The Phistomefel Movie

[Music] hello and welcome to monday's edition of cracking the cryptic and here is the new fistum of hell puzzle it's called loop sum and uh yeah we're going to be having a go at this on the channel today now in fact i have noticed when i've looked at logic masters germany that we have missed out a puzzle by fisted mafel vistamethel released another puzzle a week or two ago um but that is a logic puzzle again about touching slitherlinks uh well i read the rules and it's a cross between touching slytherlink rules and country road which is another type of logic puzzle um so my plan is that i will have a look at that at some stage for our patrons over on patreon so keep an eye out over there if you want to see my attempt at that but this one is a sudoku believe it or not although it's called loop sum um and i have even got an example look vistamavel was kind of kind enough to create an example so we should be able to understand what's going on so why don't we just read the rules i imagine this could be a very very long video here they are fill the grid with the nut digits it says digits not numbers i don't think there's much of a difference but it does say digits fill the grid with the digits one to nine such that every row column and region contains each digit exactly once the regions are sets of nine orthogonally connected cells and have to be determined by the solver okay so far i understand what's going on i think there's a massive craze at the moment for chaos constructions i.e sudokus where there are no given regions and you have to make them yourselves it seems that every puzzle we get sent and recommended at the moment is a chaos construction i don't mind that at all i love chaos constructions apart from the irregular sudoku bits at the end um but anyway what are the rest of the rules draw a loop that travels horizontally and vertically from cell to cell the loop enters and exits every region exactly once a small clue in the top left corner of a cell indicates the sum of the digits in all cells visited by the loop in that cell's region so let's have a look at the excitements and re-read the instructions and see if we can understand what's going on so this is for a six by six grid and this is obviously the solution in the colored grid on the right so right first thing i'm saying is that in the two this region this blue region there is a small clued two and it looks like the loop only takes the cell in that region that contains a two oh yeah look look at the purple region the 14 there i was wondering if the if the small clues had to always be in the top left hand corner of their regions a bit like killer sudoku cages but they certainly don't look there's a 14 clue where the 14 is is in is in the cell containing the one and the loop cells do add up yes 2 3 4 and 5 do add up to 14. so that i sort of see what's going on in the purple region 19 19 for the orange region and 11 for the grey region yeah what a fascinating idea okay well i sort of i think i can sort of understand what would what we've got to do um do have a go the way to play is to click the link under the video as usual i am not sure how hard this is it's got four stars out of five for difficulty on logic masters germany which means it's it means it's anything from quite hard to exceptionally hard and it has got quite a lot of souls i think about 30 people have tried this so um it you know take make of that what you will anyway i'm going to have a go now let's get cracking and i can't remember if i said the way to play if you want to play is to click the link under the video i probably did but i forgot um [Music] so the 43 at the top must be must be interesting wasn't it because virtually the entirety of this region is going to be contained is going to have have to have loop in it and that's because of the secret now the secret is something i only tell my favorite people but if you are watching this um and we're going to be having look well and with with solving a fist and fell puzzle you are definitely one of my favorite people because anybody who likes fistum of hell puzzles is something of an athlete when it comes to puzzle things in general and a four well the digits one to nine once each add up to 45 so a region of nine cells with a 43 clue is telling us that exactly one cell in this region whatever it looks like doesn't have loop in it and that cell must have a 2 in it now so can we just draw this region in it it can't overlap with a one region in fact the reason i'm just pausing here is i'm wondering if the one regions no the i'm sorry well i'm not being very articulate but that's because i'm puzzling over the fact that in in a one region in a region with a one clue there must be one cell in that region that has loop in it and that cell must be that have the digit one in it now what i'm wondering is i don't think these can be the same can they because the 43 is going to split them up and whatever the 43 looks like if we if we start to build a 43 region if we're then going to claim this this region and this region of the same region they're going to have to ring a 9 cell region and i well and also no they're going to have to know hang on no let me just try and do this as efficiently as as humanly possible now this is this just doesn't work does it we're going to keep we're going to run out of space and either have to also surround the 23 region or a 2 region i think um i can't yeah i can't see how to connect these one regions together i might be missing a trick here but i can't see how to do it or at least no i said i certainly can't see how to do it given this 23 and this two so these one regions are different from each other one two three four five six seven eight nine ah ah right okay this is huge so in fact fistum fell has been generous maybe this was implied by the instructions actually i'm not sure but the the point here is that because any any top left little clue um well because every single top left clue is not the same number apart from the ones which cannot be in the same region these top left clues define different regions of this puzzle and there are nine of them so we have to put every single cell in this puzzle into one of these regions which is probably very important to know but i'm not sure so the so this region has to grow like this the 43 must come to at least this square because it can't bump into the one regions this cell will make uh purple um and now we've got star i don't believe it oh come on uh this is not a very propitious start is it because really we we need to be growing growing these regions rather more well with rather more uh i've lost i've lost the ability to use adjectives with rather more gusto um okay so i'm wondering if the if this cell in the corner can be looped because it's going to cause no no of course right ah right now i see what's going on right so i'm going to switch to loop loop drawing which is the pen tool we used this yesterday if you're unsure about how i'm drawing these loops in the grid sven software is marvelous just click the cog icon on the right hand side of the grid and then enable the pen tool and you'll be able to do it now what would happen if we try and put this cell in the top left hand corner of the grid on the loop well that would happen but this is a problem now because we know in the blue region the only cell on the blue region that contains loop is the digit one so now i have to exit this region immediately and i'm going to have to exit it into orange and now the puzzle is broken why is the puzzle broken it's because every region in this puzzle um the loop enters every region and exits it exactly once so if we think about what that means that means that the loop can only cut the border of any region we draw exactly twice there's going to be one entrance and one exit however we define them and we've just drawn an entrance here or an exit doesn't matter which one it is and an entrance here and an exit here so now the loop has to entirely sit within the 43 region and that's going to be a big problem for all the other regions which now don't have any loop in them so that's not right so this seems to be important because now that's right that's a two i've got it so i've got a digit in a pistomarphel within 10 minutes this is very unusual um so yeah this must be a two because we know there's only one digit in this nine cell region that doesn't have loop on it and by the secret we knew it was a 2 so there's a 2 in the top left corner and we know that every other cell in orange is on the loop and that means that's on the loop and if that's on the loop it's a corner so that's forced and now this we can't go in here ever again we can't go into this cell because if we do whoa i'll have to take two cells in the loop in blue and there's only one cell in the in in the loop in blue and in fact i would have got another digit because this digit in purple must be one because it's on the loop and that's the last time we can go into purple wherever purple goes uh right hang on let's just so we can sort of mark this off as unenterable we can what do i do now we can i don't see what to do um maybe i've got to use this one somehow so the problem with the one is i don't know which of these cells is purple i know both of them can't be purple because if both of them were purple the loop would have to end here and that's not creating a loop it's creating a line so one of these is is unpurpled and can't be that's interesting i'm going to say that one of these one of these is purple and one of these is another color that is not orange and the reason i'm saying that is that imagine we did try and make this orange and this purple well now we know that loop must exit purple it must therefore enter orange and again i've got to close the loop because orange has been entered and exited which is not going to work so this square and this square are some combination of purple and a new color but i don't right i mean that's still helpful because that means that orange must cohere an orange doesn't have the same clue as a 23 so orange must extend down so blue must go here this needs a new color we'll make this uh what color should we make this that's not going to clash gray maybe so blue must come here now so now the loop yeah yeah now the loop must stay in orange until until the end of orange it cannot leave orange because it must take all eight cells in orange wherever they live before it exits orange because otherwise there will be a re-entry into orange and this is not space and astrophysics so it's the sudoku version they're off okay so now now which of these that's the question isn't it which of these is is the real purple which because whichever one is the real purple is not the next loop segment cell so the loop is either going to come down here in which case this will be green and this will be purple purple will have to go there and there which would push orange here or whoops i don't go away look away why would it go away um or what was the alternative oh this is purple and this is orange and no this is then green and then green has to get out so green would come here but that looks more complicated because now green ah right no there is something here right let me let me talk you through this because this is interesting um so the thing i was in fact let's do let's do this longhand let's firstly consider whether purple is in this square and let's do this slowly so if if this is the purple and this is the new color so the loop must continue out of purple down the left hand side of the grid then purple still needs to grow to be nine cells large which means purple must come here and here and this is the cell i want us to focus on this one i'll give it a yellow flash so we have to have purple here and therefore orange is going to be pushed here but what happens if the loop does not do this well in that case if the loop does if the loop doesn't drop down here that's because so if the loop comes this way that's because purple is extended downwards that's the other alternative now if purple extends downwards this is the green cell but this is the start of a new region so green must come to here and this is where it gets very interesting because the next question we need to ask is where does the third green cell live and is it in particular in the two and it's not is it it can't be in the two because that would be saying there is exactly one cell in green that's in the loop and you can see here we can't close the loop here so we're going to have to take two cells at least in green so this cannot be green but that means that's green so we've now identified that this is either green or purple but it's certainly not orange so now we can get rid of all this we know that these are still they still have the options of green or orange we don't know where the loop goes um but we do know that this cell is green or orange and therefore sorry not green or orange i can't speak green or purple and therefore this square is orange which means that square's gray which means that square's blue and that means we have to extend the loop again to here and that means what does that mean um i don't know so we've got the loop going over here well i want the small point is i can't i can't leave orange yet can i have to take all eight cells in orange so this 23 is never visited by the loop because if the loop goes there it's going to have to take two cells in blue at the top and that won't work how on earth do we do this then none of hmm none of those cells can be the one in blue i know that's not true that can be ah that's not true sorry i was i was just wondering there about how i could put one in the top row now it's not possible for these four squares to be ones that is true because if that's a one it's visited by the loop and there's no way of not taking a second blue because once the loop once we go up there we've got a turn and we're going to take a second blue cell which we couldn't do but this one this one here is different because if that's a one and if this is some other color let's make that yellow then the loop can enter uh the top row and turn there oh actually i'm not actually maybe that's not right because now what's this what's this this this mustn't be blue so it would need to be gray and that's going to make a very small blue region ah okay so maybe this can't be maybe this can't be a one there's something weird going on in the top row regarding one is that is that is that does that logic continue to apply no it probably doesn't actually what about if that was a blue one if that was a blue one and then this was some new color then blue could escape down here and we'd be entering blue and just clipping it there like that so so maybe this can't be a one a blue one but this could be a blue one um right sorry this is all this is all conjecture anyway um we have hit a bit of an impasse in this part of the grid haven't we we need to well we probably need to work out which way round this goes that's the concern isn't it maybe i shouldn't have stopped where i did so i stopped here because i could see that this was going to push the orange but maybe i shouldn't have done that maybe i should have tried to go further so let's let me think about this so let's try this again then which way do i think it's going to break the fastest i have not got a clue um [Music] we're going to go with extending the loop i don't know but i've got to make a choice right let's make that one um we'll make this one green so that means this one is purple now if this is the case with the loop must exit purple so it must come to green and purple must continue to grow so that becomes purple that becomes purple because we can't take purple which is a one clue into a two clued region so green comes down to there now green absolutely could join the two at least i think it can oh no no hang on we get into trouble again don't we because we have because we have to exit purple the loop has to continue down which means this cell is is in green obviously but if we now join green up here make this green then this can't move because this would well and it would have to be a two because there's only gonna be one cell in the region with the two clue that's in the loop so in fact green would have to go down there like that oh no maybe it could come to the six it's all getting very complicated that's quite interesting actually green can't go to the six in this case because how could it that's very interesting i'm very suspicious about that because if this is green we know that the loop is taking these two cells at least in green so green we need to make these two cells or a third cell perhaps add up to six but you can't make a domino add up to six without a one and a two and you can't make a triomino add up to six without a one and a two so the trial note would have to be one two three a domino would have to be one five or two four so this is broke well no it's not broken it's not broken it always saying is that this is not possible to be green so green has to turn two three ah right that this is broken for another reason okay so i think we do break it this way round because because what this tetromino of green has to reach a clue cell because every every digit every cell in the grid is in one of these clues one of these nine cell regions now the only one i think this can reach is a straight line to the 29 and that does not look to me very profitable for the bottom of this grid where i've now got to fill 27 cells with clues that could come from here and here and here that cannot be possible i'm not even sure i can reach this cell one two three four five six seven eight oh we can just reach it but then how do i reach that one i can't there's no way there's no way this way or maybe we can prove this a different way actually because now we'd have a two region here so let's just have a think about this let's make this red so this would have to come out here this would have to come out here what would happen next this the orange needs to grow so that would come to here the purple would come to here now the red is blocked off yeah okay you can see it you can you can take your choice about how you disprove this variant i the way i saw it very quickly was just saying the bottom of the grid has too much white space in it but if you actually try and force the top of the grid to work you can see that we're we're running into problems with we we're penning in regions before they've reached size nine and this right this is important i think because now we have categorically proved which way round the these two cells are we have proved that this was not the green one so this is the green one which means this is the purple one and now we know that the loop cannot go into the purple because it's a one clue which means that the loop must turn which means that the loop now must turn down so greed yeah green has to grow so that's got to be green now this square i think we proved this is where the loop goes next or was it where or were we proving that no maybe no no i'm not sure that's true i think we proved this was either green or purple which suggests it's now green yes okay that does make sense this can't be green can it because i think we did this logic before if this is green we should have cells summing to two on the on the path in green and these two cells cannot sum to two so that is not green so this is green this is a new color which we shall make maybe we'll risk red because the orange might not touch it and now we can have purple has got to come down here i love this sort of thing that's got to be red that's got to be green this has got to be orange this has got to be gray this has got to be blue oh okay now oh no oh yeah no this is very interesting right so this square cannot be visited by the loop this one here because if i do take the loop down this would be a two but then we have to get out of it immediately so we can't turn right and we can't turn left or south because we've already visited the purple region once and we can't visit it again so the loop must continue there oh dear and then then what does it do the answer to that is i don't know oh that was so lovely though we sort of got on a right run going up making the staircase up up to the top right of the grid so can the loop turn down there that would be a two but yeah that could work because this could be a new region here because purple could dip down here um right ah but i can extend the loop because the loop still needs to wend its merry way along orange so far orange has got seven cells in it so we still need two more orange cells still doesn't look to me very easy to put a one in the top of this grid um ah right right look at this cell how could this be gray that's my question how could that be gray i don't think it can be gray for a rather beautiful reason which is if it's gray what what are we gonna do with blue blue's only got six cells it needs three more so it's gonna have to be those three and now where are we gonna put one in the blue and you can't put it anywhere it's so beautiful isn't it it's so beautiful this is classic pistomaphel so you can't put one anywhere because if you put the one here you now can't put a one in row one at all because you can't repeat a one in a region so that's no good so you're gonna have to put one somewhere in the top row and it's going to have to be visited by the loop the moment you visit a cell in this top row with the loop you're going to have to turn the loop into another blue cell and that won't work so that's impossible and if it's impossible that means that this square is not gray which means that cells gray now let me just pause there for a second does it mean that this is blue is that the corollary of what we've just said i think it is so if this cell was any other color let's make it green the same logic just applies doesn't it we have to finish blue like that because blue can't overlap with the 21 that's a nine cell region and again we get the same problem so yes that cell is in fact blue i'm not sure what that means quite i'm not my brain is not telling me but i've now turned gray downwards so i can turn orange downwards i can turn green downwards i can turn red downwards i can turn purple downwards now this sells a new region because it can't overlap with the one so those two cells will make these blue again on the basis it would be highly strange if these blue regions met up with each other so that we went we made the staircase go up we've now made the staircase come down uh we can extend orange oh right now now now we return to the question of whether this square can be the two clue in red and the answer is no because if i go in there what's my next move you'll have to return to green which means that green's had an entry an exit and a re-entry which is not allowed so we've got to stay in green we can't close the loop yet we've got to continue uh i don't know tempted to come back to this cell though the reason is i'm i'm wondering where we put the one in blue if this is the last ever blue cell in this in this column if if blue ends here then i have to do those two as blue and aren't i in exactly the same position i was when i tried to make this the blue region i.e where do we put 1 in blue again you can't put it anywhere if you put it here you can't put a 1 in the top row if you don't put it here the one that has to be visited by the loop will need a second cell in blue which is impossible so blue does not end here which means blue must extend down again and what did we get now we get do we get the staircase again so we've got to keep going down here which means that becomes purple now this thing and the bottom has become very although we can get extra cells on it it's got to come to here now purple four five six seven purple's finished four five six seven it's got it can only take those two cells so blue must come here red must come here green must come here one two three four five six seven eight green needs to get a number in it so creep goes there that's the ninth green orange oh orange is finished i've got nine orange cells so orange must drop down there as its final cell it can't close look because we must be able to put some loop for example in blue in the bottom it's got a six clue so we've got to turn there so i still can't i can't exit green at this point can i because again i'm going to have run into the problems with this 2 clue so probably oh no no no no look look look you can't even put a two there in red if you do what do you do with the loop now if it goes through here it's got to go back into purple again and it's not allowed to so that so the loop must stay in green again but green is finished as if green is finished right right that's the seven nine pair that is so beautiful good grief how do we know this is a seven nine pair well it's because we know that green is finished by the time it reaches this 29 it's got all nine of its cells and therefore the cells on on green that are not on the loop sum to 16 because we've got 29 on the loop and so 16 45 minus 29 is 16 we cannot do that in one cell so we must have two cells off the loop and that's the most we can have because the loop has had to come to this cell two cells different digits heading up to 16 must be a seven nine pair so now the loop must turn into red well we know red is a two clue now it must leave red again ah but here is where it's gonna get tricky one two three four purple purple is finished so this cell doesn't have to be well it could be it could be blue or it could be it could be a new color but okay so i don't think we know where the loop whether the loop goes that way or that way i know it doesn't go this way right so orange is finished orange yeah orange is finished so this is this is a color we have to determine so this could be gray or it could be could it be no it can't be that one because if it's that one you're gonna cut gray off and not allow it to be nine cells but it might be able to be this one because if those three are the same that does leave the gray with an escape valve look ah no it doesn't right here's something interesting this square let's make this purple on the basis i don't think it's ever going to meet that purple at least not in this example if this if this cell here was in the same region as this cell now look at what happens to gray gray is only five cells large so it has to come to the here and it has to take two more cells but look this 21 has to get out somehow it's only it's only got six cells there in the top of the grid so where are we going to try and take that this the eighth and ninth cell in grey if we come into column 9 we're cutting off the 21s escape valve which we cannot do and we can't take two more cells without coming into the ninth column so this is wrong and that means um that that cell is not in that region and we know it's not green or orange it can't be blue blue can't get there no blue's only got one more cell to take it can't be that one so this cell is gray which is a lot of logic for not proving very much at all well we do know we've now got to stay in grey to get pick up 23 so we can't just exit grey i don't know quite how this works now so this one i'm going to make red and hope these reds never meet this one i'm going to make purple or yellow do you think maybe yellow we've not had a yellow yet although yellow is probably going to be a bit close to green hmm okay so how do we do this i've got to take one more cell in blue and i've got to make sure i put a a i was going to say a blue one in the top in the top row but i'm not sure it necessarily is blue i think it can be blue if this was the one if that's the one then can the loop not do that and no actually that doesn't work ah okay okay so this is tricky though this is tricky so let's look at this if this was the blue one the final cell in blue then we have to ask what color this is i think i think this is the critical question and i think the only answer to that is red because if this skull was yellow yellow would have to take something like these cells and red couldn't reach a count of 5 of 9 and neither actually could gray so this cell would have to be red but this is a problem because now in order to fulfill me meeting this or taking a loop cell here i enter and exit red now having entered and exited red i cannot leave again so i'm going to have to close the loop and never never make never meet my friends on the loop over there so this doesn't work i think there's some general thing that i've missed in this top row i think i could have deduced this right really a long time ago um so so all right okay i'm not even sure i'm saying very much here i'm saying that the one in the top row is not blue that's what i'm saying and it must therefore one of those two cells must be a one and probably i think be red so the red one is in one of those two cells and that means we need to ask the question ah got it right so now i want to ask the question where does one go in blue and that is an interesting question because it can't go in those cells it could go here and i think it will go here it can't go here because there's a one there if the if the ninth blue cell is here again it still can't have a one in it now the last blue cell could be there in theory but it can't actually because gray could never grow gray would be penned in and would only have to take however many cells that is seven i think so in for uh the way to see this perhaps more easily assistant is to notice this cell must be gray and probably one two three four five six seven and that cell must be gray this one might have to be gray we can't take gray into the oh no grace oh okay so great grey could go here or here for its ninth cell but now yeah let's come back to blue we've now worked out the only possible cell in this puzzle that can take the the blue one is there and that is amazing because now look that means that this is on the loop but no other blue cell is we've now created a tunnel of one not a tunnel of love a tunnel of one a tunnel of love by the way one of the great songs by dire straits and the alchemy version is incredible right anyway that's distracted me right now look at gray now where we've got to connect this and this without leaving gray oh bobbins right we've got to come down there but i was going to say it's got to close there but it could go there if gray extends can we resolve that don't know um sorry now i can't quite tell how to do that if if it did wiggle if it did a jiggle like that five six we'd have six loop cells adding up to 23 so the three none loop cells in gray would add up to 22 and that's possible we know one of them would be a nine okay so maybe what we've got to do is extend red then because i can see that red is now penned in by this gray so yeah so all of this down the right hand side has got to be red to get red out in fact red must come there in fact now yellow's got to grow and now look we need to take a ninth blue cell which is one of these which means the maximum number of cells red takes at the top of the grid is five six seven eight so red must come down there yellow must come down here we've entered red here we can't re-enter gray so surely surely to get out of the top right of the grid we've got to continue in red don't we because we can't ever go in gray again so the only way out is down here i think but then we could probably go into yellow so we've got to so that loop must take that that configuration that's red in fact one way to think about this is the ninth column blue has only got one more cell to take gray has only got one more cell to take so that could be grey that could be blue but anyway anywhere you do it those two cells are red so now red has reached a size of eight ohs now i think i might have made a mistake i'm worried about this cell was i justified in putting this cell in as red because i i thought about blue having to take one of these but i didn't consider whether grey had to it's definitely true that blue has to take one of those so the maximum you could put there is five yeah i know it is true isn't it so it does have to come down here the point is it might have to come further okay that's fair enough if that's gray and that's blue then you've got to take one more red okay uh okay oh but ah yeah here's something interesting so the 21 clue whether this jiggles that way or whether it does that it's at least five cells of redness without including the red one because the one in the top right is red it's not blue so i've got to make five digits add up to i've got to make at least five digits i suppose i could do that but i think that's going to be too many because i've got to make at least five digits add up to 21 without using a one unless i do it like that in which case i've got seven cells adding up to 21 which is ridiculous the triangular number 7 is 28. so it is going to be 5. it's going to be 5 cells it's either going to do this or it's going to do that and well 2 plus 3 plus four plus five plus six is twenty so that's impossible so it's going to be two plus three plus four plus five plus seven is the only way of doing it so that means this cell and these three cells and one of these three cells have to be a two three four five seven quintuple and that doesn't doesn't do anything oh well um oh no it does it does do something it means that we can't take any more cells in red so one of these is red but that means this cell is not this cell is red but it's not on the loop so the loop must turn so loop now enters yellow where it must stay in yellow until it reaches a count of 31 so it's got to drop down even if this is yellow it can't be visited by because then it then the loop couldn't couldn't take 31's worth of cells in yellow so the loop comes down here it's still got to take at least two more cells in yellow four stars out of been going five minutes i don't think i've been that slow have i um it's gonna be another movie if if i can even solve it i've got all my purple oh oh no bobbins okay i was just wondering where i was going to put one in orange but i can i think put it there uh it can't obviously be here or here because of sudoku i've only got two ones in the grid but i i do know a little bit about ones oh dear okay so we've got to purple is finished maybe i've got to decide which way red goes how many cells have i got in blue i have got seven so i'm allowed two more cells in blue so blue can never reach that cell so yeah okay that does it doesn't it right okay so now let's think about red well re no let's think about loop let's think about loop so the question i want to ask is does the loop do that and the answer must be no mustn't it and that's because if the loop does do this this cell must not be red axiomatically because we've fulfilled the red clue already so it must be another color we know it can't be blue because blue only has two more cells to go so it would have to actually be yellow but if this is yellow then the loops the loop never ever visits blue because we must stay in yellow and go up here and however this closes we're going to have a loop in the top bit of the grid and never visit blue so that doesn't work so the loop does not turn right that's the point so the loop must drop down now that's therefore got to be blue i want to say because it can't be yellow for exactly the same reasons this couldn't be yellow if it was looped this the next cell on the loop is not yellow so it its only other option is to be blue so that that's perhaps a different way of saying the same thing so now right this is very interesting this is so clever as well look so now where does the loop go next does the loop come into row nine that's the question we should ask i think because the answer is no because if it does how do i ever fulfill the sixth clue either either this is blue and there are three cells in blue which would have to be a one two three triple which is impossible or this is not blue in which case these two cells have to add up to six and they can't be two four and it can't be one five that does not work so we cannot visit the bottom of the grid with the loop and the loop must turn ah now that means that means red in turn must grow so red comes here red cannot really go into the loop so red extends again that means yellow comes down here one two three four five six seven eight the red has to grow again so it has to go there so that's the ninth red cell so with the loop can't go back in here anymore so the loop must stay out of red and go across here oh right this is this is so clever honestly i do not know fist my fell as usual how you even begin to set these things it's just nuts blue is not finished blue needs another cell so how do we ever make this blue if we make this blue we've got loads of problems because blue is finished and these two cells would have to add up to six which would require double three but also this would be a different thing and blue would be entered and re-entered twice which is not allowed so that is not blue so that's blue and therefore this domino adds up to six which means it means this digit is low because that we can't put 1 or 2 there so this is a 4 or a five this is a one or a two blue is finished so this is not blue so it must be yellow yellow has now got oh yeah this is interesting right yellow has now got seven cells in it and we've got to put 31 on the loop so if the loop if the loop deviates at all from just closing here then we're going to have more than seven cells on the loop because if for example we did that we've got nine cells on the loop yeah these both have to be yellow we'll have all nine cells on the loop in yellow and this should be a 45 so the loop must simply close and we've got to have two cells off the loop in yellow that add up to 14 so we're looking at either five nine or six eight how many we've got right and we've got eight cells in red so the bottom of this cell in the bottom right that must be yellow can't can't be reached by red so this square is either a 5 9 or 6 8. uh now what do we do i've very nearly got the loop built and i've got to i've got to put one more cell in gray and i think the two options are these two i've got a bit no one more cell in yellow the two options are those two i'm going to put one more cell in blue and one more cell in red and every one of those has at least two options i fear the red might have three options this one this one or this one so how do we do this then i don't see what to do um oh i can do sudoku okay when stuck always think about sudoku where do i put three in blue it must go there so perhaps sudoku is what we need to think about two two in purple is a bit restricted 2 in purple be very restricted if that was a 4-2 pair uh okay hang on a minute um so in blue these four cells here are the same as those four cells by the sort of law of leftovers in the sense that these digits whatever they are have to appear in blue so they have to be those digits but i know that the cells in the 31 cage that don't that are not on the loop add up to 14. so i want to say now that this cell it could be this it could be that one is that true though if that and that are the same then i have to put nine in one of these and then i can't leave nine off the loop isn't that a paradox i think it is so does this have to be a nine is that the point so what i'm thinking is in order for this not to be a nine it must be one of those three cells which the only one it could be is a five so these would be five but now nine has to go in there and 9 is on the loop in the 31 region which means the two cells that are off the loop should be 6 and 8 but we'd have one of them being 5 that doesn't work so that is a 9 which corresponds to that these two cells are the same as these two cells and this is so clever this is so clever because now what is the nature of these two cells we know that the other digit missing of the of the loop in yellow is five so we can't have five here so that can't be five one well this can't be five one because it would put five one there so this must be four two and that must be two four and five in yellow is either here or here nine in red has to be somewhere and it's not there so nine in red is in one of those two cells yes and i know what these four cells are i know what they are because i know they are not 5 because 5 is off the loop in the 31 region so these are 1 6 7 8 because we've already got 2 3 and 4 and 9 in yellow already so this cell is not seven which means seven is in one of ah no yeah it does mean seven is in one of those three because seven can't even be here because this is a one six seven eight quadruple this is not seven so is this what we have to do do we have to turn our attention to sudoku in order to finish the loop that's very surprising um and worrying um [Music] goodness only no oh hang on i said something about if that's two four didn't i yes okay where does two go in purple yes okay that gets me a digit that's a two so we should ask now where two goes in green maybe one of three positions i want to say can we do better than that the answer is i don't know i don't know um wow uh i can place nine in purple because of this nine 9 9 so 9 must go there so perhaps 9 is now restricted in red yes it is red 9 is restricted in red this cell can't be nine because of this nine that nine rules out that one this seven nine rules out that one so that's nine so nines are now looking a bit more profitable so nine in orange is now not in any of those cells or here so nine is in one of three places i think in um in orange wow uh oh please please get something done simon um wow i have no i really do not know where to look here this is not straightforward is it i thought that the i don't know i thought the later stages of the puzzle would lighten up a bit but i'm not seeing anything clever here at all can we okay i do not know i don't know where to look even um maybe i've got to stay on the digits i've got lots of i've got four twos in the grid which is nearly interesting but unfortunately i don't think it's interesting enough for me to get excited about it is that really true the answer is it appears to be they're all such strange shapes as well i keep thinking i can see various you know little tricks that we might be able to do and then i sort of spot something else that says no that trick doesn't work so it looks to me like two might be restricted in the gray region but then you remember you don't even know what the gray region looks like actually because we've only got some cells in it there's still there's still more to be to be done with grey and that's really annoying uh so oh goodness me where on earth do we look then we should look for maybe i've got to keep track more diligently on the totals i've got 29 there 31 there i still got to put this 5 into one of these cells don't i i don't really know how to label that um i've got two i've got the two that's correct six is correct the one is correct the 43 is correct the one is correct oh no maybe it's not that actually the 23 on the 21 we've talked about already ah there's a small point there isn't there this digit has to appear somewhere in column one so doesn't that digit have to be the same as that digit oh that's it right yeah okay yes so so the thing to think about is where this digit appears in column one not column one column nine and it can't repeat in red and it can't be nine so it must be there and it must not be red so its only option is to be yellow so now that we know is there for a 5 because we know the 31 needs 14 off the loop so that's a 5 9 that's a 5. none of those are five so now this cell must now be gray mustn't it because it can't we've completed yellow it can't be green green is done so that's gray i still don't know which of these works for being ah i haven't put two in blue yet where's the two in blue oh we don't know i don't believe it i don't believe it we don't know where it goes because we don't know whether this is blue or not i suppose we know one of those two cells is two because of this two here we can't put two in any of those so one of these is the blue two but we don't know which one ah good grief right this is really complicated right now though look at columns uh seven and eight in the puzzle i've got a two in this domino and a two in this domino so they are the two twos we're going to find in column seven and eight we can't have any more twos or there will be a third two and that would be bad due to the rules of sudoku so none of those grey cells can be a two but this two and this two are telling us none of those cells can be a two so that is a two in grey which just means those are not two and seems to place a two in green uh now what does that mean so now this is not a two how many twos have we got we've got five six seven there should be two more one of which is well that's not a two yes okay so we know that there was a two in this two three four five seven quintuple that we found well because we know that whichever one of these is two is the blue two it is not the red two this can't be a two this can't be a two that couldn't be that couldn't be a red two because that would prevent us from putting a two in blue so that must be a red two so now i should have eight twos and there should be one two that i've not placed one tooth oh now i've got oh no i've got seven twos i've got seven twos and i've got the blue two up here in one of these two and a two down there and now we have to think again and okay so can we now conclude oh yes i can ahahaha right now the gray how does the gray close because if the grey loops the loop like that now there are three cells in grey off the loop which have to add up to 22 because we'd have 23 on the loop 45 minus 23 of 3 is 22 one of those three cells is a two so the other two cells would have to add up to 20 and that's impossible so that doesn't work so the loop closes there we've nearly done the loop now we're very close to doing the loop i think i will do a loop the loop if we manage to get the loop done so now right here is something a little bit interesting here is something a little bit interesting these cells now add up to 23. but unless i'm mistaken there has to be a one in one of those cells by sudoku i seem to have one's pencil mark here in orange i've got a one here and i've got a one six seven eight quad there so one is on one is in one of these three cells in fact and that means the other three cells on this string some to 22 so they must include a nine so there is a nine in this string of cells which means that cell is a seven that cell is a nine now let's return to this three cells that sum to 22 that can't use seven must be one well must be five eight nine so i now know what that string of digits is that is a one five eight nine quadruple and that's not one or five that's not one that seems to have all the options in the world that's not nine uh now this column look has not got four and six in it which is very annoying indeed um right so now this 23 region has not got three four six and seven in it i'm gonna pencil out that and get all good lift on myself because i haven't got anything better to do that's not six or seven so that's just three or four that's not four okay that doesn't go anywhere either um that was nearly exciting wasn't it that was nearly exciting so uh okay so we've got these nines aren't quite aligning are they we've got these nines all being pencil marked in the grid ah okay there's a small point there in column four i think yeah okay where does the nine go in column four now this nine rules out those this nine rules have that one this nine rules out that one that nine rules out that one i mean there are various other ways of saying that by normal sudoku but definitely those are not nines that means the nine is in one of those cells where it's meeting its friend the nine that we need to put into red over here so this is an x-wing on nines so we're either gonna have a nine here and here but we're gonna have a nine here and here so that means that this cell in particular and this cell cannot be nine so we've got nines in those cells ah ah right this is beautiful okay i'm gonna tell you something else interesting now which is that that is not a nine because if that was a nine i'd have to put nine there in orange so this would be a nine in red remember red needs a nine so you'd have nines in these two positions and now you can't put a nine in blue because you can't put a nine up there and you can't put a nine here so that's impossible so 9 the 9 must be here in red and the 9 must be here in blue and that means that must be a 9 in orange and this must be a one and that feels like progress because now the two in blue gets placed this is exciting now because that finishes red it finishes blue well the one in the top row now has to go here because we know that's a red one this is not one this is not nine this is not nine so that's a one five eight triple this is a nine this was a nine this was a one so this is not one this is not one there's a five eight pair so this is a one that feels like it might matter but i can't quite see how to make it stick i've got two or three or four here that's just three or four by sudoku can't be two so two in this column is now sort of a hidden single i think it can only go at the bottom of the grid which is weird but it's weird but welcome so that's a two that's a four these are not fours three six seven so this is a four in grey that means that bounces back there and becomes a three this is not four anymore good grief okay um i mean this is genuinely f i still ah i was about to say i still haven't done the loop i have now done the loop because the loop cannot go through a nine we work that out we know that the loop cells to add to 21 have to be on a three two three four five seven quintuple so this is well that's just three four or seven now unfortunately all of those options seem to be available but now at least i know these squares are a six eight pair which is very interesting and does nothing and gosh we're up to 78 minutes of video um yeah this is not easy though uh please tell me studies i have done the loop i'm doing a metaphorical or an imaginary loop the loop in my mind now the thought of doing the loop um but i am very much unclear how many ones have we got in the grid now several i've got five ones is there any hope that we can do better than that the answer seems to be yes where does one go in green this one rules out those so that's a one so now i've got now i've got six ones so i need three more and they're all down in the bottom sort of bottom left of the grid aren't they i think although hang on oh no that's not one oh so the there's a one in one of those two as well which i hadn't noticed so one yeah one in red is placed it can only go there so now i've got this sort of diagonal arrangement of ones i've not put one in blue oh this one is giving me the one here i see so one in blue now must be done yes it goes there there we go we've done all the ones so we've done all the ones have we done all the twos uh yes have we done all the threes no we have not threes are actually looking very difficult um i've done all the nines i seem to have a lot of nine yeah i've done all the nines i've got a six eight pair in row in row six that i haven't noticed before so i've got to put three four and five into those three cells that's not three that's not four okay i can do a little bit better than that by looking at row seven actually yeah look at row seven now these cells here have to contain four and five in this row don't they because these can't be four or five they aren't four or five so there's a four and a five in in these cells the four in fact must be in one of two positions but i think the five can be in all three so the four and the five in red are in those strings so they're not there so that's a three that's a five that's a four doesn't do very much apparently oh are you rotten thing you rotten thing no wow wow just wow it still is being very recalcitrant right five must be in this domino in purple by sudoku how many fives have we got not many really not many five in orange is not there and not here so five oh yeah that's quite interesting so five in orange is in one of those so that's an eight and that's a five so eight in orange is now in one of three places which doesn't even give us a pencil mark you know or pencil mark elimination anywhere else so how many fives have we got now we i added to my quota of fives by grand total of one that's no longer a five oh we already knew that that's just got four or six in it five is in one of two places five has been one of two places there five is in one of two places there so the fives are sort of dotted around being unhelpful in a variety of locations okay five in the bottom row is in this domino oh that's right okay that is interesting that is interesting so five in the bottom row i think is in this domino now that seems to coincide with where i've got fives in orange look let's just double check that pencil mark that does look correct so that means that we can't have any more fives in columns three and four so that cannot be a five and if that can't be a five the five in red seems to have to be there that of course does absolutely nothing again i don't believe it okay okay sorry i thought that was going to be helpful but no uh we're almost i'm almost at the point where i'm just gonna have to pencil mark everything and pray fives fives what about fives then in books in the top blue box can we do anything with that yes yes yes the x swing rules out this cell five rules out that one five rules out that one so it has to go there now what does that do so i've now got six fives plus the x swing yes so this oh this five is doing that five okay fine and i'm just left with the x swing but at least we got another digit that's definitely good in my book so three is now one of those two cells in purple so oh we've already done three in red so that's not useful um oh goodness me okay so where on earth do we look now maybe column one we need sixes sevens and eights i can see that so let's do that do we get any elimination no it appears sixes sevens and eights are very under well or underrepresented in the actual big digits of this puzzle three four six and eight into these squares right let's look at green then we need threes fours sixes and eights see what we can eliminate we can eliminate eight from this one we can eliminate four from this one we can eliminate nothing or four again from that one and no oh come on uh no i don't see an elimination from this one oh good grief okay seven okay i know that's no good either oh there is a small point where does uh eight eight in row row four has to be in one of those cells so that's not able to be eight so this is down to just three four six right okay is that a weird x-wingy thing threes in green are in those cells threes in purple are in those cells so they are aligning and that means three in orange can't be here or here or here or here by this three so i'm going to claim three in orange is there which means that's not a three and that's not a three which means i've now got to put six seven and eight again into column whatever this one is column this one and that's not resolved there's now definitely a three in this domino ah no ah nearly threes are very nearly restricted here i was getting excited about these cells oh that actually no this is good this is good right threes are in these cells and threes are in these cells in green so that's the two threes we need for rows four and five so that can't also be a three so that's a seven that's a four and that's a 3 which makes this seem to have to be a 6 which gives me a 3 8 pair here which means that should be a 4 by sudoku three eight so this square should be known that's a six can't be seven can't be three so that's a seven and that now has to be a three that's sudoku um and i need a 7 and 8 into this column which of course doesn't want to resolve itself this square is no longer a 7. but i do know these digits now they are four sixes and eights aren't they so i'm definitely pencil marking those and hoping for a miracle four six eight triple so these two squares are five and seven and that is not resolved this 4 is looking at that cell ok so that seems to have to be a 4. again six sevens and eights isn't it it's always six sevens and eight so that's six seven or eight that needs to be seven or eight there's a seven eight pair in red which makes this square a six ah so that means that's an eight and that's a six and that's a seven and that's an eight and that's a something a six wow okay that feels like it might make a difference to something yeah this four is giving me a six at the top so that gets me an eight here and a seven here and an eight here and a seven here through the medium of redness and an eight here and a six here wow and there's something there a seven and a six here so some of these columns are getting finished this is getting interesting now isn't it uh five and eight are a pair there i think it's a complete blue i don't think they're resolved but i could well be wrong and that digit's known that looks like it's got to be a four to make that top row work so that's four and that's eight so that's eight and that's five and that's five and that's seven now this column needs a six in it these squares need to be a three seven pair so i want to say this is seven and this is three and that's three and that's eight and i'm just going to pause for a moment and try and detect whether this looks wrong or i think i can't see me nothing is flashing at me saying repeat it thank goodness for that wow 90 minutes 90 minutes door-to-door that was brutally hard how can that be four stars i mean admittedly perhaps there was no individually monstrous step there but i mean that was that was so interesting to build the regions you couldn't finish it i don't think without then doing some quite hard irregular sudoku there was almost certainly better ways of me doing that i'm i'm not sure what i missed on the irregular sudoku but irregular sudoku's i find it tricky anyway um but loved it as always from the great man fist my fell take yet another bow and um yeah i'll look forward with trepidation to your what's it touchy slitherlink country road hybrid puzzle which i will i will look at once i've had a cold towel around my head for some considerable hours thanks for watching we'll be back later with another edition of cracking the cryptic [Music] you

Channel: Cracking The Cryptic

Views: 64,345

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Id: aG2qk0fROjk

Length: 91min 51sec (5511 seconds)

Published: Mon Apr 11 2022