The Italian Spaghetti Riddle

[Music] hello and welcome to tuesday's edition of cracking the cryptic where today sees the return of aspartagus to the channel um this puzzle on screen is called raw spaghetti for obvious reasons i think and i believe it comes in two versions i think there is a version of this um where aspartacus has has checkerboarded the grid with sort of red and pink so it looks like a classic italian style tablecloth um but we're not going to do that we're going to keep it we're just going to keep our raw spaghetti fairly fairly clear today and have a look at this this puzzle's been recommended to us by the way by a couple of people that we really trust so i've no doubt it will be magnificent although i have to say i've got no clue at all whether it's going to be hard or easy probably now the thing about asparticus is he can be quite tricky he's got one of those brains that doesn't think in a conventional way that's always how i think about uh aspartasis puzzles they always have something unquirky and unusual in the logic um so yeah it might be tricky we'll have to see um now before we kick off today what do i need to do i need to wish somebody out there a very happy birthday and that person is bunny rogers now bunny i think you are on a school trip in europe at the moment um in which case i have no idea where you are but i hope that you you managed to watch this video and i hope that you get this birthday message and of course that you've had lots of european-style cake i guess depending on where you are it could be it could be nice or nasty cake there are some cakes in europe i'm not the big fan of i better not reveal which ones they are but but anyway i hope that your cake has a stupendous amount of icing on it that really is the most important ingredient in any birthday cake um other than that no other news um i said well i suppose just just to gear yourselves up for the first of july where we have this incredible sudoku hunt stroke pack coming from joseph neymar joseph if you've followed the channel for any amount of time you all know is one of the world's very best constructors and we have a pack full i think it's 13 puzzles all together all themed around equal sun lines and in fact that is the nature of the rule that we've got in aspartacus's puzzle today so if you enjoy what we're about to attempt here there are lots more coming over on patreon in just a couple of days time now let me read you the rules normal sudoku rules apply equal some lines for all the supply i.e digits on each line sum to the same total in each region they appear in so what does that mean well that means that let's pick one of these lines um yeah in fact let's let's use this line we can use this line straight away so what it's saying is that this this line of spaghetti here you can see it spends two cells in region eight of the grid this three by three region so those two cells whatever the sum is of these two cells that sort of sets the sum for this line and every time this this line enters a new box you can see it enters box nine in just one position there so this cell has to be the same as the sum of those two cells and then these two cells here have to sum up to whatever green adds up to so if green was five then these two would have to add up to five and those two would add up to five and that's how equal some lines works let's let's do another example let's look at this long line here so that's just got one cell orange is a bad color sorry let me let me try gray um ah okay so it just spends one cell look in box four as well so in fact those two digits are the same digit we can deduce from this now those two digits then they have to add up to whatever gray is gray would appear again there it just enters box two in one cell and then those two digits would have to add up to the same as gray as well so hopefully that is all clear do have a go the way to play is to click the link under the video as usual now i get to play let's get cracking and i'm tempted actually to start with this line here that we were just looking at because um it's very clear that those three cells are all the same immediately because this this line of spaghetti only enters box 4 once only enters box 7 once and only enters box 2 once so these 3 digits are the same digit it's a little interesting in terms of box 5 because where does this gray number this grey digit go in box five well by sudoku it doesn't go in those five cells and it can't go in either of these cells because if it did the implication would be we'd have to write zero um into this cell here because we'd be saying that gray plus zero needed to equal gray mathematically and that would require a zero in the box so gray is in one of those two positions um in box five now gray is also in one of two positions in box one this is probably not how to do this by the way but let me just let me just bear with with bear with myself for a moment until i decide that i've been a little bit dense um hmm actually this central well not really central but this line of spaghetti is very unhelpful because what we're saying here is that these two cells add up to the same as those three cells adds up to the same as those two cells so that's not very good um [Music] this one also looks oh no this one's better right this one's better let's have a look at this one so this one is saying that these two cells add up to the same as this cell which add up to the same as these two cells which add up to the same as this cell this is the only time that this spaghetti visits box six look and that's the only time it visits box three so these three blue digits are all the same so we've got the same thing going on in box five but we've got a very similar logic except the blue digit look is locked into one of those two cells so we can't i think do better than that let me just double check that so blue is ruled out of those blue cannot go on its own spaghetti line yeah okay just two positions so so actually it's very symmetrical isn't it so we've got this same sort of pencil marking going on between blue and grey i can't see how to improve upon it uh all right so we're left with we're left with this oh that's interesting ah okay this this one might be the key then this one here because if we study the length of this bottom spaghetti we can see this digit whatever that is is the same as this digit and it's the same as this digit so and the interesting thing for me about this one in particular is that we know that this is a red digit but can it also be a blue digit well no because blue and red definitely see each other in box three so it's not possible for this to simultaneously be blue and red that means that blue in the middle box takes the central cell which shifts gray because gray can't be blue gray and blue are seeing each other that shifts gray up here so actually look we've got all three colors now in the middle box that's lovely right so now yes oh this is yeah now it's starting to go so now where does blue go in box eight well by sudoku it's not in those five cells it can't go on its own spaghetti because we need a zero with it it's not the same as blue because blue and red see each other in box three so i think it goes in the central cell there which means that red is in one of these two cells at the top it means red is oh reds in one of those two cells now do we know can we push red onto the line here yeah oh yeah we can by using box six where does red go in box six it can't go in this this five cell sequence again it can't go on its own spaghetti we know it's not the same as blue so it goes here which shifts it out of this cell and into this cell so now in box uh six look we have four cells where each pair is adding up to red because red adds a red is the same as these two cells and red is the same as these two cells so that means red is at least five because if red was four let's see how that would work that would imply these two squares needed to be a one three pair and these two squares needed to be a one three pair which wouldn't work [Music] okay so can we improve upon this further the answer is i don't know yet gray gray in box eight is a little interesting oh no no it's more than interesting it's actually fixed sorry i was thinking it was in one of those two positions forgetting that this could be gray but actually that is gray so now right graham box 6 is in one of two places i think both on spaghettis that add up to reds so gray yes okay so whichever one of these is gray it's it's on a spaghetti that adds up to red so we now know that gray is less than red um [Music] oh yes okay now what about that cell then because here here's sort of an equation going on whatever whatever this digit is whatever the purple digit is we know purple plus gray equals red but in this box whichever one of these is gray is going to need a purple accomplice in one of those two cells in order to make its little line of spaghetti add up to red because because one of these is gray and whichever one it is it's adding up to red one of these must be purple which means purple in box nine is now in one of three plus positions look oh it's all getting a bit yes it's getting a bit colorful isn't it um [Music] okay so we've now we're now working with four four chromatic options as well as the yellows or orangey spaghetti ah no that's nearly good blue is in one of two places in box uh four over here right what have i missed here there must be some way of at least getting a bit more coloring done gray hmm there's all sorts of equations going on in the box five as well um gray is equal to the sum of those two digits so that means that these three cells together it could be expressed as two times gray but look you've got the same thing going on with um blue i think we know this cell is blue but i also know those two cells add up to blue so this little tromino here that adds up to double blue so this is double blue this is double gray we know that then these six cells add up to an even number we know by the secret that the overall box five adds up to an odd number um because the secret if you didn't know the secret where have you been but the secret is of course that any complete box of a sudoku because it contains the digits one to nine once each adds up to 45 45 is odd but we've just worked out those six cells are even so these three cells must be odd in order to get us up to an odd total but we don't i think know the parity of red uh no we don't we know red is the sum of two different numbers but we don't know their quality either so right so i can't do so presumably what we've got to do one two three four five six yes okay we've got to use maths that's what we've got to do that's really clever actually it's really weird but there's definitely um an equivalence if we have right let's stare hard let's stare hard at box five and let's analyze i want to analyze these eight cells i think because i think it's true to say because of the nature of spaghetti that these eight cells here let's highlight those in green for a moment these eight cells have the same total as these six cells in box three and probably yeah and i think these six cells in box seven have the same quality as well let's just double check this so we'll do it gradually these two cells they add up clearly to the same as those two cells by the equal sun line trick so those two are equivalent these three cells are the same as those two cells so they're equivalent now these two cells are the same as blue so that brings this one into the equation and this one is red which is that one so yes it is true these eight cells add up to the same as those six cells but we know these nine cells sum to 45 so the maximum i could make these six cells add up to would be 39 which is 9 plus 8 plus 7 plus 6 plus 5 plus 4. so that means that this cell is adding up to at least well i was going to say it's adding up to at least six that's certainly true but i can do better than that let me just put six in to these cells those we know that they are adding up to six but also weirdly i can say i think but because i know these six cells add up to the same as these eight cells but i know that the whole of box five must add up to the same number as the whole of box three i actually know that this digit is specifically equal to the sum of those three cells and the same is going to be true in box seven isn't it i'm just going to double check box seven because i didn't check it before so box seven those two add up to that so that's equivalent these three add up to these two so they're equivalent this these two add up to these two that's equivalent and red we know is equivalent to red that's fatuous so yes so these six cells also add up to the same as these eight cells which means these three cells add up to gray now ah yeah yeah okay but gray is not nine gray is not nine because we know that grey plus something is equal to red so if gray was nine red would equal 10 at least so gray is not nine so we can get rid of um oh what's gone wrong we've got letters coming up we don't want letters so gray is now a maximum of eight and oh okay and because because gray is in the sum of digits adding up to red we know red is bigger than gray so red is seven eight or nine which is this this this this this and this are all seven eight or nine is that enough can we do so this digit is now one two or three because we know this plus this equals this right got it i've got it um gray is eight i think this is just classic aspartacus because it's it is weird actually i don't know whether i'm just being slow today it might be my covered brain but the it is weird okay so let's let's do maths again because i think it's interesting to think about the maths of this we know that gray is equal to the sum of those three cells so we could in a way label these gray but we also know look that gray is equal to the sum of those two cells so i know that these five cells this u pentomino of grey here represents two lots of grey whatever grey happens to be but i also know that the triangular number for five is fifteen so the minimum i can make those five cells at up to would be one plus two plus three plus four plus five well how could this ever be six then or seven because that would be implying we know that this is two lots of gray that would be implying those five digits add up to twelve or fourteen that won't work so gray is eight gray is eight which means of course red is now nine and that cell which is purple is one so one is in one of those two cells gray is eight in one of those two cells well and i know this u pentomino now because i know it adds up to double eight which is 16 and it's five cells that is one two three four and six that's the only way of making 16 in five cells okay and i can't i know these three cells are a single gray so these three are adding up to uh eight on their own therefore they don't have a six in which means the 6 is on the spaghetti which means it is a 2 6 pair so that's 2 6 which means the other three squares are 1 3 4. these squares are 5 7 8 and that is oh and eight yeah so eight goes here by sudoku sorry i should have seen that immediately and didn't so so this right okay so let's get rid of some of my grayish now i think i've been a bit overly zealous with that because this digit is now gray apparently which means that that's grey in the corner no song for you though um and oh so i've nearly i've only got two grays left to place in the whole puzzle these these um so right okay so now we can get rid of green i think we get rid of green we reinstate gray there i know one of these is gray i know that blue blue is five or seven now and have we done any thinking about blue in terms of its quantum i don't know that we have we definitely know these cells are all blue so they're five or seven we know okay so what do we do with our new knowledge about the nature of grays and nines nines are in one of those two cells by sudoku can we do better than that the answer is oh yeah yeah no we can how could this now b9 if that's 9 9 plus this digit is equal to this digit which means this digit is at least 10. so that shunts um red into exactly this cell which means that we've got to put a nine in one of those cells and okay um um can we do better than that probably let me think i'd love to know what blue is now that feels like the natural next step doesn't it can we do some is there some sort of weird maths we can do to work out the value of oh i tell you something i worked out those three scales were equal to gray didn't i so these are equal to eight which means they're either one three four or one two five they definitely have a one in them and that one is not in this cell it's fairly likely there will be a one on the spaghetti but probably but not proven yet um okay so how are we going to do this then what is it that i meant to be what is that i'm meant to be picking up here um [Music] if if this is a five obviously then the only way we can make five in sort of two cells is either going to be one four or two three i don't think that looks to be incredibly impossible so we might have to we might have to think harder about this um [Music] hmm no i've got nothing so okay so we're gonna have to think i think a bit more i know one of these is an eight one pair either this one or this one i know that do i can i do something using so i know those two cells add up to eight which means they're either three five two six or one seven these three cells add up to either 13 or 15 depending on what the nature of this one is and these two add up to five or seven right i know how to do this let's come back to box seven if this was five those two cells would add up to five and these three cells add up to eight that only gives us thirteen for five cells which we know must add up to at least a triangular number for five which is fifteen so that's not five so now we know that that blue is seven which means that this line has got 13 on it which means those two squares add up to 6 because of the 7 in the middle so these are either 1 5 or 2 four that's not one so that's not five using the power of sudoku um right now hang on these two cells add up to 13 and they can't use eight five or four nine so that's a six seven pair which which is done so that's seven that's six seven is the blue digit which means that this is not seven this is seven this is not seven and therefore this is a seven in the corner which gets fully blurrified and we can place a blue in one of two places in box one as well so almost all of our sevens are done we've got we've got two left to place and okay can we go further than that the answer is possibly but i don't quite know how yet we could hmm we could argue about yeah don't know we could right how do we make this eight total work then i know these are either one five or two four ah ah where does where does one go in box five you can't put one on the eight uh equal sum line because it would need a seven with it so actually it's just as simple as saying where does one go in the box because it can't go on that line and can't go there it's in one of those two cells which means that's not a one and this is a one and we know one is purple and we know purple has to join its friend the eight to make nine so this is now gray which means this is not gray this is not gray oh sorry if i no that's not true because this is gray that is gray so our x-wing of eights is unwound this is not gray we can get rid of some pencil marks in those cells all of our eights are now done we've now got an right so now we've got a one in one of these two cells by sudoku this is no longer purple we've got what else have we got then is that has that worked some magic somehow some way possibly um or possibly not ah okay if this was a one this would be a six so this would be one six this would be three five and what are these adding up to six then so they'd have to be two four okay um oh this little line here those two add up to nine look but they can't be one eight and they can't be two seven so this is either three six or four five which is not really ideal so two is in one of those three cells and ah that can't be a one because this domino adds up to seven that's nice so this is this is where it's not resolved but we now know this is either two five or three four and the one that we know existed in this line because we knew this line added up to eight is now here which is a purple digit which means that's not purple which means this is purple which means that ah we can get purple now in box three and we can put a three four pair oh that's beautiful look at this three four pair there's probably more we can do with ones though as well just let me just pause and take a look at ones um [Music] no okay but i want i want to look at this three four pair because this three 3-4 pair has to find a home there which means that's not four which means that's not two so this is quite low oh this is on a nine a nine line so this three four means that's oh five or six oh bobbins i think both of those things are possible yeah this is a two five six triple oh that's that's that's disappointing i thought this was going to do something magical but it's not quite done it okay so maybe do we look at this line then one two five and six into the gaps let's let's put the options in and see if we can narrow anything down this is the one i think that's most likely to be narrowable down we know these two cells add up to seven so if this is a six this would be a one and we know that's impossible so this is one two or five now so this is either a two five or a 6 which ah ah no lovely okay so let's study this box harder what's the digit i've not pencil marked three and three has been forced onto the 8 equal sum line which means it must be a 3 5 pair which means this is now 4 which means that's a 2 to add up to 6. this is now so we've used 2 and 5. so that's a six this is a one this is a five by seven so that's a four that's a three because we needed those two to add up to nine and suddenly we're away again um stunning this isn't it it's just stunning um two there so that's two that's six this square should be a writing of five i think and okay there's all sorts of new information with just this five is giving me a three here the central box is done so this is not five so that's not four this is not three so that's not six um that might be this is probably a sudoku way of resolving this but i don't see what it is quite okay but we now know these digits they are one two and four and we know that's not one and therefore we must know these digits which must be three six and nine ah and that sees six and nine so that's three look at my red x-wing here well that's quite interesting because that means if i put 6 here i have to put 9 here because i'm going to have a 9 there but if i put six here and nine here this can never add up to enough the maximum that size this could be would be six plus a four which is ten but we'd have a nine here and those two squares having to both add up to one that will not work so that needs to be the nine which means this is the nine this is a six oh which me ah that means there's a six on this line as well which might be interesting let's just have a think about this so so this can't be a one because if it's a one these two add up to ten and there would need to be a one on this line as well to make it be six one three and we'd have two ones in the column so this is not one which means this is one now this is either adding up to 11 or 13. so if it adds up to 13 um we need seven more there wouldn't we which would have to be one no that doesn't work you'd have two sixes wouldn't you if this adds up to 13 these have to add up to seven without using one six three four or two five yeah there's two ways of thinking about that but basically it doesn't work so that's got to be two that's got to be four this has to add up to 11 which means it's got to be one four six because it can't be two three six because of this two and now that that digit is known that's a three which means this is not a three four pair this is two five that's a four to make seven this square is known that's a three by sudoku and these three digits are now known as well they've got to be two five seven oh and that can't be two because i can't make both of those equal one so this is five or seven if it's five this has to be either one oh it'd have to be one four because this is a two three pair looking at this cell so it would have to be one here four here absolutely four so but that could work all right what if this is seven if this is seven oh there's probably a few ways that might work let me just think about this for a second can i even eliminate any option if this is seven i'm not sure i can so i could do i could do one here six here that's possible if i'm looking at two five i'd have to be looking at two here five here and if i'm looking at three four i have to be looking at three here four here don't think any of those things are ruled out right that's not five by sudoku oh or seven that's a two okay so that's not two which means that's not five that was the only option i think that went with two so this is down to one or four ah that's not three i've just seen okay so this is one four six and three that was three the only way that that went with four if this is four and yeah if that's four what's this well it's either got to be three or one and neither of those things are possible apparently so this is one which means this is not one we've got a four six pair so this is one we've got loads more purpling to do we've got and we've got four five or six at the bottom i can't see whether we can improve upon that uh what about what well okay let's have a look at these two squares because in theory they're two three four or six but they already see for a four six pair here so that must be a two three pair which means that's got to be four that's got to be five that's five that's two this square is now not five so it's four or six this four does the order so four six six go into the grid this is a two three pair which is apparently not resolved and these two squares at the top are two and five and no they're not two and five i've already got two here they're five oh they're far i see they're five and seven but this little deadly pattern is going to get unwound by this being a seven now by maths so that's seven that's seven that's five that's five and we might need some help unraveling this one i'm not sure i can't immediately see how to do this but this column that's got to be the two in it because it can't be three so that's the three that's the two that does the two and the six which does the six and the four the four and the three the three and the two and we are yeah we're home and host i think um these two squares have got to be three and six which we can write in these two squares are four and five which we can write in we can click dick and that is how to solve another brilliant puzzle it's been a while since i've done an aspartagus but absolutely lived up to my expectations just really gorgeous setting very interesting and yeah i'm not sure how hard it was there may have been easier ways to figure out that there was some maths going on along the spaghetti there's not often you get maths going on your spaghetti but in this puzzle you definitely did i think you have to spot something around you know the sort of relationship between the number of cells on spaghetti and box five and the slightly shorter or smaller fewer number of cells that had to have deal with um spaghetti in boxes either three or seven it's really clever though it's really clever i look forward to the comments on this be interesting to see how many of you have just aced this and race through it we do have some absolutely speed demon-like solvers some of the times that get posted are just phenomenal there are there are definitely some of you who should be representing your national teams in the world sudoku championship take my word for it um but it might be it might be that aspartagus has you know this is a sort of puzzle i think also that could fox you for a while um yeah as i say i look forward to the comments with interest i do enjoy them especially when they're kind and we'll be back later with another edition of cracking the cryptic [Music] you

Channel: Cracking The Cryptic

Views: 44,954

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Id: 7UZKP82Em14

Length: 42min 48sec (2568 seconds)

Published: Tue Jun 28 2022