Use Knowledge Bombs To Solve Sudoku!

[Music] [Applause] [Music] hello and welcome to monday's edition of cracking the cryptic and a puzzle that seems to have been made with us in mind um it's by the constructor arpaio and it's called knowledge bomb five does not equal six um now arpaio himself did in fact email us about this puzzle suggesting we might like to solve it on the channel and he said that if we did we should keep an eye out uh for opportunities to apply this knowledge bomb during the solve so this sounds quite fun to me and the test to say this is a lovely puzzle not too difficult today it's a sort of three stars out of five for difficulty and um i do like arpaio's puzzles in general because they're always clever but they're not normally brutally tough now before we get started i'll read you the rules uh i would recommend if you've not seen it yet do have a look frankly at both videos yesterday but especially this classic sudoku that was discovered by philip newman it is absolutely astonishing and if you haven't seen it you'll wonder why well basically what philip has done is put the 22 the initial 22 digits of pi into a sudoku grid symmetrically arranged and made a classic sudoku that solves absolutely beautifully it is quite it's quite unbelievable it is unbelievable that sudoku exists and yeah it's a very classy puzzle so do have a go and i've been amused reading the comments and how many people have been very pleased at beating my time so well done to everyone who did you weren't explaining it though it takes time to explain um now over on patreon at the moment we've got loads of stuff we've got the wonders of the world sudoku hunts which is still getting lots of correct entries every day and we've been so pleased with how that's gone and of course we've got scott strosal's video on how to solve his tracking the triptych sudoku challenge which was that was a challenge properly difficult and there is now a one-hour video over on patreon where scott talks through the puzzles and that's very entertaining and probably tomorrow we will release mark's um speed solving attempt at solving last week's times crosswords all of them from monday through saturday six puzzles he's trying to average a time of six minutes per puzzle so if you want to see uh crossword speed solving at its best then do have a look at that um now what are the rules of papaya's puzzle let me read them to you we've got normal sudoku rule supply cells separated by a knight's move in chess cannot contain the same digit now a pair who loves the night's move constraint and the thing is he doesn't overuse it because he uses it very cleverly in general i think the last puzzle i did by him was knight's move but that was very enjoyable digits along arrows must sum to the total in their white circle okay and digits may repeat along arrows if allowed by the other rules along thermometers digits must increase from the bulb end so let's just take a look at some of those rules there aren't a great many thermometers in this puzzle in fact there's one this one and it's one cell long so this is the most marginal of uh of things basically we know that this square has to be less than this one that's what this thermometer is telling us now in terms of arrows um for example whatever goes into those two squares you would add up those yellow squares and that's what you would have to put in that arrow circle um so that's how the arrows work and then in terms of the knight's move let's just talk about that let's imagine this square was a one if it was a chestnut in that central square of the grid it could jump to all of these yellow cells and therefore none of these yellow cells can contain a one so bear that in mind when you're solving and you'll be good to go and of course as usual on cracking the cryptic you get to play the puzzles if you want to have a go just click the link under the video it'll take you to a page that looks very similar to this one where you should be able to play on whichever device takes your fancy and with that let's get cracking um and see how we solve this one we can well i'm seeing this arrow that's a four cell arrow that looks like it's the longest in the grid so probably this is where i'll start i'm just trying to see if there's anything else that's immediately obvious not immediately obvious i don't know why i noticed things like this square here can't repeat on this arrow up here so that's anywhere on this arrow because of the knight's move constraint so those four squares all have to be different digits and when they're emanating from the same circle that feels like it might be an important restriction maybe not yet but maybe one day this will be relevant um i mean let's let's start with the easy stuff a three cell arrow where you can't repeat a digit and you can't along those three squares these would have to be a minimum of one two and three so this square has to be at least equal to six the same is true of this one and this is before we get to the one i think is going to be the most interesting which is of course this one now if i was mean i would say that mark would do this um and make sure he fully pencil marks his thermometers because he always does that at the start of all thermometer puzzles and it always amuses me but i'm not mean um now let's have a look at this one so well you can see very simply this has to be at least seven because those squares are all in the same column they've got to be a minimum of one plus two plus three this square then still needs to be added in to whatever those squares are so the minimum we can get to is seven so this is at least seven and the other thing you can see is that it's not possible for all of these four squares to be different digits because then they would add up to ten one plus two plus three plus four equals ten so this square must repeat in these three squares um i don't know whether that's worth coloring it probably is so whatever goes in that square has to repeat in these squares it could still be a three though rather irritatingly because we could have one two three here and a three here and then that would make nine which would work so this squares one two or three so this ah so this that bounces back this way we're playing ping pong with the arrows this can't be six now because that would require this to be one two and three so that's not six um now what do we do we've got so if the thing is i can see this square here the purple square can't repeat in this cell obviously because there are knights move apart but i think it can repeat in either of those two cells so we're gonna have to look for something different here whatever's in that square can't go here uh um sorry about this one second we've got i'm a bit baffled actually um this square is on a one cell arrow so that square has to appear here so that's a six seven eight or nine so that's got to be in one of those squares but it could it could theoretically even be here if this was double six and this was six you could still fit one two here that would make this a three that would still be fine okay there's something i'm not seeing um and that's annoying i'm sure it's annoying for you guys but it's also annoying for me so it feels like this arrow is the key doesn't it this is this is by far the longest arrow ah ah yeah okay good grief right okay this is this is really difficult i think um this square can't go in those three squares in in row three and it can't go in those three squares in row seven so where does whatever goes in this square go in this row well the answer is we don't know but we do know that it can't be on an arrow because it's too big to be on an arrow if this is seven even we can't put seven on a three cell arrow because we'll we'll breach the total of ten so whatever goes in this square has to go in one of those two positions let's highlight those make them green now it's just i think it's the same along this this row here obviously this can't go on its own arrow so if this is seven you can't put seven in here so it's not in those squares it can't go on a three cell arrow so it's definitely in these two squares and here we have an x-wing so whatever goes in this square either goes in those two positions or it goes in these two positions because we know we know whatever goes in there has to appear in row three it has to appear in row seven and it can't appear in the same column aha and it can't this breaks the x-wing that is so lovely right if this square right so if the x-wing is sort of a top left bottom right x-wing so if these two squares are whatever's in this square let's just highlight that let's imagine that whatever is red went here in in row three you can then see it would have to go here in row seven and the puzzle breaks because this little arrow points it back in this direction and it plays ping pong up here and we get repeat it repeated red in column one so we mustn't do that so the x the x-wing must be a top right bottom left x-wing so those two squares are the same digit oh as this right so this is the same digit as this that's quite i see i do i do just really enjoy arpaio's puzzles because look this now works very nicely on box four you can't put red here because of the knights move from there you can't put red here because the knights move from here this becomes red let's actually label those up seven eighths and nines now can we do something yes we can we can place it where does red go in box five of the grid it can't go here by night smooth or here by knight's move from that one so that's red let's make sure we fill it in properly now can we take this any further i'm not sure it's awfully close isn't it so red has to be in either this square or this square in box eight i'm sure it feels like one of these must be impossible [Music] um i mean if it was seven and this was one that could still be eight it's in one of those squares and you can see i mean if it's it's likely to be on the thermometer actually top end of the thermometer is not really restricting this square so maybe it's not likely to be on it because otherwise why is this thermometer here it's more likely to be there frankly because that really would um force this square if you had a pretty high digit in that square then this square would obviously have to be even higher anyway this is all conjecture let's have a look somewhere else can we do more with reds we can red can't go there because of the knights move from this one so reds in one of those three oh red can't be on its own arrow so this whatever's here can't go on in those two squares in box three so it's ruled out of all of these squares by a combination of sudoku knights move and not be on its own arrows so one of those two squares is red now that means one of these two squares is red that's really clever okay we can do something with that i think because if we know one of these two squares is red let's come back to box eight again red is not in those positions here so red is in one of these two now if red was here red in box nine would have to be on its own thermometer so this would be red and this would be red well you can't then the thermometer is broken and if red yeah and the only other position for red is here which is in the same row as this position so this cannot be red this is red and that that plays ping pong over here forces this knot to be red and that's what i was after because now this has to be red and therefore it has to be seven oh whoopsie it has to be seven eight or nine it can't be nine because this square has to be higher so this is an eight or a nine and now we know that all of the reds are not nine so they're all sevens or eights which means puts an awful lot of pressure on this green arrow now because the minimum these two squares can add up to is eight so we can remove six and seven there remove six and seven here um so there's a red up there i think that's probably is worth penciling now there's a red in one of those two as well ah now now there is no red on this no there is there is a red there is a red it's right there but there is no nine in this circle so those three squares must include a one because in order to make a total of seven or eight in three squares you have to have a one so this is not one oh this is so clever it's just absolutely lovely now this square not being a one what's the minimum i can make these three add up to well if i use one two and three that would be six plus the minimum here is now two that's eight and i can't go any higher because this cannot be nine so now we know that red is eight um and that i can see is going to be nice because it's going to give us why is this green is that the same as that or is that just me forgetting about my x-wing pencil marks have i proved that's the same as that um no in fact it's definitely not the same as that because this is the same as that whoa that was nearly a bad error but it's been avoided these have got to be nine nine can't be on this arrow so nine is in one of those two cells these are one two and three this square now is two this now is one three four because it can't be one two five get rid of the one two can't go here because of the knights move from this square probably get rid of the coloring for this square these are eights now um i don't think i really need to color the nines this square's got to be at least four because it sees one two three in the column so it's four five six or seven this could be double four so that's a bit irritating that's got to be one two three or four it can't be two actually so that can't be six nine ah this this being eight fixes this as nine of course because it's got to be higher and that's lovely right okay nine can't go there because of the knights move from here nine is in the circle nine oh lovely right let's leave this is a classic knights move trick see this nine pencil mark here in this domino you can't put nine in either of those two squares because it will break these two squares if you try a nine here it removes nine from both positions so nine can't be here nine can't be there can't be on these arrows it can't be on this arrow because this will be a double digit number so i think nine goes there that ping pong straight into box one and gives us that digit nine is now in one of those two positions in box three now can we yes we can oh this is again beautiful nine nine can't go here by knights move so nine is in one of two places in box six this square if we make that nine rules both of those out this one by sudoku that one by night smooth so this is not nine you can delete that one this is nine of course that allows us to play ping pong that this square's got to be at nine now this is not nine nine might be placeable in the middle yes it is in fact have we done all the nines yes we have so all nines are now done not quite all eights um now what shall we look for look at then ah this arrow is probably where we should look that's got to be a one just to make this arrow add up to the right number so this eight arrow now is either two six or three five because it can't be one seven this can't be a one up here so now the one is in one of those two squares on this eight arrow which rules it out of this square in box five it's ruled out of this square in box five by this one um i'd really like to know whether this was two three four i don't think we do know that oh nine hang on yeah just by simple knights move this one rules all those squares out so there's definitely a one in one of two places in box eight ah look sudoku helps us here ones have to be in one of these positions but one can't be on the arrow because if one's on the arrow the eight will have to join it therefore the one goes in the corner does that matter um not sure is the answer to that question feels like it should matter somehow but i don't really not really seeing why this nine arrows still got three options it can still be four five three six or two seven one you now can't put one on this arrow for what it's worth it can't go here and if you try and put a one here it rules one out of both of those positions because of the knights move so no that is the most modest of deductions isn't it okay so now we're getting stuck which is not terribly surprising it's just a little bit annoying um one over here can we do something with that one's got to be in one of those cells oh good this is right okay we can believe it or not one is in one of those four cells in box four one is not here because of the knight's move and one is not here because it would rule the one out of both of those squares so one in box five is in one of those positions it can't be in the circle of the arrow in fact in fact i've just noticed it can't be here either because that would rule a one out of both of those squares so in fact one is in one of those three positions which means one is in one of those two positions but the same point is now valid which is where is the one here it can't go there so it must be there which means it's not here so there's a one in this domino at the top of the grid which means there's no one there which is not terribly surprising um this yes this one bounces back in here doesn't it okay good so this square is a one now therefore there look at this this is quite incredible it just feeds through the grid now this has got to be a one now this has got to be a one this one sees this square so this has got to be a one so the ones and the eights are now you know we're left with little x wings in these two positions but we've actually done a lot of good work there um this is three or four so this can't be seven anymore double four or five three are the options [Music] ah but whatever that is where does it go in box nine this square here can't go in those positions or this position so this is a three or a four and that might be another opportunity to color actually ah not quite three four this is five or six is on the nine arrow now so these squares here have to sum up to eight without being one seven so this is two six or three five i'm not sure if we can narrow that down or not got lots of squares in box seven that can only be two three five or six [Music] um two sorry about this i'm a bit stuck um [Music] this is the same as this isn't it i mustn't forget that so one of these two squares is purple one of these three squares is purple um okay i feel like i'm really am starting to reach a bit of an impasse now ah no i've got something else this this is all forced bother this has probably been sitting here for a while look eight can't go in this circle so what's the maximum i can make this square well the maximum is seven but what's the minimum i can make this square well it's three so that we can see that this has this this is all forced this has to be a three four pair this has to be a seven in order to make this arrow even possible eight so this square is a five or a five or a six i've got to remember this because the knowledge bomb that we have to bear in mind is that five does not equal six so maybe any squares that are five and six i should be highlighting these two i'll make them blue um [Music] oh no but they're not the same they're not the same i was about to do something really daft there i shouldn't probably highlight them no i don't want to highlight them i'm going to if i highlight them i'm going to think they're the same and i almost did then and i don't know they're the same i just know they're fives and sixes ah okay seven has to be in one of those two squares in box eight so seven has to be in one of these two squares in box seven one of those three squares in box nine it's probably something i've got to do with this arrow i think three four ah yeah here's a simple deduction there's a three four looking down in into box five now this square i don't think can be three or four because well what are we going to put into this square the the most if i make that four the best i can put into this square is 3 because 1 and 2 aren't available but this can't be one so that doesn't work if i try 3 it's immediately broken because what do i put into that square has got to actually be higher than 3 so we can say i think that 3 and four are a pair into those squares so now this has to be at least five i've got a three four pair actually got all sorts going on is what we've got um have we got anything simple though that i can actually use this square here it's got to be at least five so it looks like it can be five six or seven can't be eight or nine this can't be six therefore or five actually this one can't be five or six anymore because it's got to add on to three or four so this is two or three i've seen two or three somewhere else in this puzzle oh up there that's not helpful um this nine arrow now needs five or six into this square so there's a virtual five six pair now in this box because there's a five six here and there will be a five or a six in one of the cells on the eight arrow i've got another five six there so i've got three cells now that are fives and sixes and i still haven't found my knowledge bomb um let me just think about this hang on though whatever that is where does it go in box eight the answer is i don't know because we don't know whether this is different or the same but i do know it's in one of those three squares because it can't be there now if whatever this is is in one of these three yellow squares here's a knowledge bomb for you five and six do not equal eight or nine so this square must be the same as this square so that is interesting and i'm absolutely prepared to highlight that let's get rid of the highlighting in the night i just want to get rid of the highlighting of the nine now unfortunately these two both see this square so we haven't quite we don't quite know what's going on there do we in the sense that i don't quite know which one of these squares is blue i know it's one of them if it was this one it would force this one to be blue um hmm okay feels like this is very important not least because of the title of the puzzle one two three four i've got five six and seven to place in those three squares is that useful i don't feel like it is almost but i know very little about sevens in the wings of the puzzle or fives or sixes can we do seven four three this can't be seven there you go this can't be seven because if it's seven those you have to make that square four and that square three and what are you gonna put in that square nothing nothing will work this cannot be three or four this is not seven that's another five or six oh that rather kibosh is my hope that well six oh seven now seven now has to go on the left side box five so seven is not here oopsie it's not there either but it's definitely not here so seven is there seven is not here by knight's move uh no um [Music] now now i do know which of these squares is blue it can't be this one it must be that one this is blue does that matter this is blue i suppose just by sudoku because blue can't go here blue is not three or four now this now this is blue so now i've got can i keep going with this then that can't be blue must be in one of those two squares one of those two squares not quite i don't think it quite it propagates much further so whatever's blue is not on this arrow how do we get this resolved is it possible this is blue no it's not that i don't six six six would force two oh sorry right okay there's a simple way of doing this okay ask the question can blue be five the answer is no because if blue is five these two squares are five but now we have a big problem in this square because the only way of making five work in this arrow is with three and two but i need a three here for the nine arrow to work so this square has no good options and that means we can actually just write six in to all of the blue squares and now that fixes the nine arrow we now need a two here it fixes the six arrow we need a four here four fixes to five the three we know that the three is the same as this square there's no three there anymore so there's no five here there's no six here because of the so there's no two here whoops there's no six here right oh this is just five three because of the six there that's pretty been a sensible way of doing that um now look we might be able to keep this going now this is four so this is three these two squares now are four and five yes we can keep that going five and four go into the grid these two squares are 2 and 7. i'm not sure we can resolve those but we can certainly write 4 into that square now we need 2 in this row so it must be there these squares have got to be 4 5 and 7. there's probably stuff we can do here i mean i can see this can't be five and this can't be four by nine's move ah seven sees this square so that's five four seven ah can't quite see so this this square's a four or a seven as well whoopsie four or seven no um can't see how to resolve that okay so let's have a look at the top of this column where we need five and eight doesn't seem to be resolved three four here so here we need two five and seven i'm not sure whether we can resolve any of that we can certainly get rid of five from this square and two from this square ah and two from this square so this square has to be 2. now can we keep this going a bit further 3 6 and 7 into this row not sure actually again it's a situation where i can see we can do eliminations like i can get rid of six from this one twice because this six also sees it by knights move i can get rid of three from that one by knights move is this one seeing anything i don't think it is okay let's take a step back what are we not spotting here we've used arrows have we think so this three is seeing this square by knights move there we go fourth that gets us a bit more joy four's got to be in one of those squares um uh three where does three go in box one it can't go those into these two squares by the knights move so there's a three at the top there now that means three and three can't be here by knights move good grief this is a three now three has to go there by sudoku which forces this to be two this to be three the two means one of these squares is now a two which does ah now look we've now got two's aligning we found some twos in column one and column three so there can't be any more we well where does two go in column one the column two sorry it's got to go there and that's gonna allow us to place the one place the one here there's got to be a two in one of those squares it's got to go in the corner look two four and eight go in eight and five go in this five sees both of those squares so the only place for five is going to be there this must be a six seven pair and we can see we can just rewrite that in seven is in one of those two cells which is nice yeah okay look at that seven because seven can't go here in box six it's got to be in one of those two that square sees both of those squares this one because of knight's move this one by sudoku so that's got to be four that's got to be seven that ping pong's up here gives us the six and the seven the seven goes here by sudoku this is four seven five i don't want to say anything but it's suddenly looking a bit promising isn't it four and two go in there two and seven go in there that's a seven by sudoku these squares are five and six the five here is going to be helpful as is that five down there and these squares at the top are also five and six so six and five go in we click check and that's how to solve a beautiful puzzle again from a piyo i do love his puzzles um i think i was a bit slow today i'm not sure i think this whole business around here got a bit complicated for my little brain um but let me know in the comments what i've missed and let me know in the comments what i found and we'll be back later with another edition of cracking the cryptic

Channel: Cracking The Cryptic

Views: 45,024

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Id: WM-SO_4qzAE

Length: 39min 54sec (2394 seconds)

Published: Mon Mar 15 2021