A Rather Magical Sudoku Experience

本站添加: 2026-05-17

[00:00:11][music] >> Hello, welcome back to Cracking the Cryptic. I am looking at a puzzle by Black Raven today, whose second puzzle this is apparently.

[00:00:23]Um, it's quite a complicated I don't know. Is it complicated rule set? It's an unusual rule set, let's say that. It's not that complicated. It's just um, on a different path, which is probably very inappropriate metaphor for a path puzzle. But, I'm looking forward to giving it a go and uh, first of all, I am going to tell you about our hunt this month. That is our patron reward for May. It is Spider-Man Sudoku and if you're very skilled at Sudoku, you'll be able to defeat the eight enemies of Spider-Man and save the city.

[00:00:59]Um, and we urge you to give it a try.

[00:01:02]This solution that um, if you get a correct solution, you'll be in a draw to have a collaborative video with Simon and I think you'd enjoy that if the chance came up.

[00:01:14]Um, what else is going on on the channel?

[00:01:17]Well, on Patreon, there's of course crosswords and connections and gridogram videos amongst other things. There's other Sudoku.

[00:01:25]>> [snorts] >> Um, collapse of solves, stuff like that on in our apps. The latest one is the worm, the blobs Sudoku worm. It's eclectic worm. It is really good fun. Do give it a try. We have other apps of course, including Lion Sudoku and classic Sudoku 2 and they're very good fun, too.

[00:01:47]Um, and there's merch. Marty Sears rat run merch is the latest, but there's all the slightly older caps and shirts and hoodies, etc. Do check those out.

[00:01:57]They're great fun.

[00:01:59]Um and they identify you as being a fan of the channel and we want you to do that and you want to do that, too.

[00:02:06]Right, let's have a look at Black Ravens four magic.

[00:02:10]And um I'm going to go through the rules. So, normal Sudoku rules apply.

[00:02:14]That means one to nine will go in every row, column, and three by three box.

[00:02:19]We have to draw an orthogonally connected path, so only moves vertically and horizontally.

[00:02:27]That does not branch or touch itself, not even diagonally.

[00:02:31]Oh, the path starts at um in one square and ends in the other.

[00:02:36]And it visits each box at least once.

[00:02:42]Any set of four consecutive cells on the path contains digits with different modularity when divided by four.

[00:02:50]Now, for those of us who are non-mathematicians, it then explains that in every set of four digits along the path, there is one from the set 1 5 9, one from two and six, one from three and seven, and one from four and eight.

[00:03:06]Which is like the three modular line rule, but different.

[00:03:11]Um arrow cells are off the path and count the number of path cells in the indicated direction. Circle cells are off the path and count the number of path cells in the eight cells around it.

[00:03:23]So, that is counting the number of path cells in this group.

[00:03:29]Digits on a purple line are a non-repeating consecutive sequence in any order.

[00:03:36]Box borders divide the blue line into segments with an equal sum, so those four will add up to the same as those two and those two.

[00:03:46]And digits separated by a white dot are consecutive.

[00:03:50]That's it. Give it a try. It To me with that rule set, this seems an incredibly sparsely populated grid. I'm very very impressed that we can apparently draw a four modular path through this whole puzzle with this few clues.

[00:04:08]But we will see how this works because I may have I may have underestimate I was about to say mis-underestimated as though I was George Bush. I was I probably underestimated how much some of these clues do. But I'm looking forward to finding out which ones.

[00:04:25]Right. Waffle waffle waffle, let's get cracking. Here we go.

[00:04:30]So.

[00:04:33]Right, I'm going to color those cells there on the path. Cells that are not on the path, I'm going to color yellow and we've been told that the circles and arrows are not. So the path goes through this cell.

[00:04:46]Um I know this is not much so far.

[00:04:51]The path might go through this path through the middle.

[00:05:01]Um oh, these arrows. Right, the path does go through this cell because these arrows have got to have different digits. They're in the same row. That one is counting how many path cells there are here, one, two, or three. This one can't be the same number so it must be adding that cell in. So this is two, three, or four. These are consecutive digits and this is on the path. Right, if that's on the path any cell that's not a square basically has an entry and an exit point on the path. So this one must go through those two.

[00:05:37]So the path that's where the path goes up through row five. Well Well, no. The path has to be in row five here. Now, okay. I was thinking First of all, I was thinking a shape a bit like that.

[00:05:57]Then I was thinking a shape a bit like this.

[00:06:03]Now I'm sort of thinking could use all three of these.

[00:06:10]And that might mean a shape a bit I mean I you know, I don't know exactly, but a bit like that.

[00:06:21]What about this Renban?

[00:06:30]Well, I don't know. I mean, obviously not all low digits. They can't be from 1 2 3 4 because of this too, but there's this white dot as well.

[00:06:44]I don't think the circles are any use.

[00:06:46]I'm discounting them. This is obviously somewhere south of six.

[00:06:53]Um but which of these cells are occupied? Cuz there's at least one.

[00:07:02]I don't know. Where I mean, I haven't thought about the modular rule. I haven't thought about the um the blue line rule.

[00:07:13]And these three are on the path. Okay.

[00:07:15]Okay, yes.

[00:07:20]Right. Given that this box is going to use two of the lower digits here.

[00:07:31]If this cell was on the path, what is the minimum total here?

[00:07:38]I suppose this could be one and two.

[00:07:41]Oh, hang on. Hang on.

[00:07:43]This Yeah, sorry. I'm trying to focus. Can we rule out this this cell being on the path by determining that the minimum total for these four would exceed the maximum total for a pair up here.

[00:08:04]Now, if all four cells were on the path, they would have to contain two from one of the sets that we're allowed and one from each of the other.

[00:08:20]Now, normally at an absolute minimum, you could have one, two No, they wouldn't. Sorry, that's nonsense. They'd contain all one from each of the four sets. So, normally they could be one, two, three, four. In this central box, they can't be that because of these.

[00:08:37]So, maybe one, two, five, six. That would add up to No, five would be a repeat of the one class of digit.

[00:08:51]One, two, six, seven is clearly possible. That uses all the sets. There might be a number that's a little below that. If you used two, three two, three five, six. Doesn't that use all the sets as well?

[00:09:16]Two, three, five, six adds up to 16.

[00:09:21]That's too big.

[00:09:24]Oh, that's interesting. Right.

[00:09:27]What was the other one I said? One two, six, seven. That also adds up to 16. Oh, I mean, this is pretty complicated.

[00:09:38]Right, let me try and explain why 1 2 6 7 and 2 3 5 6, I'm just going to aid memoir the sets up here.

[00:09:54]So, these are the four sets of digits we're allowed. And if that was on the path, these four sets, these four cells would need one from each of these sets.

[00:10:05]But only two of these low digits, 1 2 3 4, because two of them are going to go in these cells.

[00:10:12]So, [snorts] the minimum it could have in the two low digits here are one and two.

[00:10:18]Oh, then it would need seven and eight because it couldn't use three and four.

[00:10:23]Well, that's way too much. I will explain in a moment why on these bits of the blue line 16 is too much, but it is.

[00:10:35]So, then we have to kind of dial it back and have we couldn't have 2 3 4 5 here. Actually, we'd have to have 3 4 5 6 here.

[00:10:47]Because these have to be low and consecutive.

[00:10:56]Well, I think it always adds up to the same thing and I I finally understood it.

[00:11:01]Because if you look at that group of eight digits, two of the really low ones are in these cells.

[00:11:07]So, you can select the other two low ones, but then you have to select higher ones from this group for the other two cells if these are all on the line.

[00:11:17]And that way you're always getting these minima plus two lots of four and that always adds up to 18. That is weird. Okay, but if that was on the line, these would add up to 18. Now, we can tell that 18 is impossible in these cells. I will also tell you why 16 and 17 are impossible cuz if it was 16, that would be a 9 7 pair, but this would also be a 9 7 pair and you'd have too many sevens and nines in this row. Same applies with 17 and 9 8 as a pair. So, these have to be different pairs adding up to the same total and that maxes them at 15.

[00:12:00]And I think that proves that we cannot have four cells on the line in this path in this box at all, whether it's there or there or there.

[00:12:15]Because of these two. Yeah, I mean, it would have to be 18.

[00:12:20]So, this path passes straight through the box like that.

[00:12:27]So, that there's only three cells in the box. No. No. That's not That's not No. That is not the proof that I've just done. That is nonsen- Is that nonsense?

[00:12:41]Or is it I don't know. I'm suddenly thinking that I'm not relating No, that is not something. If the path went to that cell, that's fine cuz it's not a blue line cell.

[00:12:54]I'm adding these blues to get to this total. Oh, well, I mean, these blues maybe on Well, I do think that is not on the path. That we know.

[00:13:05]So, the path must go to that cell, not that one.

[00:13:10]That's That I have concluded.

[00:13:18]Now, even even in this world, getting these four cells to add up to a number low enough to be 15 or below is not that easy because these three have to be from different sets. This one is allowed to repeat the sets, but we're still only allowed two of these very low digits from 1 2 3 4. I'm just going to I'm sorry. I'm going to stick my aide-mémoire back in here and just think about that.

[00:13:49]15 is the maximum for this group.

[00:13:53]So, you can now have a repeat digit, but you still can't have more than two from this set because of these arrows.

[00:14:00]So, if you had one and two you have to have one from a higher set.

[00:14:10]And a repeat. So, you've still got two lots of four which is the addition to get from these digits to these digits.

[00:14:21]And you've got three different sets. So, you've got a minimum of six and another one is seven and the two lots of four.

[00:14:33]So, that's what it's got to be. You've got to have two from this minimal set, 1 5.

[00:14:40]Either then then you've got to have one from this set and one from this set and one of them is going to be low.

[00:14:49]Right.

[00:14:51]So, this line contains 1 and 5.

[00:14:56]This digit does not contain one and therefore this does not contain two.

[00:15:01]These are consecutive.

[00:15:04]If I don't put two on this line because I'm putting it in one of these arrows, they are two and three. Then this arrow is 1 4 5 6.

[00:15:18]And that adds up to too many. That adds up to 16 which busts this.

[00:15:23]Have I got that right? Why that doesn't feel like the right calculation. Yes, cuz then I'm using a digit from the 4 8 set, and I'm not meant to do that. I'm meant to use 1 and 5, a digit from 2 6, and a digit from 3 7.

[00:15:42]But these I think I have to use two. I can't use three and four cuz that would use a four. Right. So, I'm using two on this line.

[00:15:51]Not two here. That's a three. That's a four.

[00:15:55]And now I have to keep these down, but use use a third set.

[00:16:05]Right. These digits use This one is one from the one or five.

[00:16:10]Sorry, one from the one or five set because otherwise it would repeat too quickly on the modular line.

[00:16:17]These are two, the other digit from one and five, and a digit from the 3 7 set, which is now seven.

[00:16:27]So, this line adds up. It's 1 2 5 and 7.

[00:16:31]It adds up to 15.

[00:16:33]And these cells are selected from 6 7 8 9. One is a 6 9 pair, and one is a 7 8 pair, and I don't know which way around they fall.

[00:16:41]But these digits, let's get rid of the corner marks and make them central marks. These are from 1 2 5 7.

[00:16:49]This one off the line is one of the 1 2 5s. Right. That digit is four or eight because that's the next Oh, I tell you what it is. That is a definite four. If it was eight, none of these cells could be eight, but this must contain each of the digits from 6 7 8 9, and that sees them all.

[00:17:07]So, that is a four.

[00:17:10]And the next digit on this path to the south is four or eight as well.

[00:17:15]Well, it's definitely eight, whichever of those cells it's in. None of them can be four.

[00:17:21]But, I don't know which of those cells that eight is in.

[00:17:28]This is a very, very interesting puzzle already. Now, this three and this four, bam, that is coloring path cells for us.

[00:17:37]Oh, this this blooming Renban can't have one or two on it now cuz it would always need a three.

[00:17:44]So, it's either 5 6 7, 6 7 8, or 7 8 9.

[00:17:48]It's got a seven on it. That digit is not seven.

[00:17:55]That's strange.

[00:17:57]Um And let's think about the modularity of these digits, which are clearly consecutive along the path. In fact, they make these two yellow cuz the path can't branch. So, the path must go up here.

[00:18:12]Now, now this is really interesting. I was assuming this kind of path coming down south through here, up north there, south here.

[00:18:28]I'm not sure though. Why couldn't this do a U?

[00:18:32]I mean, that's the simplest type now.

[00:18:37]And maybe we could even loop around here. No, look, we can't because of this. Right.

[00:18:46]I don't know what that means. Does that mean we can't come in I don't know what it means.

[00:18:54]This digit is now four or five depending on whether that is a purple path cell or not.

[00:19:06]What are these? These are a modular distinct modular group of three.

[00:19:12]Oh, three and seven, they don't use that. So, they're from the other modular sets.

[00:19:18]One of them is from the 4 8 modular set and is not a four. One of those digits is an eight. That keeps eight off this bit of the path. Oh, sorry, off this Renban, and that must be 5 6 7. Isn't that brilliant? Now, this is one or two, and nine is definitely over here.

[00:19:34]Nine is the representative of the 9 5 1 group over here.

[00:19:38]And in those three cells, therefore, we can't put one, so that's in the middle.

[00:19:42]That is fantastic. That digit is two.

[00:19:46]That's five. That's seven. I've got digits all over my puzzle.

[00:19:52]It's crazy. Oh, this is a circle.

[00:19:55]There's Well, you know this isn't eight or nine.

[00:19:59]Because the maximum number of digits that could be on the path around that is seven. So, that digit is a six.

[00:20:10]And everything everything is working in harmony. This is beautiful, Black Raven.

[00:20:16]Oh, and these are now 9 8 2.

[00:20:21]Quoth the Raven, "Nevermore."

[00:20:26]This digit is not from the 2 6, the 4 8, or the 1 5 9 set. It's from the 3 7 set.

[00:20:34]So, it's the next digit on the path, be it there or there.

[00:20:40]Six is in one of those cells.

[00:20:49]Actually, it's really weird. I don't know the order of this path.

[00:20:56]Let's The path starts here. We'll so we'll deem that the path starts here in row nine, column nine.

[00:21:05]It either goes this way, so that 4217 is in the order of the path, and then it heads round here.

[00:21:16]Or it might go this way, so that 7124, the opposite order, is the order of the path. And then come round here. And that gives different orders for this direction, which is really strange.

[00:21:33]Also, Oh, my good Okay, I'd never thought of this. How about this path?

[00:21:40]This is perfectly legal.

[00:21:44]Okay.

[00:21:49]Now, that is 3 or 7, cuz it couldn't be any of those sums.

[00:21:54]If the next step on the path is 3 or 7, and it's here, that's a pair in the row.

[00:22:07]And that digit would be 1 or 4.

[00:22:14]I don't know what that means. Okay, I do know that the next step after this 4 on this path is going to be a 7 or 3. It's Sorry, I didn't explain earlier that the modularity along the path repeats every four set Oh, no, it's every five cells. Well, every four cells. Every four cells. So, that group includes one from 159, one from 26, one from 48.

[00:22:44]So, they're always paired or quartered with a 37 cell. On that side, clearly.

[00:22:51]And on this side, there must be a 37 cell. If it's there, it's a 7. If it's there, it's a 3. If it's here, it's a 3, cuz this cell sees all those again.

[00:23:03]In fact, that digit can be limited already to 1 2 3 5. We know these are 1 9 6 pair and 1 7 8 pair.

[00:23:18]Okay, I don't really know what's going on now.

[00:23:27]I mean, that's this is great progress, but I don't know what to do next. I do feel like I'm beginning to sort of gradually understand how we step through this puzzle and how all the clues work together, but I might have reached a bit of a sticking point, if I'm honest.

[00:23:49]That type of No, that type of digit is going to replicate there. So, it's either from 2 6 4 8 or 1 5 9. I mean, that really doesn't narrow it down much, does it?

[00:24:03]I want to know what this order is.

[00:24:08]No, I don't.

[00:24:12]If this wasn't a five, it would be a four.

[00:24:23]And that would be yellow.

[00:24:26]And the path would turn there.

[00:24:33]This digit would have the same Ah, that's very different. Yeah, okay.

[00:24:39]If this digit was purple and on the path, it would have the same modularity as that one.

[00:24:53]Oh, look. That's fabulous. Right.

[00:24:56]How could these two have the same modularity?

[00:25:00]They couldn't be both eight, they couldn't be both nine.

[00:25:04]This one couldn't be seven.

[00:25:07]They would have to be a six and a two.

[00:25:09]So, it is possible, but look what happens then. This digit becomes a six, and that is not the next step along this path.

[00:25:18]So, suddenly this path, which would have a purple cell there, would have to turn up here and have a purple cell, and that's impossible cuz it's going to have to come out and connect up, and that's no good.

[00:25:30]So, the path does not turn into that cell. It goes straight on up there, and this digit's a five, which is not what I wanted to find. Four would have been more helpful giving me a five-six pair, but still that's very interesting. And also, now the path can go up here again, which is a bit of a shame. But still, that digit must replicate its set up here. If that's a two, it sees this cell and makes it a six. If it's an eight, it makes this a four. If it's a nine, this is one or five, but it couldn't be five, so it'll be one.

[00:26:07]So, we do at least limit that corner cell. Also, these are off the path now.

[00:26:15]Now, where is the other three-seven digit? It's there or there. If it's here, it's a three.

[00:26:22]That was a beautiful deduction. I mean, that has been set up absolutely gorgeously.

[00:26:31]And it was weird. It relied on having this six pencil mark. I've got so few pencil marks in the grid, you know that was deliberately relevant.

[00:26:42]Um anyway, eight and nine are up here.

[00:26:44]That's not very interesting. They're putting a few more pencil marks in the grid just to try and convince myself I'm doing something.

[00:26:52]Right, this group of three is the same as this group of three.

[00:26:58]But, it's not so easy. They could repeat as digits here.

[00:27:03]Because they don't suffer the indignity of having to be different like those two cells.

[00:27:12]Okay.

[00:27:14]Do I know the direction of the path now?

[00:27:18]No.

[00:27:19]It could still shoot up through here and come back down through here. Ah, can it Oh, I've got this six.

[00:27:32]That's going to require a lot of these cells to be populated with path. Not quite all of them, but lots of them.

[00:27:40]Okay, this digit is on the path. How do I know that? Because otherwise, if that was yellow, these would all be purple.

[00:27:50]And yet divided, and the path would diagonally touch itself. So, that's purple.

[00:27:57]Um what about this one? If that was yellow, then the path would do this.

[00:28:06]Yeah, I think that's possible.

[00:28:13]Well, although I haven't thought about the modularity of these digits.

[00:28:21]Which would be lacking a two or a six.

[00:28:27]I don't know. The modularity thing is not really very restrictive at the moment. I mean, I know we got something with it here.

[00:28:34]And we're working on something with three sevens here, but Oh, I've just had an insight. I've just had an insight. There's a There's a sort of bishop's move thing in this puzzle.

[00:28:49]Right. The path moves orthogonally, only horizontally or vertically.

[00:28:57]And that that has a very significant impact. Now we know anything about one of the digits on the path. No.

[00:29:06]Now we know about all four digits in one part of the path.

[00:29:12]What I'm going to tell you is that four and eight if we were to checkerboard the grid four and eight would always be on the same bishop's color.

[00:29:24]So, what I mean is let's highlight all the cells of one checkerboard.

[00:29:35]So, all these cells with blue inside their cell.

[00:29:40]Consider them to be one color, black or white.

[00:29:44]And four, when it's on the path will always be in these cells and eight.

[00:29:50]It mustn't be outside them because the path turns it the this path moves in even segments because there are four digits in each sort of segment. So, four repeats four and eight repeat every four or eight cells along the path.

[00:30:10]And that means they could end up in this cell but they couldn't end up in this cell from here. That can never be four or eight away because you're always making one, two, three turns or moves.

[00:30:26]Anyway, that is going to impact these.

[00:30:30]Two it's bishop's color is there.

[00:30:35]One of these is a two, but those two can't be two because two's bishop's color would would prevent any number of moves. However far you went, doesn't matter whether you went this way round to get there.

[00:30:50]You would still be making an odd number of moves by the time you got to that cell, and that's not when two and six repeat.

[00:31:00]So, they can't be two. That's two.

[00:31:03]One of these is eight and one of them is nine cuz they're from the four and one sets. That's fine.

[00:31:10]I mean, maybe maybe that is all this is going to tell me. No, it tells me more.

[00:31:14]It tells me that this is either from the four eight or the one five nine set.

[00:31:21]So, that is one eight or nine. This is either from the two six or the three seven set.

[00:31:28]I mean, that is weird, but it really does apply, I promise.

[00:31:37]Now, does this help?

[00:31:40]Cuz that would only it place this two, that's not nothing.

[00:31:49]This couldn't be six and on the path, not because of the bishop's color, but because of the actual movement from that cell.

[00:31:58]So, if this is six, it's off the path and the path goes up here through a three seven.

[00:32:05]But, if it's not six, then it can be on the path and it will be three.

[00:32:11]No, that's It's not the only way it can be not six.

[00:32:17]I was going to say, is this digit three or six, but it could be off the path and still not be six.

[00:32:25]So, I mustn't overstretch my logic.

[00:32:30]You may think I have already.

[00:32:33]Okay.

[00:32:34]We're okay. 28 minutes in. I've done stuff.

[00:32:38]I'm pleased with that bishop's move inside. Oh, this digit bishop's move from 1 5 9 4 or 8.

[00:32:48]Um Yeah, it doesn't really do anything. Oh, what does it do for these? It might tell us that these three can't all be on the path.

[00:33:05]I can't even work that out. No, it doesn't. They could all be on the path.

[00:33:11]Seven would be in the middle, I think.

[00:33:17]Oh, no, they can't all be on the path because seven and six come from the same set of 2 3 6 7 and they would both be vying for that spot.

[00:33:32]Uh I mean, is that >> [snorts] >> Yeah, that's a bit interesting. I was wondering earlier whether this cell could be yellow and then all of these would be on the path and this would be a corner.

[00:33:47]But now we know that all three of these pink cells can't be on the path, so we'd have to go up like that. Well, that does look possible.

[00:34:01]It's a very odd puzzle, this.

[00:34:05]There's a two in one of those cells.

[00:34:06]That's just Sudoku, not nothing interesting.

[00:34:13]Now, I still need to make deductions about the path.

[00:34:20]What I really want to do is find out whether we're joining from here or here because then I would know what order we're going in in terms of the actual modular sets.

[00:34:30]So, maybe it's this six that's I don't think this circle's any use.

[00:34:35]That could be two, three, four, or five.

[00:34:38]I It's just not telling me anything. So, it this circle might be telling me something.

[00:34:44]One of these three cells is yellow, and the others are all purple.

[00:34:49]I think a straight path through there is very possible.

[00:34:56]What I do know is we can't come twice into into this region.

[00:35:03]We can't do that because the path would touch diagonally.

[00:35:07]So, we can't pass twice through here. We can pass a maximum of once through there or no times.

[00:35:17]Oh, not Well, if this is a purple cell, then we definitely do pass here. And we don't do a threesome, so I mean, those three can't all be on the path. So, we must go straight down if we hit this cell.

[00:35:38]I think. Or Well, no, we could wiggle on the path.

[00:35:42]But, we would have to go both north and south. That's really strange. If this cell is on the path, we have to be going north and south through this box or through row five over here, at least.

[00:35:57]Now, if that cell is not on the path, then these are all on it.

[00:36:08]Ah.

[00:36:12]No. Yes.

[00:36:14]Yes, that is not the path because this digit would be from the two-six set.

[00:36:21]So, this digit is on the path.

[00:36:24]That would be four cells away from the two.

[00:36:28]And you'd be alternating back to the 2 6 set, and that can't be two or six, right? So, this is on the path, and in terms of its bishop's move, this is either from the 4 8 or the 1 5 9 category. So, that is a five.

[00:36:44]Wow.

[00:36:47]That's not a five now.

[00:36:50]This is on the path, and one of these cells is on, and one is off.

[00:37:02]Right. Um if this is Okay, well, if this is on the path, then it can't be from the 2 6 category. It has to be from the 3 7 category, and it would have to be three.

[00:37:17]Ooh, and that would be a seven. Um and this would be an 8 9 pair. This would be 1 2 4. There'd be a lot of Sudoku done.

[00:37:25]If this is on the path, it has to be a three.

[00:37:34]And then that direction, five to three, is the same as this direction, one to seven, and that feels like it would be right.

[00:37:47]This [snorts] would be an eight in that circumstance.

[00:37:54]>> [sighs] [snorts] >> It's so complicated.

[00:37:58]Oh, botheration. Um Right, what if this is yellow?

[00:38:08]Then this has to be Then this has to go north there, because we've worked out it must go to here.

[00:38:21]They can't all be on the path. This is the important thing. So, if that's yellow, this is on the path, and that's on the path.

[00:38:33]And that digit then is on the path, and the path then goes round here. Now, can we falsify that? 1 2 4 3 1 or 9 2 or 6 4 or 8 7 5 2 or 6. No, it seems to be all right.

[00:39:08]Okay, that was if this was yellow. So, if this was yellow, then these are both on the path.

[00:39:20]What does that do?

[00:39:23]And it sends the path Well, the trouble is I don't even know what direction the path is going.

[00:39:33]Wow. I mean, I'm just completely at sea now.

[00:39:38]Oh, well, I'm not. I mean, you know, I've made good progress. I'm I'm getting an understanding of the puzzle. I'm just not sure what the next step is. That's all. That's all.

[00:39:49]That's a perfectly reasonable position to be in.

[00:39:53]I must not panic.

[00:39:57]Just because I don't know. I really want to know where this continues. Does it go north or south? It's just such a huge difference.

[00:40:05]If it goes south, this digit has to be a three.

[00:40:10]And that's a six, and that's seven, and this is 1 4.

[00:40:16]After the three, we'd get an eight or a nine. Then I think we would know the direction, wouldn't we?

[00:40:33]Well, from a three here, we couldn't join straight up there cuz three and seven would be too close together. So, maybe we could go round here.

[00:40:42]I don't know. I mean, why isn't this six circle helping a bit more?

[00:40:47]It's It's done a lot, to be fair, but it just hasn't done everything.

[00:40:56]Um four coming round to eight there.

[00:41:05]That would put eight here and seven here and a six-nine pair.

[00:41:10]God, you'd get a lot done. You'd get eight there, nine.

[00:41:26]This is crazy.

[00:41:29]Oh, goodness gracious.

[00:41:35]I mean, that that looks tempting because one and five are in the same category, but I don't think it's allowed at all.

[00:41:42]Because what way would the path go?

[00:41:45]It would have to go north there, and this U-bend just couldn't be on the path cuz then it would never connect up.

[00:41:57]Oh, that's okay.

[00:42:01]Something I said earlier, and I have not followed through on, is once the path touches here, it comes south from row five, and also goes north.

[00:42:14]So, the path I must either go through that cell or that cell north.

[00:42:19]And it must either come through this cell or this cell south.

[00:42:29]And it it doesn't Oh, it has to go into every box. I haven't thought about box seven, have I?

[00:42:42]Well, have I? I don't know. I haven't really not thought about it.

[00:42:55]Oh, I don't know. I've got the path in in loads of boxes. I mean, it's clear I don't have any problem with it going into box eight.

[00:43:03]So, it's only box seven that I need to make sure the path goes in.

[00:43:11]I don't I don't think that's difficult.

[00:43:13]I hadn't thought about this rule much, but I mean, I just don't see almost how it avoids going into box seven at the moment at all. So, trying to force it in is not is not my problem.

[00:43:25]So, going north and south from here, that is my problem.

[00:43:35]Because we did work out these three can't all be on the path cuz these are meant to be on the same bishop's move colors.

[00:43:41]If that is on the path, it is a seven because six is never next to five.

[00:43:50]Because the 159 Oh, hang on.

[00:43:54]No, it's this one that couldn't be on the path, isn't it? If that's on the path, it's seven or six. This one This one can never be on the path as a seven or six in that position. That's so strange.

[00:44:09]Seven has to be on that bishop's move color and six on that one.

[00:44:16]Yeah, that's never on the path. So, we are passing through this box here.

[00:44:25]But, are we passing through there or is that This is the constrained one. If that's on the path and this isn't, we go this way. We've got to do that.

[00:44:44]What is the problem with that?

[00:44:53]I worked out digits for all of that path, didn't I? So, it's clearly not impossible.

[00:45:01]And I mean, I know I am ignoring longer loops, but actually it's quite interesting that one of these from that six, one of these is on the path.

[00:45:10]So, the longest possible loops Oh, I don't know. I was going to say they're forbidden, but actually I've just seen this possible loop. I mean, that is about as long as you can possibly be.

[00:45:21]And I haven't really thought about it at all. So, goodness me.

[00:45:25]Um bother.

[00:45:33]Right. What next? What next? What next?

[00:45:40]This I needed that to hit an eight in one of these cells.

[00:45:46]And then a two or a six after that.

[00:45:48]Maybe I should think in those terms.

[00:45:51]But, I don't know what its path is. I just don't know where it goes.

[00:46:02]Or maybe the fact that we passed through here once is telling me the direction.

[00:46:11]We passed through here once. We passed through Yes. No, what it's telling me is where this goes.

[00:46:18]This cannot wiggle to the north.

[00:46:23]Because these two go straight through.

[00:46:28]And you can't join it all up.

[00:46:34]I don't I don't I can't articulate this, but there's no way if you have Yeah, okay. You would have three loop ends in the northeast of the puzzle like this.

[00:46:44]You can see them here, here, and here.

[00:46:47]You can't join up three loop ends. You can only join up even numbers two or four.

[00:46:53]So this this silly thing doesn't have a U-bend.

[00:46:57]This has to have a south side so that we have four loop ends in the south.

[00:47:05]And exactly two in the north. If it went north, we would have three in the north and three in the south.

[00:47:14]And we couldn't join them up. So this goes south. There we go.

[00:47:18]I mean, that's taken me a ridiculous length of time to work out. It's blindingly obvious if you consider loops and paths and things, but there we go.

[00:47:26]Three there, six there. That's yellow.

[00:47:30]Right.

[00:47:32]Now I know about the direction of the path. Because obviously if we're to consider we start from here, then towards the end we go this way. Oh, that's a seven now. We've got three here.

[00:47:44]Um we go this way.

[00:47:47]And therefore and here we must be going this way.

[00:47:54]Because we can't go up through there, back down through here, and then get to there. We must be going up through this side, down through here, and then up here. So, this direction is the same as this direction. So, the thing that comes before a two or a six is a four or an eight.

[00:48:13]Right. There we go.

[00:48:17]So, here we would go 4 2 1 7, and that's the equivalent of 8 2 9 7 8 2 or 6 1. Right. Eight there puts eight here in this group of four cells that are the high digits. They have to add up to 15 each time, and now they're suddenly all filled in. That digit becomes a two.

[00:48:42]I mean, digits are coming thick and fast now. That's a 3 8 9 triple. This is a 1 2 4 triple.

[00:48:49]Might get this done in an hour. That's come from nowhere. Now, this path can't go through there because it would the three and the seven would be too close together.

[00:49:03]So, that digit's yellow. This is on the path, and it is a nine equivalent.

[00:49:11]Um I was going to say this is on the path, but I don't know that yet.

[00:49:16]Oh, this group is 6 3 4, and on the white dot we have 3 4, and that digit is 6.

[00:49:25]Now, can we say they're off the path?

[00:49:27]Let's start with a thought like that.

[00:49:31]Uh six would be in the wrong position.

[00:49:33]So, yes, that's off the path. Bishop's move. So, those must be off the path. It can't just loop in there and out without touching itself. How about these three?

[00:49:44]One of them would have to be two or six because that isn't if those three were on the path.

[00:49:50]In fact, it would be this one. So, they're not. So, that digit isn't cuz it would be two or six and they're not.

[00:49:58]Okay.

[00:50:00]This is good. This is good. This is something. The path doesn't do exactly that or the three and the seven are the wrong distance apart.

[00:50:15]I So, I'd almost rather do Sudoku now.

[00:50:18]Um is it possible?

[00:50:22]Oh, and this path is the same direction.

[00:50:26]So, we're going up through the five. Now, I mean, we might be wiggling, but after the five, which is a one or a nine, comes a seven or a three. Well, that's got to be a three there now.

[00:50:40]No, that's not true. It could be a seven there after the five.

[00:50:47]And after the three comes a four or an eight. And that could be there or there.

[00:50:51]And after the seven would come an eight.

[00:50:54]Oh, bother.

[00:50:56]Okay, I thought that was going to help.

[00:50:58]Before the five from this direction comes a two or a six. Oh, that could be either of those positions.

[00:51:06]Oh, I thought that was going to tell me everything.

[00:51:15]Oh, just before this four comes a seven or a three.

[00:51:20]For some reason, yeah, that was going to be in one of these cells.

[00:51:24]And then before that comes a two or a six. So, the seven or three So, this is actually possible. That's weird.

[00:51:34]And the one before that would be from 1 5 9, I think.

[00:51:47]Wow, I mean, imagine if this does go round here.

[00:51:51]I'm certain Oh, that eight is looking at this cell. That's Sudoku, right.

[00:51:55]Oh, that does not decide whether we turn into an eight here or an eight here.

[00:52:04]Oh, we don't turn into a cell here because this path comes south through here and joins up to that.

[00:52:13]This path is going to join up to that.

[00:52:15]If we went there, we'd be diagonally touching.

[00:52:18]So, we don't go there. We go here to an eight.

[00:52:22]Okay, well, that is tidy bit of Sudoku done.

[00:52:26]Sort of No, it's path logic done, isn't it? Right. Now, we can connect up there, but we can't connect up here.

[00:52:37]But, we could loop a bit.

[00:52:40]Okay.

[00:52:42]I want this to get easier, and I'm not finding it getting easier.

[00:52:47]That digit is two or six by Sudoku.

[00:52:54]Um after the eight, we need a two or a six. If it's there, it's a two. If it's there, it's a six. If it's there, it's a two.

[00:53:06]Don't know.

[00:53:12]Yeah, I just don't know. I bet it I bet it just does the tight loop. Oh, we still haven't fulfilled this silly six.

[00:53:22]If that's pink pinky purple pinkle, it's a three.

[00:53:28]And that's one or nine.

[00:53:33]Oh, and Oh, this Oh, look. I've got eight nine looking at this cell. That's a one.

[00:53:40]That's interesting. These are from 235.

[00:53:48]After the one comes a two. So, if it if that cell was pink, it would be a two.

[00:53:56]This would be eight.

[00:53:59]Okay, it still looks like that works.

[00:54:03]28 75, that does work.

[00:54:09]Oh, this can't be one anymore. That's just Sudoku, that's nothing to do with the path.

[00:54:15]After five, we would need a two in this direction.

[00:54:20]After the If we were going this way, it would be 5 6.

[00:54:29]Um and then something from four or eight, that would be four.

[00:54:34]Oh, well, that's quite interesting.

[00:54:36]That's just a weird Sudoku thing. So, if the path comes this way, south, this is a four, and that's forced to be a two. If the path comes this way for south, that's forced to be a two by the path. So, that digit is always two, whether it's on or off the path.

[00:54:56]Right, if it goes this way, we go six four and then a three or a seven here.

[00:55:07]Oh, this circle might come into play soon.

[00:55:13]It's a tiny bit unexpected.

[00:55:16]There's an eight somewhere up here.

[00:55:21]That's just Sudoku.

[00:55:28]Um eight some um there's more Sudoku in this puzzle than I'm allowing for at the moment. This digit is 347 or 9. If the path came down there after a two, I expect that has what it Yeah, it would need a four. That would be fine.

[00:55:47]Um Oh, I'm sorry. This is This is This is a slightly wearing bit of the puzzle where I just struggle around.

[00:56:06]Three.

[00:56:11]I thought when I found the direction, I'd really know what was going on. It hasn't quite materialized. And so, as we go north, this direction, after the five, we need seven or three. That's three there or seven there.

[00:56:30]Then we need Oh, well, this can't be on the path then.

[00:56:34]These can't be on the path because five and one would be too close together.

[00:56:38]It's perfectly simple, guys. So, that's on the path to make the six work.

[00:56:43]Here we go. This is the three because it's got to be the equivalent to the seven. Now, the path has to come down through there. This now must be on the path. It's just joining path logic. Right.

[00:56:57]And this digit is a two because it's from two or six. This one is from four or eight, so it's an eight. This one is not from two or six, so it's seven.

[00:57:06]This one's a five. This is now path cells.

[00:57:10]Two, then this is from 1 5 No, this is from 4 8, so that's a four.

[00:57:18]These are yellow, clearly to keep this path apart.

[00:57:23]Um Now, we're going to join up efficiently in some way. That's yellow. These are obviously yellow. The path can't get in there.

[00:57:34]Right, I can yellow all of this, which is pointless, but it cheers me up to color the grid. That digit's become a five. These aren't eight.

[00:57:46]Okay, Sudoku is happening. This digit can't be four or five. So, it's either two or three, and therefore this digit is not purple.

[00:57:55]And therefore, the path continues to here with a digit from three or seven.

[00:58:00]That could be either.

[00:58:04]Um if that's three, that digit is seven.

[00:58:08]Okay, never mind about that. Let's That can't be four anymore.

[00:58:13]One of these is a two.

[00:58:17]Oh, digits, digits.

[00:58:23]What are these? Three four pair is possible.

[00:58:27]But then so is anything Oh, that can't be eight anymore.

[00:58:33]If that's eight, this has to be nine.

[00:58:39]I don't know. Um right, I probably need Well, I need to finish off this bit of the path as well.

[00:58:46]Now, surely this path either does that, which is possible, that, which is not possible based on how close the seven and three would be, or that, which is possible.

[00:58:59]So, I think that cell's yellow.

[00:59:02]This one's obviously yellow.

[00:59:07]Right. Now, what would go wrong if we went all the way down to the bottom?

[00:59:12]We would need to be repeating various sets. We would be going six, five or nine.

[00:59:22]Ah, this one would have to be from seven or three, and it cannot be.

[00:59:26]So, those are ruled out. Those are all ruled out therefore, and and this is on the path, and now we can start filling in some digits. So, this is from 2 6.

[00:59:39]Well, we knew that was from 1 5 9. That hasn't really changed anything, but now that's a 6. This is a 1 4 pair.

[00:59:47]6 is down here.

[00:59:49]And 3 actually.

[00:59:52]That's a 5 9 pair. This is a 1 2 pair that can be filled in.

[01:00:00]This is a 5 7 9 triple. I don't know much about that. Look at that 3 X-wing.

[01:00:06]That's keeping 3 out of both of these cells.

[01:00:09]Using up the 3s in rows 8 9. Now, 2 there means that's pink and this isn't.

[01:00:17]The The coloring is complete at last. Uh this digit is from the 1 5 9 set and is 9. This one is from the 2 6 set and is 6. This is from the 4 8 set and is 8.

[01:00:29]And the path is complete apart from one digit. That's fine. These are 1 3 and 5.

[01:00:36]I can't believe I don't know how to fill those in. I've found 8 at the top. It's not on the dot.

[01:00:43]Uh the dot is either 6 7 It can't be six There's no 6 on the dot. The even digit on the dot is a 4. The odd digit is a 3.

[01:00:51]It's a 3 4 dot just like that one was.

[01:00:54]Weird.

[01:00:55]Well, not that weird. I mean, a chance that occurred. Right. 9 in the top row is there.

[01:01:05]And now, this is a 7 5 pair. This is a 4.

[01:01:10]These are 6 7 9. I know where the 6 goes, then I know where the 7 goes, and that's all done.

[01:01:17]This 3 9 pair has been done by the 9 at the bottom.

[01:01:22]Um how are those ever going to be resolved?

[01:01:25]I don't know.

[01:01:29]In this row, six there deals with a number of digits, keeps three out of a corner.

[01:01:36]We might still get a three in a corner just at the end.

[01:01:40]413, that can't be nine. We've got a two there and five or seven here. That's part of a pair in the column.

[01:01:48]Four in the column is there.

[01:01:50]These are a 18 pair. I can do those.

[01:01:54]579 remaining. This is five or nine.

[01:02:00]How are these going to disambiguate?

[01:02:03]That's not seven.

[01:02:08]Are they going to disambiguate?

[01:02:11]I'm sure they are. I'm sure they are.

[01:02:15]Um I can't use the path or the circles or the arrows anymore or the dots.

[01:02:22]So, it's just Sudoku from here on in.

[01:02:24]Oh, that's a 59 pair.

[01:02:28]What? Oh, I see that can't be a seven by Sudoku and that can't be a one on the one on the path. Oh, that's beautiful, actually. That really is lovely.

[01:02:37]This whole thing has been a a journey of joy and I am going to finish in under an hour.

[01:02:43]In turn, the video has probably just gone over an hour. It didn't get three in the corner, but the puzzle is complete.

[01:02:50]Oh, that's excellent. Very good, Black Raven. That's your second ever puzzle.

[01:02:57]Absolute entertainment from the word go.

[01:03:00]Super stuff. Thank you so much for following us on the channel.

[01:03:05]Don't say never more to doing it again.

[01:03:06]Come back and we'll see you again. Bye for now.

[01:03:13]>> [music] >> I