Only one Sudoku Rule Applies

[Music] hello welcome back to cracking the cryptic and um it's not going to be a sudoku today now this is going to be the start of what i'm calling debut week uh we'll be featuring well i hope it's going to be four puzzles by setters new to the channel um constructors uh that we haven't featured before uh that is rather dependent on whether i'm correct that we haven't featured them before and on whether i can solve all four puzzles and they make videos so we shall see about that i don't know for sure what the situation there is but um that's the plan and uh these will be kind of they might get interrupted i suppose by a guest video but the next four videos of individual puzzles that i'm going to try to do are by four debut setters and this one is by overlor which if my schoolboy french is right is kind of the french for catch that thief um to the thief although i seem to remember volley can mean to fly as well as to steal so uh maybe maybe there are alternative interpretations now this is not a sudoku this is a pencil puzzle a phelomeno specifically although with an interesting sudoku twist we'll get to that in a moment don't forget all of our content on patreon will be working up towards the first of the month soon and some new content uh for patreons a new competition that we always release on the first of each month and we've got i mean we've been putting up loads of content there basically so patreon is always a a good source of further puzzles um and so is discord where you can also chat away about sudoku and other puzzles to your heart's content with a like-minded audience who are very welcoming uh we've also of course got all our apps and do check out everything in the links under the video but the first link is to this puzzle it is not a sudoku it is called a v and what you have to do in a phenomenon is divide the grid along the lines into regions called polyaminos so that no two polyaminos with the same area share an edge so you could have a region like that which would be a five cell polyomino then you could have another one like that which would be a three cell polymer now in this puzzle uh oh sorry each cell contains a digit which is the size of the polymer it's in so if you did have that as a five area and that is a three area we would fill in the numbers like that so that is disobeying the normal sudoku rules of not having numbers in the same columns or next to each other so i'm going to have to get used to that something i find difficult when switching to pencil puzzles i have to admit now we have some v's and x's the digits and two cells joined by a v sum to five and in two cells joined by x sum to ten all possible x's and v's are given now this is important um there is a huge i imagine negative constraint in this puzzle all possible x's and v's are given so if if these two added up to five there would have to be a v between them so they can't and they also can't add up to ten that it's an intriguing idea to mix with a philomono um and i'm not sure i've ever seen a phelomeno before with no given digits in the grid in fact when i looked up the standard rules of philomono to copy them over um on gm puzzles they began with there are some given digits in the grid and i had to kind of cut that out because there aren't so that is the puzzle we have do give it a try on the link under the video i'm not sure that the software is going to understand the correct solution here so you may just have to work out that you've done it right or compare it with mine at the end of the video but um i'm looking forward to this i'm going to start now let's get cracking and i mean this is this is one of the puzzles where i say let's get cracking and i have no idea how to get cracking okay i mean i guess we know that there are region boundaries wherever the v's and x's appear no no that's not true there are region boundaries wherever the v's appear i mean i could go into the pen tool and draw draw lines but i'm probably just going to try and do this by coloring right there are region boundaries where the v's appear okay i'm beginning to get an idea now so they have to be in different regions now i know that because a v means it's separating either a one and a four or a two and a three um and therefore they're different regions because they they have different content markers um now x i was going to say the same is true but of course x could be five and five oh hang on hang on hang on hang on right x could be five and five but none of the x's in this puzzle are five and five and that's because of the negative constraint rule all possible x's and v's are given so if these two that i'm in we're in a five five we're in a five pentomino well the problem there is that pentomino would need to have three more fives so if you had one here well hang on where's the x between those two cells so you could get very close here they could be fives but you still need one more five cell and it would have to have an x to whichever of those cells it was joined onto so actually no there are always region boundaries between the x's and the v's in this puzzle you could come up with a phenomena xv where there wasn't but you would need five x's five five strung together with x's right now i am beginning to get an idea here because yes yes this is great okay look i can fill in one four there why can i do that because if these were two three look what would happen to to this orange region it would have to go there to make up at least two and the purple region remember this is going to be different again because it it's separated by a v so the purple region would have to come here and now you'd have purple and orange together they're clearly the same digits as they are up there that's how phenomenal works but there's no v there so they're not two and three and this is a one four pair let's actually make that a different color now one of these does extend out right i don't think this can be the one oh hang on maybe it can i was just thinking if this is the one how's the four going to extend out because it can't come here so it would have to go through the x but it could it could do that okay so i don't know the truth there um that's also one or four because it's on a v with that one oh come on can i not work out which way round one and four go if that was a one that would also have to be a one that would be a four um oh and it couldn't go there or there so we'd have to come here no but again this could work you could have six oh no look this doesn't work okay i'm sorry if this feels like bifurcation i mean i could visualize this but it does help to show it this is brilliant this doesn't work because of this cell yes you could create four like that now why didn't i put four here because if i'm gonna have to put a six here on the x then i'm gonna have to put six here as well to make a six shape so no four there that's why i bent it round to that side fours obviously can't touch the ones but what can this be it can't be four because it would be touching one it can't be six because it would be touching a four without an x and it can't be a new shape because it would be another one and the rule is that no two polyaminos with the same area share an edge so that is not a one wow okay so this is the wrong way round and in fact it goes four one four at the top and i think now this shape has to be the one i drew because four can't go into that cell because it would have a v so we get a four there then it has to keep extending to there it clearly can't extend to here because that's now a six by the rule and that's a four um actually what i might do on the colors is let's use i'll see how far this can go anyway i'm going to use the colors um of our palette like if you if you were in the colors the color button and you pressed four you'd get green so make them green that makes one light gray and that four is green so right now we've got this six that cannot go here or here because they would use the negative constraint they would have to have an x to the to the green four so six can't touch a green cell so it goes here it also can't go in a v cell so this six has to now bend down here avoid there and there and go there and we know four of the um of the six shape after that i can't seem to stop it going into any of those actually i can stop it going here because this isn't allowed to be a one four or six for the same sort of reasons that wasn't allowed to but that doesn't really help it i i don't know whether the six carries on into either of these or both of them so i'm kind of limited now this four can't go south because it would touch a six and not have an x so it goes there then it can go here or here or both this calm this cell can't be in a one so it's got to be in at least two um [Music] okay so i'm going to go off piste on my color scheme and join them together with with blue i mean i doubt very much that it's a nine shape in fact it can't be a nine shape because of that one but it is bigger than one now we could have shapes that are bigger than nine in this puzzle but they won't be touching the x's or these if we do um and they'll be difficult for me to notate in our in our software because i can't write 10 in a cell but i doubt that it's gonna happen now does this have to be or cannot be in the blue shape blue could be two i don't think that's breaking any rules ah this one ah right this can't be a four one pair on the v because one of the fours would touch the six so that is a two three pair oh and now this is constrained i think there's no yeah that's interesting is it hang on well i'm gonna say that this cell can't be a two or a three it also can't be a one it can still be a four it can't be a one because it would need a v with the four the reason i think it can't be a two is because that would make this a two and that would be shutting in a two cell region so that would be two twos there sharing an edge with a two two pair there so it can't be a two can it be a three and i think the answer is again no because it would join on with this cell it would have to finish there but this would be a two here so where would the v be between two and three so this cannot be one two or three it can't be five because it would escape here and we've worked out there's no fives on the x's because there aren't enough of them it can't be six because it would need to join on to the four now it's either huge therefore and of course if it is seven or eight it could join on to those i think one it can't be nine oh well this cell could be nine if that's a two enclosed i don't know i'm very tempted to think that it is a four but i'm just gonna write four seven eight nine as a sort of as a sort of placeholder because it could be a 10 or an 11 but now actually it can't because it's got to go through that x if it does so it certainly isn't a 10 or an 11. right 4 7 8 nine i think those are definitely the possibilities there i'm not really sure how to progress working them out now i was tempted to write this as a 1 4 pair but actually i don't think that's right because it could be a 2 3 pair with those joining together in the same shape in fact that seems quite likely oh crumbs how do you get going in this i mean i barely feel i've started um now does that have to be a four if it wasn't this four would go like that yeah and that wouldn't work because this shape ah if that is a 4 this shape is going to have to come out here and this is going to be a two or a three and this is gonna have to be a seven or an eight so if this is a four this is a seven or eight which is a bit unlikely but anyway it means this shape doesn't go that way this must be a four um and we've worked out this doesn't go north this can't be a two or a three for two different reasons to do with this so actually this shape does come out here let's make that yellow i don't think it's going to finish well it's not it's going to finish being dark gray or black for two or three and this is two or three it's part of the same shape so this is seven or eight here ah well that's interesting so this is gonna have to be seven or eight whatever happens to this seven or eight shape it's gonna have to come into this cell now it could still be occupying some of these it can't it cannot be here the same seven or eight there can't be here because they're both yellow beneath and if they have an x in one case they'd need an x in another so this is not seven or eight it's clearly not nine now because that can't fit in so it's four wow this is intricate but this is now seven or eight okay so the four shapes finished this shape's finished that's a two let's color it dark grey to follow the the palette coloring it hasn't told us whether this is a two or a three ah now this shape can't come here because again you'd need a v there so that carries on down here let's make that one blue for now one of these needs an extra digit being a three that extra digit is not here because it would connect to either blue or yellow so this is a one four pair i could have written that in earlier but not for the reasons i was thinking um oh this is this is fascinating this puzzle now this cannot be yellow because the 7 8 has come out here and would have to join up so that this is finished that is a two let's make it dark gray this one is a three therefore and is black and needs another digit in one of these two positions oh and the six yeah the six can't come here because that would enclose this yes we worked that out earlier so six there we've got five six cells we need another one in one of those positions the three could easily curl uh the two right this seven eight can't come down here it can come to here i suppose it could get out this way well otherwise it's going to go it seems quite likely that it i don't know no hang on right now if it was to fill one of these x cells well it can't get to this one because it would have to loop around here or through here and then it would touch this cell as well and that's impossible because if there was a if this shape was giving a seven or eight to that cell its counterpart two or three and an x would be there and then you'd need an x between those two so it doesn't get to there so if it goes into this x pair it goes in here and then it mustn't go here or here or it would need an x to here so if it goes into the x to get seven you're going to have to come into this cell if it doesn't go into the x and i suppose you don't have i thought i was going to prove this cell was part of that seven or eight shape which doesn't come here does it now if this was a four it would have to come down to here and to avoid that six it would have to come all the way down if this was a four it's it's a vertical line and that's because it can't come through this cell because if that's a four that's a one and then this can't be another four or you'd need a v between them ah this is so interesting the logic here is so different from anything i normally do i'm i'm quite potentially being much slower than you to understand how it works but you'll have to bear with me because i'm not used to either phelomeno or or this particular constraint and negative constraint i mean it's definitely the negative that's the most interesting thing here now i can't work out whether to continue thinking about the one four or the three or the six or maybe this cell this can't be a one so it joins on to this or do i maybe i should just work on the seven eight which cannot come down here so does it definitely come to this cell tempted to assume it does if it goes there it must also go here because this can't be shut out as a one or it would join to a four i don't know i just don't know whether it touches this right it can't come here so if it doesn't go in there then it would have to go all the way along here if it doesn't go into this x pair and the only place it can go is that so if it doesn't go into there it must come all the way along here and that's six and then it can't come down here so it would have to be there so if it avoids this x pair then all of those then it must be a 7 oh it's not a 7. honestly it's an 8 because it's next to a 2. right now i do know and now i do know because it cannot avoid it can't avoid this x it's not allowed to come here if it avoided this x because it can't come here it would have to go along here remember it's avoiding that x pair it would have to come into this cell now it has to avoid the bottom cell of this x pair because there's no x to connect it to so you could get seven cells but you wouldn't be allowed there to make up the eight so it must come into this x which is really important i think that well in the sense that it gives us a two here as well now where now it can't go through here and it's an eight so it's got to come through this cell to get out uh the maximum you could oh no the maximum you could have here is six and it's not allowed there so it's got to come out through here oh this is so clever um ah look this two where does that go it's not allowed here because there's no x between those two cells if it came here you'd get another eight here that isn't allowed there or there because there's no x there so it doesn't come here so the two finishes up here now that can't be an eight one two three four five you could make that an eight but we still need two more somewhere further down here i don't think i can do them at the moment but let's not worry about that okay let's be quite interested about what if this was a one what happens here it obviously can't be another one or it would kind of join join on well it would share an edge that's the point it can't be part of this because that's complete it can't be part of eight because that would touch a two without an x and it can't be anything else because that would start a new region so that is not a one that is a four that's a one four is green now i think we can probably say well yeah this can't be a one because it would be touching a four so it's something that's already started it's got to be a four it's not allowed to be an eight again so there's a four there four there that's three of that four it could go here but it would be blocking the eight quite hard um it can't go here it could go here but that would create a six oh i don't know i don't know what's going on what about this two thing though what what ten shape is this next to the two the eight's not allowed in it this this yellow eight shape that we're creating oh and whatever cell is here can't come round to here so this is well it's one two it's one or two because it's not allowed to be as big as three it can't come around here because there's no x between those two and it can't be two that's got to be a one so this is a nine this is a genuine nine which can't come out through the v so it must come out through here um it can certainly touch the two and eight ah now what's going on with these v's right this one this side it can't be a one because it would be next to a nine it can't be a two because that would shut in one cell which isn't allowed to be a one or a two so this is a three must be and that means this is a two pair now i'm cracking on this is part of a three that must come down it's not allowed to go there now the nine is forced into all of these cells um ah the nine can't come out through here because that would make this a one but it can't be a one because there's no connection there so maybe the nine could go here but that would only be five six so the nine needs three more so it can come through here if that's a one no it can't because one of those twos are four i don't know which one but one of them's a four and that doesn't have a v with this cell so that can't be a one so the nine doesn't come through here so it's got to come through now the only reason i'm not extending that one more is because i just want to count them up five six seven we could still have a nine here right but we are going to have one more at least here wow oh no the eight has to come out here one two three four five they can't both be eight because that can't be in fact what's this cell it's not allowed to be two or eight and it's in a region that's bounded there so it's got to be a one and this now can't be one or f or well it can only be eight so we've got six cells of the eight and we're going to finish it off now because it has to come out here we've got most of the top four rows done that's quite exciting oh and the eight has joined on to a cell with the x so that's a pair of twos now the nine five six seven eight we need one more nine does it go no it doesn't go there because the 3 needs to go there that's the 9 and that's really helpful because that's on a number i mean it's on an x is what i mean so those are both ones that is another nine again good grief this is an incredibly helpful run of x's that i didn't think would happen so this new nine region has to come along here can't go up there touching the one so it has to keep going here can't go into there because that would make a one here which isn't allowed so it carries on here and that's about as much as i can do but that is six cells of it already done this pair has to form at least a two i don't really want to color them yet um right the four we can finish that off into this cell that gives us another one here no that's an x read them read them carefully you fool that's a six oh that's a six and it's not part of this shape because that would take seven cells so that six comes down here might go here this i think can be a three or a six but the three could come straight down or curl and this could be a new shape if it curls six can't come here but it could go there or obviously here wow i mean this is fascinating this puzzle it's so intricately clever i haven't done a puzzle like this i think simon's done quite a few not not of exactly this sort but he he thinks his way through these much more cleverly to be fair now come on what next do i know what that is this thing this thing i maybe shouldn't color it blue because i'm now beginning to get used to blue being nine and eight being yellow and so on i haven't had any fives or sevens yet yeah okay that's an interesting thought i started wondering are we going to get any fives because they can't touch the x's we worked out now i'm beginning to think we don't have very many cells left to fill and yet we've got an x there that can't be part of oh maybe it could be part of this six i was going to say it can't be part neither part of it can be touching any region we've already begun but can it be the six no it couldn't come here and be six because that would be a four and how are you going to make up this four shape just nonsense can that be a six and the answer is no again um for well for at least two reasons one is that you kind of got to shut in a pair of cells that can't both be ones can't be a two pair because they'd be touching a two but also because this would become a four and would have to come out through here so that's not a six i don't think that can be part of any shape we've already started now why i'm getting interested about that is because this can't be part of anything we've already started as well so this x pair is representing a combined region of 10 cells and they have to come out somewhere the maximum they can get in the white cells we have here is eight so they have to come out there and there or there and there or there and there or if they don't use all of those eight further but that's quite interesting because the six can't carry on down forever in fact can six go there what happens if that's a six and look this is really interesting it can't because the furthest the nine could go let now i'm trying to maximize the area in which this pair of cells that forms a 10 can occupy and that's only 9 cells but the 9 can't just come along here forever because it hits this v cell so the 9 would have to turn up there and with a six there you'd have hemmed in nine cells in an area that needs to be ten so the six does not go there this six has to come left to keep going and that forces this six to finish left as well i don't know that this is all one shade i'm going to uncolour those cells this one ah bother it's a one or a three um this six now has to turn south because it can't go there now this region that i'm anxious to avoid bounding in three five eight nine it has to use this cell this is part of this exciting new i'm gonna color this region purple it's gonna take those two cells it's definitely going to take that cell oh it can't take both of these i believe and the reason is that these two have to be different shades of purple i don't know okay let's let's let's let's use different colors let's go purple and red and make that purple or red so the the region of at least the region of ten cells that is purple and red it can include these two although it doesn't have to but i don't think it can include both of those that's what i'm going to say because either either you get purple here which needs an x to the red here or you get red here and then you get either red or purple here and there's a missing x again so it can't include both those i don't think six can come in here six isn't allowed there and we worked out six can't get there so this is gonna have to be nine or one it's not in the region because we can't use both of those so that is probably blue but i'm not writing the nine in oh no it can't be one because it would be touching a nine so it is blue it is nine this purple and red escapes through here well in fact this is on the purple side of the cross of the x so they're all purple um and i bet these are purple and these are red how hang on let's finish off the nine one two three four five six seven eight nine that finishes off the nine oh now that's bounded in oh it hasn't bounded in enough oh hang on i've got something wrong ah yes i have i've miscounted nine that's a relief oh gosh okay because once i added that in that was a sixth a seventh cell a seventh cell not a sixth so i don't need all these three so that we will get rid of the nine has to come here and finish now the purple has to keep escaping here it doesn't have to go any further necessarily if those are both purple and those are red seven and three that would work so i don't know that purple carries on in fact we're now into this v territory oh and this can't be a one because it's next to a nine so this needs to escape up here and that bounds in the purple uh i bet that's a two but i don't know let's call it yellow for now but the purple and red have been bound in so purple well what color oh seven should be red sorry and but this is a three and that should be black so three is black and we'll make this purple area red and give it a seven and that's all done and now this r now this can't be a three because it would be touching a seven oh i was tempted to say it can't be a four because it wouldn't be allowed here we've worked out it can't be a one so it's two three or four to be sitting on a v um it can't be three because it goes there so can it be four yeah no it can't be four because if that was one that wouldn't be allowed to be four so the four would have to come up here and would would clash with the six so that is a two brilliant that's brilliant what a brilliant puzzle this is so clever so those are twos this is a three and it's not allowed onto this cell because it would be touching a two so it's got to come up here hit the x so now we get another seven suddenly we had no red at one point now we've got tons this can't be red so red oh the six has to finish off it's only got four i could take that so the six has to come here that's orange oh this can't be a six it's touching a four you numptician right that's a three this must be a one now uh six needs another cell it's got to be here this is sealed off one that's all right that doesn't clash with anything now this seven right i mean the max it could have if it used those was four then it has to come all the way up to here but the max it can get up here is six so it's going to use that so we need they're all they're all red we need one more seven cell and the other one is a one and one can't be here because it would be next to a four what a brilliant puzzle i did not expect this oh i didn't expect wow hats off to sven apparently the uh software's able to recognize a phenomenal solution i mean it might it wouldn't understand the xv bit i wouldn't have thought so we would have to make sure that that's right but look at that i think this all works and that is an incredibly exciting puzzle so clever i mean once you get used to the negative constraint it just gets better and better as you go and there's such big shapes in it nines eight sevens and sixes everything but a five which we ruled out in the first minute oh that's so brilliant what a puzzle love it thank you overlord that is a real treat um i hope you enjoyed trying that and maybe even watching my solution but i really enjoyed it so i hope that came across thank you so much for watching as always and uh hope to see you again during um wow well it's a great auspicious start to debut week isn't it that's brilliant thanks overaller and thank you bye for now [Music] you

Channel: Cracking The Cryptic

Views: 32,102

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Id: wYttOMMuiJc

Length: 40min 35sec (2435 seconds)

Published: Sat Mar 26 2022