a three what's this square going to be oh hang on i've got i have got stuff going on in this column right ah right i've got a one four five triple that's quite interesting given that has to be at least a three that definitely can't be a one ah yeah good this is good this square can't be a one because i've got a one in the column so the minimum value of this square is two the minimum value of this square is three and two plus three equal five so we can't possibly make this a four so that's a five that's a three that's a two um okay so we can get rid of those squares there's two ah this ah yeah this two sees that square so that becomes one that becomes two that becomes one that becomes two now i can't put six next to two on this whispers line so that's a seven and an hour so this is the higher whispers line that's a nine that's an eight by sudoku and this is the low whispers line so that must be six and seven and that's four and that's one and the puzzle is now filling itself in that's an eight nine pair oh it's an eight nine pair with an eight here so that's eight that's nine this square here is no longer eight um one two so three fours fives and sixes has to be a three in one of those squares one two i okay and we can go for now we might be able to get into our wheel because look at this square it can't be eight or nine and yet it's arrow cells can't have a one or a two on them so that must be a three four pair adding up to seven whoopsie that's the only way it will work so the rest of row nine now needs to be five eight and nine in some order that square can that really be 5 no because ah here's something nice if this is a 5 think about these five squares in column 5. what's the minimum we could make these five cells add up to well the triangular number for five is fifteen so one plus two plus three plus four plus five is fifteen and that means that these two circles must add up to at least fifteen and therefore this can never be a five or that would have to be a ten um so these uh but these could be the same digit so that we can't say that these add up to seventeen they could be double eight or double nine [Music] right let's have a look at this little cell because you can see i've got three purples in box four already so the only way this can be a high digit on its whisper is if it's a six but if it's a six that has to be a one and that won't work because we've already got a one in column four so this square must be a low digit which means it's a 3 or a 4 which means this square is a high digit which means and it has to be 5 away so it's an 8 or a 9 and that's doing two things that's doing two things actually firstly it's giving us a seven eight nine triple in column four which is quite interesting but more interesting it's giving me an eight nine pair look in box eight so that square becomes a five now now we've got some sort of skyscraper going on in on eights and nines can we do something with this probably just have to work out what it is um eight nine eight nine come on simon how do we do this this column we need threes fours and fives ah yeah okay that square's a naked single because it cannot be four or five so that's a three those are a four or five pair is the three helping us somehow probably is the answer to that um two five two yeah okay we should do some sudoku i know i tend to resist in these sudoku puzzles but sometimes it's forced upon us and here we've got a 2-5 pair and a 2-5 pair so those squares are a 2-5 pair which means that those squares are a one-sixth pair and that means these two squares are a seven and a something a four we've got to get this adding up to eight or nine yeah okay one one way of thinking about this is to say how how is it possible there's no one on this arrow if there's no one on this arrow the minimum it adds up to is four plus six which is too many so there must be a one on the arrow which means it must be a one seven arrow going with a four six into the other cells that's no longer a six oh right this is beautiful again simple but beautiful one here that's a three cell arrow that can't have a one on it so that must be two three four adding up to no oh adding up to nine not adding up to a border nine eight nine eight uh seven eight um and that's a four or five pair so that can't be a four this column still needs a six and an eight and there's an eight here so the eight must go into the circle this must be a six this must be a three five pair because we can't use either one seven or two six and you can see the five here means that's got to be the three that's got to be a five that's a five by sudoku it sees a three and a four in the column oh hang on oh i was about to worry i had a deadly pattern but it's i think it's going to be fixed by this arrow this arrow has a has a role to play in determining row one column seven and that will determine how these four cells here need to be arranged in the finished grid thank goodness that can't be an eight anymore um this 3 makes this square a 2. so now on this side we must oh look yeah we've got a 1 and a 2 and a 3 here so 3 and 4 go in the grid and yeah okay they add up to three we can't so we can't make this a six to get to nine so that must be a seven which means that square's a four that square's a three that square's a four that square's a three three lives in one of those two squares in column uh yeah in column nine that's quite interesting for the oh no it's not i was about to say that's going to allow me to determine the eight arrow but i'm not sure it does actually what about those squares four and oh four and nine okay that we can do that that's four that's nine and that does determine the nature of this eight arrow because it can no longer have a three on it if it's got a three on it would have to have a one and a four as well and the four here prevents that so the three must move down which by maths gives us a six here that's a nine that forces no it doesn't it's the wrong way around to force anything oh but the three is useful that's four that's four that's five this is nine okay it's still going quite well can i get this two five i can five and two go in the grid one and eight into those cells don't know how to do that yet um what do we need in this box we need threes fives and sixes so three goes here five goes here six goes here what do we need in this box four five six and nine so that's a five six pair and that's a four nine pair which we can do and now nine is in one of those three can't go on an arrow can't go in column eight so nine goes here nine eight so it's probably gonna be this whispers line that finishes the puzzle off i think that's a one by sudoku two and five into those squares these squares here are sixes and eights okay well that that's quite interesting in that it tells us this square is high so we now know this square is low and what can it be it can't be three four or two so that's a one that's a one that's a two that's a two that's a five that's a five that's a six that's a six that's a seven that's six that's an eight that's an eight that's a one and we still need two and seven into those squares which i think resolves that way and we click tick and that is a sensationally good puzzle it is yeah it's just a perfect perfect puzzle for cracking the cryptic because it's it's got elegance beauty it hides its secrets a little bit but when you find the secret it makes you gasp and that is everything you could ask for in a sudoku puzzle absolutely love that oddly even and thanks so much to those of you who sent that in to us because that is a stunner and it's an oddly even is a name i'm going to be looking out for in the future thanks for watching i hope you enjoyed it i look forward to the comments on that one and we'll be back later with another edition of cracking the cryptic [Music] you

Channel: Cracking The Cryptic

Views: 41,324

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Id: 070UQuPIbqs

Length: 37min 28sec (2248 seconds)

Published: Mon Jan 03 2022