100%-Rated Sudokus Are Pretty Clever!!

[00:00:11][music] Hello and welcome to Saturday's edition of Cracking the Cryptic where a couple of weeks ago I did Loopins Loop number four on the channel and today I'm going to try Loopin's loop number five. This is an incredible incredibly popular series um with good reason. I I think it sort of picked up the mantle of Marty Sears uh Rat Rum puzzles with many people comparing um the styles of these two series favor favorably. This one's by um well it's it's always by Rab Rabberon Rab 3on. Um and the last few of these have had a 100% rating. I don't know. Oh, let me just check. Can you see that on the screen? I don't know. Maybe.

[00:00:58]No. But it does have a 100% rating. And let me tell you, that is a difficult thing to maintain over any length of time. And this has done that. Um, and they have they come with backstories as well. Let's see what the backstory is to this one. Professor Lupin escaped the collapsing city with the aliens greatest secrets. Or so he thought. But when he tried to open the files, they refused to open. The data was real. Oh, why why is my phone buzzing at me? That's uh nothing important. Um, sorry. Well, the data was real, but incomplete. Then Lupin noticed the pattern. The aliens had been several steps ahead. They had split split their secrets into fragments and scattered them across Earth, hiding each piece in a different country, inside ordinary places no one would ever suspect. The first fragment was already in Lupin's hands. The rest were scattered in secret locations, each protected by strange alien markers and blocked paths. Alone, each fragment was useless. Together, they would reveal what the aliens were truly planning.

[00:02:04]There was only one problem. Once the first fragment was activated, the others would stay readable for a limited time before sealing forever. To access the data, finding every fragment was not enough. Lupin had to find them in one correct loop order, a single route through every piece, beginning and ending, where the first fragment was found. Only then would the aliens full secret unlock. The countdown has begun.

[00:02:29]So, that's what we've got to do today.

[00:02:32]Um, and you can see there are all sorts of flags in this one. I am slightly worried that I don't know what some of these flags are. Mark is a total expert on flags, by the way. You could ask him, you know, what's the flag of Togo? And he would be able to tell you. I am less um I never I've never learned my flags.

[00:02:54]So, there are some flags here that I'm looking at with with more than a little um is this to do with the World Cup?

[00:03:06]Isn't that Ghana? Isn't that Ghana?

[00:03:08]Aren't they called the Black Stars?

[00:03:12]I I'm not sure. Maybe the ah Argentina, Brazil.

[00:03:26]H I don't know actually. I'm not sure.

[00:03:29]There are some I definitely don't know.

[00:03:30]Um anyway, we'll read the rules of this one in a moment or two's time. Now, I don't have much to tell you about today.

[00:03:36]I'm going to um just recommend if you've been following the channel for any amount of time, please do like, please do subscribe. Um, we've been most grateful for that. We, um, over on Patreon, which is sort of our Sudoku club attached to the channel, it's a couple of bucks a month to join us over there. And we have got some absolutely wonderful extra content, including, of course, our monthly competition. Um, which this month, uh, is Sandra and Nala and Pantheras. Um, let me see if I've got the There we go. Detective pets. Um, so there's some fog of war, Japanese sums, puzzles, lots of things to delight you, and you still got a couple of days left um to enter that if you'd like to win the chance to come on to the channel and uh appear in a video. Um, now I've also got birthdays to do. Let me look at my list.

[00:04:26]Greg, Greg, you turned 45 uh a few days ago, actually on the 13th of July. Um, I know this because we had an email from Mel.

[00:04:37]You're over there in Sydney, Australia.

[00:04:39]Um, and apparently the two of you, I don't know what to make of this. The two of you have a special hand gesture for when I say, "Let's get cracking." I hope it's not a rude hand gesture.

[00:04:54]I don't know what that hand gesture could be, but the mind mind boggles.

[00:04:58]Anyway, Greg, uh, it's a it's a propitious birthday, isn't it? A 45th birthday. I hope you have a great one.

[00:05:03]Um, Mel, I know was planning to make you some exceptionally well iced chocolate cake, so enjoy that. Um, next, Samantha, I'm late with this one as well. July the 12th, it was the It was your birthday, Samantha. You turned 31. I know this because your friend Victoria wrote to me and told me you've been watching for 4 years with your cats. Is it Monster and Ticky? So, I hope they enjoy the channel, too. And Samantha, many happy returns. I hope your birthday was great.

[00:05:32]And then finally, TA turned 23. I know this because your partner, Rico, over there in Ukraine wrote to me, uh, and told me that you often fall asleep when the video comes on. Um, Rico says, "You're an amazingly joyful person, Tanya, um, who brings so much sun into the world, and he loves you more and more each day." Which is quite a nice message to get, isn't it? Any day really, but particularly around your birthday. So Tanya, many happy returns.

[00:06:04]I hope there was also some chocolate cake. That's all the news. Shall we have a go? Loopin loop five count. Count countercount. I didn't read the title, I don't think, last time. Counter count.

[00:06:16]Um, what do we have to do if we're going to finish this correctly? We have got normal Sudoku rules applying. So we're going to put the digits one to nine once each and every row, every column. Oops.

[00:06:27]And every 3x3 box. A greater than sign points to the smaller number. So there are I think two of those. So that's bigger than that and that is bigger than that.

[00:06:39]Draw a single route for the airplane that travels orthogonally from cell to cell. So let's make sure we understand what that means. An orthogonal movement between two cells is a movement in a north, south, east or west direction. It is not this. That is a diagonal movement and that is not an orthogonal movement.

[00:06:56]So don't make any um diagonal movements for your aeroplane.

[00:07:02]Um draw a single route. The root never branches, crosses, or overlaps and eventually closes into a loop. So it could be ah no it couldn't because I did a diagonal. I mean it could be something like that.

[00:07:18]Now now the rules will explain why it couldn't have been that.

[00:07:24]The route starts at the airplane, passes through every country, and returns to its starting point. Thick black borders represent heavy turbulence that the airplane cannot cross. So, we can't do that or that. Oh, whoopsie. Or that.

[00:07:43]If a digit n appears on the root, then the digit n appears exactly n times in cells not on the root. Oh, that's strange. Right. So, if if there's a five on the route, if the digit n appears on the route, so the airplane is on the route, um, then the digit five appears five times not on the route. So it' only be on the route four times. That's a very peculiar rule.

[00:08:18]If okay, if two countries are directly connected by the root, their digits differ by the length of the segment connecting them.

[00:08:32]Wow. Okay.

[00:08:36]If two countries are direct. Okay. All right. I I think I do understand that.

[00:08:41]If a country So let's let's just do a sketch of that. So if they were joined together is that so the digits different different by three I think is how that reads.

[00:08:57]Um if a country and the airplane Oh. Oh hang on. So this rule is not for the airplane. Hang on. If if a country and the Oh, sorry. So that that's wrong what I just did cuz that's not joining two countries. So that is probably true.

[00:09:15]That's probably difference by three. But where the where where the aeroplane is involved, there's a different rule.

[00:09:23]If a country and the airplane are directly connected by the route, the digit in the airplane equals the length of the segment connecting them. So if that was a segment, the digit in the airplane.

[00:09:45]Ah, hang on. There's another rule here.

[00:09:47]It says, "Note segment lengths include both include both end points.

[00:09:54]Two objects are directly connected by the route if no other object lies between them along the route." Good grief. Right. So if this was if this was the journey the airplane took the length of that segment I think is five cuz it includes the two end points. So those digits oh hang on no and this hang on hang on this has got the aeroplane on it the digit in the aeroplane.

[00:10:21]So that that digit would be a five because that is the length of the segment. But if we change that and we say instead that these two are connected, say they're connected like that, then actually neither of these would be a five because that segment is five in length, which means these digits have to be five apart. And so if if this was a five, how could this be five different from it? It couldn't be because 10 is not a Sudoku number and zero is not a Sudoku number. So is this could be something like one and six I think. Um that is how that is all the rules. So there are quite a few things to keep track of there. Often this is the often that's the most difficult thing with these puzzles that are very involved.

[00:11:13]It's actually keeping the rules clear in your head. But do have a go. 100% ratings are they do not grow on trees.

[00:11:20]The way to play is to click the link under the video as usual. But now I get to play. Let's get cracking.

[00:11:29]So So does the plane start from sort of Gatwick or Heathrow? Is that what we're seeing by it being so close to the uh UK?

[00:11:43]I don't really know how to start this.

[00:11:45]Let me just Sorry. Having said that, the idea is to keep the um to keep the rules in your head. We've got this weird rule that if a digit n appears on the root, it appears n times not on the root. So nine never appears on the root.

[00:12:11]Is that right? Yeah, that's right.

[00:12:13]Because if n if nine was on the route so say oh let the countries are all visited so let's make Germany nine if Germany was nine then it's visited by the loop because it's a country and yet the this would be saying there were nine nines not on the loop. Well there aren't 10 nines in sudoku. There's only nine.

[00:12:42]So once one of them is on the loop, you can't have nine not on the loop. That is a paradox. So perhaps what we do to start is we know all the nines in the grid are not are not on the loop. So the nine in that box is in one of those cells.

[00:13:03]The nine in this box, it's not worth I'm not pencil marking seven cells.

[00:13:13]Okay. But we do have to visit all the countries, don't we? Visits every country, right? So, we've got to go to this country. Is that Jamaica? It might not be, but it I think it might be Jamaica. So, if that's Jamaica, that's visited by the loop. So, we've got to go in and out cuz it's a loop, right? So, this is not a nine because that would put nine on the loop.

[00:13:38]Now that is that Colia maybe. [laughter] What's that?

[00:13:50][clears throat] Oh, I I see. I No, I By the way, when I say I see, I do not know what that country is, by the way. I don't know what flag that is. But um these are in sort of the western, you know, this is South America, Central America.

[00:14:08]Um and then sort of Caribbean.

[00:14:12]Oh, America, Turkey.

[00:14:23]Oh, so if that Okay, if that was Ghana, Turkey slightly north and to the right of it or to the east of it, Germany. So that's okay. So, what is that country?

[00:14:38]That is to the east of Germany. And I mean, I know that's not the Polish flag.

[00:14:48]What country is that?

[00:14:55]I don't know. I'm sorry. I don't know that one. I don't know that one. That looks like Sweden.

[00:15:04]Iceland, Norway.

[00:15:09]Those two I don't know. And that one down there, I don't know. And that one, I don't know. Bobbins. Oh well, never mind. Anyway, so there's some sort of approximate um map of the world going on, isn't there? And how do I so what do I so I know that any digit so if I put eight on on the path then then eight would eight would appear on the path once wouldn't it because there would be eight eights not on the path right so the the maximum length of the path in this puzzle is 36 we can say that straight straight away because what what we're counting if you if you think about eight um sorry I'm not I haven't explained that very well but I I can see that quite clearly so imagine you put one on on the path that's saying there is one one not on the path so there are eight ones on the path there are nine of each digit so the maximum number of any digit that of the the most prolific number that could appear on the path would be if there is a one on the path because if there is a one on the path there are eight ones on the path. If there is a two on the path there are seven twos on the path because there are only two twos missing from the path. So in order to work out the maximum length of the path we're adding 8 to 7 to 6 to 5 etc. And the triangle number for 8 is 36. So the path is maximum 36 which actually is not a very long path because if you think about I mean the perimeter of a sedoku is only 32 isn't it? Have I missed I might be wrong. I think it is I think the whole perimeter is a 32.

[00:17:05]Two nines plus two sevens. 9 seven to connect them.

[00:17:14]It's 32 and we've got 36 to play with. But we're going to have to do a lot of wiggles here, aren't we? Right. What I'm going to do is I'm going to work out what the minimum length of path is.

[00:17:28]Um, and hope it's equal to 36. 1 2 3 4 5 6.

[00:17:35]See, it wouldn't matter. You could go there, there, or there. There. There. It would be a free choice. 1 2 3 4 5 6 7 8 9 10.

[00:17:49]We've got to pick this one up, haven't we? Before we go up there, I think.

[00:17:55]Yeah. 11 12 13 14 15 16 17 18 19 20 21 22 again doesn't matter. So 24 25 26 27 28 29 30 31 32 33 34 34 is the minimum.

[00:18:17]That's not what we wanted.

[00:18:20]So I think some some approximation to that is the minimum with possibly there are there are different ways like you could go rather than go up like that you could go like that there and then but if you're as efficient as you can be that I think is is pretty good.

[00:18:43]But unfortunately well this this is going to help isn't it? Because now we know the minimum length of the path is 34. So we can't miss a one out, for example. Cuz if you miss a one off the path, the maximum length drops to 36 - 8, which is 28. So that's not going to work.

[00:19:05]So there's all sorts of digits that now must be on the path.

[00:19:11]Ones, twos, threes, fours, fives. If six was missing from the path, uh 15.

[00:19:24]No, no, no, no, no. Careful, Simon.

[00:19:27]Careful. If six is missing from the path gosh, this is if No, no, let's do it the other way. If six is on the path, it contributes three, doesn't it, to the path length? Because there are six sixes off the path.

[00:19:49]So if six is off the path, then the maximum length of the path drops from 36 to 33, which won't work. So there is a six on the path, but seven might not be on the 7 and 8 are the critical ones that might not have to be on the path.

[00:20:08]Okay. All right. But how about that then? Is it possible to adjust the length of this minimum path by one? I bet it isn't because because you can't do a diagonal movement.

[00:20:22]Um so now so how do I sorry how do I explain that? What I'm saying there is that if I if I introduce any inefficiency to this model which is efficient I mean obviously we could make different choices about how we get from here to here say we could do that we could do that but but what but in making those choices I I've never taken too many cells the minimum is 1 2 3 and whether I go that way or this way I've taken three. But if I decide to be inefficient, I could go I could go that way as well.

[00:21:03]Um by say overr running, I could go 1 2 3 4 5. Well, that differs from three by two.

[00:21:13]This is so because what you can't do is go 1 2 3 and then a diagonal movement.

[00:21:21]So yeah, so this is interesting because basically what we can now say is either seven is missing from the path and this this and therefore this is the perfect path which is length 34 and it's got the maximum number of ones 2 3's fours 5 sixes eight on it or it wiggles.

[00:21:52]And if it did wiggle, let's say it did that, then it has to be 36 because it can't be longer than 36. And it would have all of the numbers from 1 to 8 on it. And it would have 8 1's, 7, 6, etc., all the way down to 18. So, the question the question that we're left with is, do you wiggle?

[00:22:20]Well, do you? [laughter] Um, I personally don't think I do wiggle. I'm not very good at wiggling. Um, I am notoriously [clears throat] terrible at dancing.

[00:22:33]Like, like truly terrible.

[00:22:36]Um, so I mean, how on earth [laughter] are you meant to work this out? Do you have to do I have to use these other rules?

[00:22:47]What were the other rules? There was something about the aeroplane, wasn't there? So the aeroplane, the airplane, whatever's in the aeroplane is the length of the segment joining it.

[00:23:04]So it probably is going to do that is it? Oh, and that would be a two then because the segments include the end points because because one thing that's clear from that is because it's a loop the length of the segment that goes so say say we were going from the United Kingdom to the airplane that's a two-length segment which requires us to put two into the airplane. But now the airplane can't go off to the United States because that wouldn't be a two movement. So, so the length of the final segment is the same as the length of the first segment, if you see what I mean. Which makes me think it is going to be those two. I mean, it may maybe it doesn't have to be, but it feels like it does.

[00:23:53]I bet that's a two.

[00:23:57]Um yeah and what was the other thing? The the other thing was yeah see we might be able to gro something about how that the path has to approximately move like this which is going to mean these digits are very different by a set number like that segment. If if if if it does go from if we go from America to Jamaica, one, two, three, three. I have to do count. I do have to count the ends, don't I? 1 2 3 4 5 6 7. That is a length seven segment.

[00:24:39]So yeah, that would have to be 1 and 8. It would have to because you can't we can't use nine on the path. So neither of the um neither of the countries can be nine and we need digits that are seven different. So they'd have to be one and eight.

[00:24:59]Yeah, I dimly start to see why there's there's a constraint operating.

[00:25:05]Oh no, no, that's it. I've got it. I've got it. Right. Um right. Oh, this is beautiful and and actually quite straightforward. Um, I'm just going to change the color there cuz I couldn't see that red thing against the background. I don't like that color either. Um, what color should we have for our path?

[00:25:28]Gray. Doesn't seem appropriate at all, does it?

[00:25:33]Well, okay. No, maybe I'll just change that color. I'll change I'll change the color of the of the path or the loop to green. And then I'll make the path purple because that one appealed to me. Um, no.

[00:25:50]But here is my thought. Such as it is.

[00:25:56]My efficient path through this box was this.

[00:26:04]Now that doesn't work.

[00:26:08]That cannot work because that's a whole series of length two segments.

[00:26:16]And I think you'd have to have nine as one of those digits, wouldn't you? Cuz cuz if you're saying, and I think we are saying that those digits are two apart, they all share the same parity and they're all different. And that is possible. Well, you can do that in Sudoku with five different digits by using 1 3 5 7 and 9. But that's the only way to do it. But 9 is not on the path.

[00:26:43]So that doesn't work. So that means that we cannot be efficient. The p the loop cannot be efficient through box 7. And if it can't be efficient, we can't do a 34length path. So we must be doing a 36 length path because we can't do a single we can't do a single cell wiggle.

[00:27:10]So now this is this is wonderful actually and actually this isn't this isn't quite as difficult. Last one of these I did I found very hard but this one this one I'm finding more intuitive. Right.

[00:27:25]Um, what I want to do is look at Colombia, I think, because I know that the loop goes into Colombia because of the um the turbulence. So, it goes into So, Jamaica is a corner of the loop and I'm in Colombia.

[00:27:42]Now, if I go from here, I don't know what this country is. Oh dear.

[00:27:49]If I go into this country from Colombia, how do I get to Argentina? I can't go there next because I can never get to Argentina without the loop having to turn back on itself. So I have to go to Argentina and then I have to go to Brazil and that creates the problem which I so this is impossible.

[00:28:12]So what we've got to not do is go from Colombia to there. So that is forced.

[00:28:17]Then we've got to go to Argentina.

[00:28:22]Well, then we have to take this cell.

[00:28:24]Otherwise, we we're going to close the loop. So, we've got to go there. Now, this is a corner. We mustn't close the loop. So, that so that is how we move through box seven. Now, this should be no more that we're going to have to count this very carefully. I don't want this to of course cause too much inefficiency cuz I've only got two two sort of degrees of freedom if you like from my 34 to 36 length loop. So, so if I went the quick way, my box seven path would have been 1 2 3 4 5 6.

[00:29:12]Well, and then I'd have had a choice, but it would have been six to get to Brazil.

[00:29:18]And now it's 1 2 3 4 five six seven eight. Get to Brazil. That's fine.

[00:29:24]That's fine. That's two difference which I can c I can cope with. I can cope with that by by forcing all digits other than nine to be on the path. And therefore these cells are not nine. They are on the path. So that's nine. Now now I'm going to change my color scheme again.

[00:29:44]So I'm going to mark that with an gray.

[00:29:47]We can see we have to move orthogonally.

[00:29:48]So, we have to go up and [clears throat] we have to be super efficient through all of our other movements.

[00:29:58]Um, so we've got to go there, we've got to go there. Now, I now know we're going to Turkey and Ghana, but I don't know how we're doing it. There's there's a variety of ways. But then from Ghana, we're going to go to the UK.

[00:30:14]I don't know how to do this. Um, and then from the UK, we have to be efficient. So, we've got to go to the airplane to Germany.

[00:30:25]We can't wiggle anymore. We've got to be super efficient every time we can. Then we're going to um Iceland, but I don't I don't know whether we're doing that or that. We're doing one of them and then we're being super efficient. And then I don't know how there's so many ways to do this movement. We could do it in a whole variety of ways, but we're doing one of them. We're going from Norway to the United States [snorts] and then from the United States to Jamaica now.

[00:31:07]Okay.

[00:31:10]So, [snorts] oh, I tell you what that. So, this is this this is a two then cuz that's a length two segment and that's a length two segment. So, the airplane is a two.

[00:31:26]Now, this is good actually. This is I'm going to start here then. I was going to go down there, but I'm going to start there because this digit.

[00:31:39]H, no, hang on. I need to check this.

[00:31:41]I'm not sure if the airplane if a digit I can't remember how it works. If the airplane is joined to a country, what you put the country, what digit you put in the country?

[00:31:59]um it passes through every country returns to the starting point.

[00:32:06]If two countries are directly connected by their route, if a country and an aeroplane are directly connected by the route, the digit on the airplane equals the length of the segment connecting them.

[00:32:24]So, so where the airplane is connected to a country, I don't think I do know what this is, do I?

[00:32:37]I was hoping I was going to be able to say it's that's a length. Hang on. If two countries are directly connected by the root, their digits differ by the length of the segment connecting them.

[00:32:56]If a country and the airplane two objects are directly connected on a loop if no other object. [snorts] So I don't think these these are connected directly on the loop because the airplane's in the middle. But I don't actually think the rules cater for what this this digit is. I might be wrong, but I don't think they do.

[00:33:28]So I think all we actually know is that well actually we do know some things.

[00:33:32]Germany and whatever this country is differ in value by three.

[00:33:39]This country and that one differ in value by three. These two differ in value by two.

[00:33:45]um these two differ in value by three.

[00:33:48]These two differ in value by three. To get from here to here, I don't know what the route will be, but it must be efficient. So that's a five length segment. So these differ in value by five, which means neither is a five. And then to get from this, so maybe we do have to start down here to get from here to here, we have to be efficient. So 1 2 3 4 5 6 7 and various routes are available to do that. We could go straight down like that. But the point is that they have to be a 1/8 pair because neither can be nine and they must be seven different.

[00:34:24]And then these two digits are two apart. So this is three or six.

[00:34:32]Now Colombia and Argentina are three. That's that's a three length segment. So this is six or three. It's not nine. It could have from six. It could have gone to nine, but it can't by sedoku. So that's a three six pair. And then this we're retaining the par, aren't we?

[00:34:54]See? So these are two different.

[00:34:58]So if this was 1 3 6 this digit is 4 or 8 and then oh no this is complicated and then that's a three difference back to this one but with this being something depending on what this is I don't know how to do this without really pencil marking it.

[00:35:34]Okay. But Brazil, whatever the difference is to Brazil, it's the same difference to this one.

[00:35:43][snorts] Whatever country this is, I apologize if it's a famous country and I should know it. I apologize to any country. Um, but what I'm thinking is what we can't do is say this was four.

[00:35:56]There's a three difference to this one.

[00:35:58]So, we could go seven, but then that would be impossible because then you'd have to go three different from seven.

[00:36:04]You can't you or you can't go four. In fact, four is just impossible, isn't it?

[00:36:09]Yeah, eight's possible, but four isn't.

[00:36:11]Four isn't possible because you go one and then that's four again. Or you go seven and then that's four again because there isn't enough space. But if this is eight, you can do it cuz then you can go 52.

[00:36:24]So that is not four.

[00:36:28]But that does that mean this is six? No, it doesn't because because I only pencil mark this on the basis this was six. I didn't do the pencil marks if this was three. Okay. Well, let's keep going. So if this is eight, this is five, this is two, and that's four. That is how it would have to look. And that looks very plausible, doesn't it? But I haven't catered for this situation.

[00:36:56]And that's the situation where this starts with eight goes to six goes to three.

[00:37:04]Now this can't be five.

[00:37:08]Oh no, it could uh No, it can't. If this was five, which it could be by par this is three different from five. So say it's two, but then it has to bounce back up again. So that can't be five. It's going to have to be one.

[00:37:23]And then this would be a four. And this would be a seven. And that would work.

[00:37:28]And then this would be Oh, it couldn't be nine. That would be five.

[00:37:34]So that's the other way it works is with a one here. This is four or five. This is 2 or 7. And this is five or four.

[00:37:46]And unfortunately, I'm afraid, unless I am missing a very obvious point, I don't know how we're going to resolve that.

[00:38:06]Oh, no. I do actually. That's brilliant.

[00:38:09]That is absolutely brilliant. Right.

[00:38:13]It's simple and I've made a mess of it, but but it is simple, right? Um, these two, this is where I should have started.

[00:38:23]These two include an eight on the path.

[00:38:26]Well, then we know eight eights are off the path. So, this could never be an eight. That has to be a one because otherwise there are two eights on the path. So, that is an eight. That is a one. This is a six. This is a three. and it's going to go and there. So that's going to be 475.

[00:38:45]Okay, that's much better and much more understandable than me doing a whole load of pencil marks. Now those are a 5 seven pair by Sudoku and we get an extra two here. Look, I love this. This is fantastic puzzle.

[00:39:00]Now what's that? Because we know getting from Turkey, no, sorry, getting from Ghana to Turkey is going to be a length four segment. 1 2 yeah a length four segment of some description. I have no idea how it's going to happen but it's a length four segment. So this is one or nine and it's not nine. So it's one. And now getting from Turkey to the UK is a four segment. So this is back to being a five again.

[00:39:30]Two three four.

[00:39:33]And now uh and then it then it breaks down, doesn't it?

[00:39:37]because I don't know how to do the I don't know how to do the Germany one.

[00:39:42]We probably are we can work backwards from America because that we know is a length five segment of whatever description. So this has to be a six [clears throat] which means and then there's a length three segment. So this is three or nine.

[00:39:57]Well, I know it's not nine because nine isn't never on the path. And then it's a length three segment which has got to go back to six again. Zero is not on the path.

[00:40:07]And then it's a this digit is a four or an eight. Well, it's not eight, is it?

[00:40:12]That's exactly what we've just worked out down there. So, this is a four. Now, this is a length three segment. So, this is one or seven.

[00:40:22]And then this is a length three segment.

[00:40:25]So, if this was seven, this would be four. If this was one, oh, it's all that's always four. It's always four. But that one I don't know.

[00:40:37]Bizarrely, there's that. The only country I don't know is whether that's one or seven. That makes that's very strange and slightly worrying.

[00:40:49]Okay. Don't know how to deal with that.

[00:40:51]So somehow or other from here, right? What's going to So what determines everything now? is going to be making sure we have the right number of digits on the path. So, wow. So, nine is in one of those three.

[00:41:14]It can never be on the path.

[00:41:19]Eight has appeared on the path. So, is never on the path in any box other than this one.

[00:41:28]Seven is on the path in box seven. Ah, that's it. That's how you get this one, right?

[00:41:36]Seven is on the path in box seven and it's on the path again in box eight.

[00:41:41]There are only there are seven sevens not on the path. So, we can't have any more sevens on the path otherwise there'd be 10 sevens in the puzzle. So, that is a one. So, that I see. And now we get some sedoku. So, ones is probably where I should have started. Where are Yeah.

[00:41:57]Nearly. Yes. Okay.

[00:42:02]How many?

[00:42:07]Oh, no. It doesn't work actually. No, it Oh, I see. No, it does. Oh, this is lovely. I've got a lovely point. Right.

[00:42:14]I was going to start talking about ones and how they all had to be on the path when I realized that no, the rule means one one is not on the path. And then I realized I knew where that was. Where is the one one in this puzzle that is not on the path? And the answer is it must be one of these because if you pencil mark ones in box six, sorry, box four here, they're over on this side. Now I can't wrinkle over here. If I rinky dink and wriggle over there, this is an inefficiency between Jamaica and America. I've got to be moving always along this segment either north or east until I get there. I can never go west because if I go west, young man, um, it's an inefficiency. My my loop length cannot afford. So, this is the only one that is not on the path. So, now here's a question. Where is the one in box eight?

[00:43:10]I know it's in one of those three. These two are impossible because they're not efficient from here. We can never go south from here. We've got to go here somehow.

[00:43:21]Um, not that. Not that one. But so the one has to be there.

[00:43:27]And then I've got a lot of difficulty believing this can be a one cuz that's an inefficiency between Norway and America if I end up going there. So I've got to go there. That's got to be on the path.

[00:43:41]So, I'm going to go there.

[00:43:48]And now this is a Oh, that's okay.

[00:43:51]That's okay. I was going to say this is a one. It's on the path, but it can be cuz I'm going from Turkey to the United Kingdom and I'm going through that cell now. So, we're not doing that. Oh, I see. And that gets me this.

[00:44:04]So, that they're all the ones.

[00:44:08]Let's give them a color.

[00:44:13]Now, now I don't know what to do.

[00:44:29]Six [clears throat] by Sudoku. I can place in box one.

[00:44:37]I can.

[00:44:40]No, I can't place it in box eight.

[00:44:46]It's probably twos, isn't it? So, twos.

[00:44:51]There are exactly two twos not on the path. Do I know where they are?

[00:45:06]I I think I know the two in box nine is not on the path. I I don't know where it is, but the two in box 9 is in one of those cells and none of those can be on the path because I'm going directly from Ghana to Turkey somehow.

[00:45:23]This can't be a two by Sudoku and then I'm going straight from there to there.

[00:45:28]So I'm no I'm not taking any more cell n to put it a different way none of those cells are on the path and one of those cells in box 9 is a two. So that's one two that's not on the path. Ah yeah this is oh no cuz that could be oh that's near it's nearly it. I was going to say the two in box six can't be on the path.

[00:45:50]But what if that was a two? Then I could put that on the path. bother.

[00:45:58]Okay. So, that's not that's not the correct way to do it.

[00:46:03]Sorry about that. Okay. All the sixes in the puzzle that are on the path have been positioned already on the path. So, all the sixes in the puzzle are not on the path. All the other sixes.

[00:46:22]I've got to go through this cell. So, I've got to be efficient. I've got to go down to it. And then then it's a case of whether I do that or that.

[00:46:35]Um, if that was a nine, it would be useful because then I couldn't go to it and that path would have to do that. But, but again, there's no reason that has to be the case.

[00:46:50]Um, wow.

[00:46:55]So, if it's not ones or twos, I've got a few fours dotted around the piece. I've got three fours on the path.

[00:47:08]And I'm meant to have five [snorts] fours on the path altogether because there are four fours not on the path.

[00:47:13]So, I've got two more fours to put on the path.

[00:47:22]Golly gosh, I don't know what to do then. Okay, let's What about this row? 3 4 8 9. Maybe we can do some sedoku on Whoopsie. Whoopsie. Maybe we can do some sodoku. Three is not there. So, no. So, four. Yeah, four. Three and four come out of this cuz if this was four, that would have needed to be three. Six comes out of there.

[00:47:46]Four comes out of here. Aha, that's Oh dear, I've missed pencil marked it. Nine is a digit here. Three, four, eight, nine.

[00:47:59]Oh, bobbins. Four, three. Okay, let's four. Yeah, I see that cell is the one that's under pressure. It sees three and four. So, it is eight or nine, but the inequality helps us for once. 8 9 3. Now four. Now that four is definitely off the loop. That three is definitely off the loop.

[00:48:28]Um that eight's definite. Oh, I see. All right. Let's come back to the earlier thought then. That is a nine. That is definitely a nine. So I can't go to it.

[00:48:41]And I've got to be efficient in going from Ghana to Turkey. So the path is fixed there. [snorts] And that's very helpful because now to get from Turkey to the UK, I have to go north. I can't rinky dink at all. So I have to do that cuz I need to use the one. So that's done. That's actually done quite a lot of path.

[00:49:04]And didn't we did we say something about six having been used on the path enough times? Yes. Yes, we did. Look, I've had three sixes on the path. That's all the sixes I'm ever allowed on the path because there must be six sixes off the path. So, this is a six. Oh, I thought that was going to I thought I was going to get this digit, but apparently I'm not.

[00:49:25]So, it's a six. I get to place. Six can't be on the path. I get to place it.

[00:49:33]So, sixes are quite interesting. Now, let's give those their own color. I've got sort of an arrangement here of sixes.

[00:49:42]So, one of those is a six. And so, if Yeah, that's beautiful. This is so beautiful, right? What would happen if this was a six?

[00:49:53]Well, then how could I be efficient in going from Jamaica to the USA? I'd have to go round the edge of it. And I can't wrinkle dink that much. I can't have a westward step in going from here to here or I can't my 36 cell path would be too long. So I have to put the sixes there which means that is the forced. Now to get up to here I've got to go north to get I've got to go south from America. That that's been available forever that step. I just didn't see it.

[00:50:26]And then I don't know how that closes.

[00:50:33]So I've very nearly done a lot. Oh, the one here has to be on the path.

[00:50:39]So that's forced that segment.

[00:50:43]So I'm really close to having the whole loop figured out now. I've got this closure and this closure. I think everything else is done. So I've got to just make sure I populate everything with the correct digits. Where's eight? In box eight, the answer is there. So these digits are now known. They're 2, three, four.

[00:51:06]So this digit is five or seven by Sudoku.

[00:51:11]This is not two.

[00:51:19]Now there's a three in one of those cells.

[00:51:27]Uh, I thought I was going to get a four, but no, I'm not. Eight. Let's give eight its own color. Make those lime, shall we?

[00:51:36]We know there's no more eights on the path.

[00:51:42]Um, bobbins.

[00:51:52]So sorry if this is totally obvious. It probably is a bit obvious actually. I think if you if you have the thought to to attack the right digit, it will be very clear what you have to do.

[00:52:13]It's probably to do with sevens and eights, isn't it? I've had all my sevens and eights in these boxes that can ever be on the path. I've had two sevens and one eight. So in any other box, the sevens and the eights must live off the path.

[00:52:32]So that can't be a seven or an eight.

[00:52:37]So is this a 7, eight? Yeah, I think I think that has to be a four, which is the most peculiar deduction. Yeah.

[00:52:44][snorts] Okay. The way to get that is to look at column six and pencil mark it to death.

[00:52:51]And if you pencil mark it to death, you get 3 4 7 8. But you know this can't be seven or eight by by the fact we've had all the sevens and eights we can ever put on it. And then therefore it becomes a four.

[00:53:03]And now this is a four by Sudoku and four is on the path here. So how many fours have we now put on the path?

[00:53:13]One.

[00:53:16]2 3 4 five. We can't have any more on. They've got to be four. Fours off the path. So, these can't be four. So, this has got to be three. This has got to be two. That's got to be four.

[00:53:30]Or is in one of those two cells.

[00:53:37]Okay. Well, that's still a win for the goodies. Okay. These don't include the three anymore. So that is a 78 pair.

[00:53:48]Um these digits are what? 2 3 5 9. So that digit is three or nine. But it could be on the path if the path goes into a three.

[00:54:03]Three is no. It's a little bit restricted in box one and a little bit restricted in box two. as a result.

[00:54:19]But okay.

[00:54:21]Okay. What about threes then?

[00:54:27]Because in terms of the puzzle, there are three threes that are not on the path and six threes that are on the path. Well, that is a three that's definitely off the path. Let's double click all the threes. This one is definitely a naughty.

[00:54:43]Now, the three in box five, I haven't got a clue where it goes, but it's not on the path because the path is going from here to here, and it's got to do it with elacrity. It can't dip down here. So, there is a three in one of those cells that's off the path. There's a three there that's off the path now.

[00:55:10]Oh, it's close, isn't it? It really is.

[00:55:13]I mean, if see, if that was a three, then all other threes would be on the path.

[00:55:30]Oh, I don't know. I'm I think that's close to being a deduction.

[00:55:36]Or if that if that wasn't a three or sorry I'm jumping around a bit here trying to find some logic. What about two 2579 down here?

[00:55:57]So the two down there is definitely off the path.

[00:56:02]There can only be two twos off the path.

[00:56:08]So that ah hang on. So there's a two up here.

[00:56:18]If if two is on the path in box six, it's in one position and it's quite difficult for two to be on the path in box.

[00:56:33]It's actually actually it's impossible.

[00:56:35]That's it. That's the crucial thought.

[00:56:37]That is the crucial thought. Yeah. Where is two in box one? And the answer as usual as so often is I don't know. But it's tucked away in the in the top 2 by two and definitely not on the path. So the two twos that are not on the path are in box one and box 9. And every other box has to have a path two. So we can take that. That's definitely not two. One of these is a two and it's on the path.

[00:57:04]two two has to be here. It has to be in one of those two cells by Sudoku in this box because it's got to be pathed. So this is a two four pair. Now the two has to be on the path in box six. So I now know where that is.

[00:57:22]Two has to be on the path in box three.

[00:57:24]So I know where that is. Which place which places the two in box it's nine now. So let's let's give twos didn't have their own color which is totally remiss of me. So two aha is there and that's pathed remember.

[00:57:42]So two is two's in the corner.

[00:57:47]So let's let's re remake our twos.

[00:57:50]Actually I get all the twos. Look at that. And I get more. I have never given fours a color again. Totally remiss of me. But I've done all the fours and I've done all the twos and I I've got to make sure this two is on the path. So I've got to be efficient.

[00:58:08]I don't know which one of those. It's probably one of those has to be a three.

[00:58:12]I want Okay, I'm going to think about threes in a minute cuz I don't think you can visit.

[00:58:19]Well, I'm going to go from there to there. And in doing that, I'm either doing that or that. And I can only pick up one of the threes from that box. in that box on on that on the way. We'll do that. So, that's probably worth thinking about. Fives need their own color. We'll make those indigo.

[00:58:41]Now, um [snorts] Okay. Don't know what to do again now. Uh 57 5789 is what we need in this box. This is an appalling pencil mark I'm about to make by the way. Sorry about this.

[00:59:03]Yeah, that's really that was really a disgraceful pencil mark. There was no value extracted from that. Um nines.

[00:59:17]So the path is well I see. Yeah. Okay. I'm going to go back to my thought about threes because what what we can say is that the three in box five is not on the path because the path has to be efficient joining to these. So it's either doing that or that and efficient joining these two. So, it's either doing that or that.

[00:59:47]So, it's never go it's never getting a three in box 5. It didn't get a three in box 9. And here's the kicker.

[00:59:54]The three in box one is in one of two places. And the three in box two is in one of two places. Now, I can't get both of those threes on the path because to do that, I'd have to sort of do a diagonal move or something. I'm either doing that or that. So there's only one more three from either of these two boxes, which means every other three in the puzzle that's not in box five, box one, box two, box five, or box 9 is pathed, which means that is a three.

[01:00:26]Uh whoopsie. Now three gets orangeed, doesn't it?

[01:00:33]So So also ah this is good. Now, there has to be a three on the path, therefore in box six. And this three I've just put in limits the possible positions of threes, one of which could never be on the path. Yet, we've just said we need a three on the path. So, it's got to be there, which places a three here. That's rather pretty because now that's going to have to be a three to get on the path. Therefore, this is a nine.

[01:00:59]So, and that is pathed. And this is pathed. And that has closed everything.

[01:01:05]Whoops. No, no, no. Not that. That is how it closes.

[01:01:08]And I think we've now drawn Loopin's fifth loop completely.

[01:01:15]And the only thing beholden on us from here is to make sure I mean there's very little I mean we're going to get that digit I think just by counting digits along the path and making sure we've got enough of everything.

[01:01:32]But okay, let's think about that. 578 into column three.

[01:01:39]That's weird, isn't it? That that does I can't actually resolve that.

[01:01:46]What about those 5 7 8 9? But we can we can do some or take some care and attention with the No, we actually can't.

[01:01:56]Oh, well, that can't be seven anymore cuz it wouldn't be able to be greater than that. So, these are very big.

[01:02:05]And that digit is a se ah that digit is not right. There's an 8 n pair in this row now. So that's got to be seven.

[01:02:14]That seven is nice here. That's got to be five.

[01:02:17]Which means this is a five in the corner. That's a seven.

[01:02:22]Now those two digits now are a seven 9 pair somehow unresolved. Therefore this is a 58 pair in the row. So this is a seven or a nine by Sudoku and it's not nine. So that's seven, that's nine, that's seven.

[01:02:40]And in this column we haven't put in a something which is the technical term or a three.

[01:02:47]Oh, we could which we could have got ages ago. Sorry. Uh so this is an eight or a nine but I said and in this column we've not put in a five.

[01:02:59]And let's double click the fives and indigo them all.

[01:03:03]So this is this is an eight or a nine by Sudoku.

[01:03:09]This is 58 or nine by Sudoku.

[01:03:16]It's this digit, isn't it? We can see this. I mean, it can't be eight. We're only allowed one eight on the path. So that's five. This is eight. That's nine.

[01:03:27]So this is five. Now by Sudoku, this has become a 78 pair.

[01:03:34]Uh, which means this is a nine, which means that's a nine and that's a seven and that's a five. Keep going.

[01:03:41]That's an eight. That's an eight. That's a seven. That's an eight. That's a seven. That's a seven in the corner.

[01:03:49]This. Oh, this is an eight by Sudoku. So that's a five by Sudoku. That's a nine.

[01:03:54]98. We've done it. We've done it. But we have we haven't colored everything. So, we do need to improve. Did we never give sevens a color? That's an outrage. I'm sorry. Yellow.

[01:04:07]Nines. We did give a color. Eights we did give a color. It was Yeah, lime green. That is And I don't know.

[01:04:13]Hopefully, you can see. I'm just going to go through the loop and make sure that I'm happy it is connected. It goes there. Let's count it as well. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 3 25 35 26 27 28 29 30 31 32 33 34 35 36 and that's what we were expecting and that is I mean it had to be right it's brilliant absolutely brilliant loopins loop number five countercount I did a lot of countercounting um raberon and you should take a bow because that deserves absolutely it's 100% rated puzzle because it's fantastic. Fantastic idea. Fantastically executed and I I hope you can forgive my ignorance. If you're from any of these countries, I couldn't do I feel terrible. Um and [clears throat] um yeah, you can all you can all berate me in the comments. Let me know how you got on in the puzzle uh in the comments. I enjoy the comments, especially when they're kind. And we'll be back later with another edition of Cracking the Cryptic.