One Of The All-Time Great Sudokus.

Added: 2026-06-03

[00:00:14]Hello and welcome to Tuesday's edition of Cracking the Cryptic, where I'm actually I've got my light on in my room. It is 2:30 in the afternoon where I'm going to be starting this video, and it is practically dark outside. We had the most massive massive thunderstorm earlier which featured the clap of thunder that is is the loudest I've heard in my life. It sounded like it was sort of well right in my my right ear.

[00:00:43]Um and it made me jump like you wouldn't believe. Anyway, I'm rambling. Um this video, what are we going to or what am I going to be attempting as my phone buzzes? I'm going to be attempting a puzzle called 20 Almost Balanced Lines by Rocky Rower, the American maths teacher, who has started setting again.

[00:01:03]I did a I did Rocky Row's new puzzle um uh just a few days ago on the channel, but this one, which I think is also pretty new. Um we we have had one recommendation for it, but we've had three emails saying people have tried it and haven't been able to do it. So, could I have a go at it? So, that's what I'm going to do. Um, it's got a really, really short rule set. Um, and, um, yeah, I'm looking forward to having a go at it. 20 almost balanced lines. And, and the basic idea is that along each line, let's look at that line. I mean, we'll do the rules properly in a moment, but the sum of the odd digits on that line is one different from the sum of the even digits on the line, I think, is how it works. And that that's basically all the rules. Um anyway, um we'll we'll we'll we'll work through the rules more formally in a moment or two's time. Let me look at my list of things to mention before before we kick off. I have got some birthdays to do. Um a quick mention for the fact that we have got our um our brand new Zeta Math app. Is it that one?

[00:02:12]Yay. Um a new app out featuring the puzzles of the great Zeta Math. Um so get involved in that. The puzzles are lovely. They really are lovely. Um we we've had some great feedback already.

[00:02:24]Um and that that app is available in all of the usual places.

[00:02:30]Now the other thing that we've that's um just launched on the channel. It launched yesterday afternoon is our brand new let me go back over here.

[00:02:41]Sedoku hunt, Alien Invasion, which we themed on the fact that there's been this um big new release in the states of um or declassification of um all these files related to alien activity on Earth. Um and you can see uh Blobs very kindly provides this sort of solve counter for us each month. Let's see. Actually, I um I only launched this this morning, but if I reload it, let's see if the numbers have moved at all.

[00:03:10]F. Yeah, they have a bit. So, Uranus, is that how it Uranus Ur Uranus? I'm not sure what the actual technically correct um pronunciation of Uranus Uranus is. Um but 536 souls of of that one. 744 for mini Uranus Uranus. Um and um 78 looks like it's the lowest number there. So, very many congratulations to all 78 of you who've basically solved the whole thing already. That's very impressive. You you actually have till the 20th um to solve all the puzzles if you'd like to be in with a chance of winning the competition which will uh afford the opportunity to come onto the channel and solve a puzzle and hopefully appear in a video. Um but the feedback we've we've got two main threat threads to the feedback so far.

[00:04:00]Firstly, the puzzles are slightly easier than last month. So if you did get stuck last month, don't worry. This month they are slightly easier. Secondly, apparently people really like the puzzles even more this month. Um, so that's that's rather lovely to hear.

[00:04:13]Anyway, it's over on Patreon right now.

[00:04:15]Do get involved. Now, let's do birthdays.

[00:04:20]Bridget, Bridget, you're turning 16 today. I know this because your best friend Brooklyn wrote to me and told me that you watch before bed to relax of an evening. Um, so thank you very much for for watching. I hope you've had some great chocolate cake today and it's been incredibly heavily iced. Um, next Jude, you're turning the big three 0 today and I know this because your wife Charlie wrote to me and told me that the videos are the soundtrack of your household. I love the thought that you know at all hours of the day there could be a Sudoku video in the background. That's that sounds like the sort of house I'd like to live in. So Jude, many happy returns.

[00:05:02]I hope you have a great 30th birthday.

[00:05:04]Um, and I hope the chocolate cake was very fine, obviously. Oh, now the next one. I'm terrible. I don't know how I missed this. I meant to I meant to wish Max a very happy birthday yesterday. Um, from your mom, Mary. I I I got the most amazing email, Max, um, about you. I know you're a sophomore at Oregon State University doing philosophy and English.

[00:05:29]Um, and your mom basically then wrote a lot of very, very, very nice things about you. I know that you always show up for people. You're thoughtful, generous, funny, um, a very talented writer. I think you're also becoming a very talented or you are a very talented and becoming a very proficient musician as well. Um, and um, you're you're adventurous and well, she's basically very very proud of you. Um, but it was lovely to read. And Max, I'm sorry. I'm I'm I I got them. I I did get the message. I checked. I just don't know why I didn't put it in my phone. I do spend a lot of time every day keeping track of people's birthdays. You wouldn't believe it the number of mistakes I made, but I do try and I messed up. And I'm sorry, Max. And I But I do hope you had a great birthday yesterday. Um and then the last birthday is for Niels. Niels, you turned 35. I think today your wife Sophie wrote in and said you might like a shout out. I know you're over there in Germany. Um, and you introduced her to Cracking the Cryptic. I'm so grateful whenever I hear about people sharing this hobby with their friends and family. Um, now the only bad thing about today um, Neils is that your birthday, your chocolate cake, I think, is going to be happening at the weekend when you you get together to celebrate with your friends and family.

[00:06:50]So, I hope you'll be able to wait until then. I have not been told about how much icing will be on your cake, but I will advise Sophie it should be a lot.

[00:06:58]Um, many happy returns. That's all the news. Shall we have a go? A Rocky Rose new one. 20 almost balanced lines. The rules are not going to take long to read. Um, what do we have to do today?

[00:07:10]We have got normal Sudoku rules apply.

[00:07:13]So, we've got to put digits one to line once each and every row. Whoa. What has gone on there? Every column. That's the That's the rain. The rain did that, wasn't me? Um, and every 3x3 box.

[00:07:25]Now on lines, the sum of the even digits and the sum of the odd digits are almost equal. That is, they are off by one.

[00:07:34]Digits may repeat. Oh, digits may repeat on lines if Sudoku allows. Okay. So that digit could repeat on that line because Sudoku would certainly allow that. Say this was a I don't know five. then you could put five there with certainly without breaking Sudoku.

[00:07:51]Um let's actually do a full example then.

[00:07:55]So if they were both five that would add up to 10. So the even digits on this line there would have to be two of them to get Oh no. Uh well there would in order to get to one different um Hang on. This isn't going to work, is it? I'm going to have to adjust this.

[00:08:17]I'm going to make that eight.

[00:08:21]Hang on. What's going on? One different.

[00:08:26]Oh, hang. Yeah. Okay. I'm going to have to be a bit more structured about this.

[00:08:29]I'm realizing I just can't do it. So, I'll make that nine now. And now I'm going to put three even digits on it in order that I can actually make this work. And the three even digits are going to add up to 10 or um eight I suppose. But we could okay but we could repeat digits. So we could do 2 4 and that finally I believe to be a valid example of this line.

[00:09:01]So the evens add up to 10, the odds add up to nine. They are one difference. So, I think I think that's how the puzzle could work. Do have a go. The way to play is to click the link under the video as usual. But now I get to play.

[00:09:15]Let's get cracking.

[00:09:18]Now that it's very difficult to know maybe I should start here and think about this again because one thing I did learn then yeah okay let let's take this back to very basics.

[00:09:40]What is the sum of the digits on any one of these lines?

[00:09:45]Now the answer is we don't know exactly what the sum is but we do know the nature of the sum because the digits the sum of the digits and on the odds and the sum of the digits on the evens differ by one.

[00:10:00]They're going to be consecutive. If you add two consecutive digits together, what do you get? What do you always get?

[00:10:07]You always get an odd number because one of the digits you're adding will be even, the other will be odd.

[00:10:14]So, so every single line in the puzzle adds up to an odd number.

[00:10:29]Yeah. So, so two cell lines are going to operate exactly like white croppy dot um dominoes, aren't they? They're going to be a consecutive pair. Oh.

[00:10:42]Um that's fine. Um that's a different different thing and yeah and and okay and that and what we can look at let's go back to this line that was the example line we were thinking about and I was getting myself into a pickle and the reason I was getting myself into a pickle is I put two odd digits on the line. Now the problem with two odd digits is that they sum to an even digit and you could never make the even digits on any line sum to an odd number. So every line must have an odd number of odd digits on it in order that the line overall sums to an odd number.

[00:11:35]but rather annoying. I've now realized that I was hoping that was going to give me the chance to write or to deduce exactly how many odd digits were on this line, but I've realized it could have three. That's so annoying cuz if this especially if that was a one, you could you could actually add the odd digits to a very small number and have three of them and they would only add up to five, which means you could even have the even digit being a four or a six. Both of those would be both of those would work.

[00:12:06]Okay. Sorry. Um I'm not terribly surprised this isn't where to start.

[00:12:12]But so each of the twodigit ones are white crop key dots.

[00:12:37]I'm not sure is is it the bottom row?

[00:12:42]I I know the parity of that one using my my principle.

[00:12:46]Um because what what what we what we've just said is that the digits on any line sum to an odd number overall.

[00:12:54]So we can use the secret. Goodness me, there's now some sort of emergency outside. Um, so if we can use the secret being that this is something I share with only my very favorite people, but of course if you're watching, you are one of my favorite people. The secret of Sudoku is that any complete row of a sodoku indeed any complete column or any complete box because of the rules of Sudoku contains the digits 1 to nine once each. Now the digits 1 to nine sum to 45. That's the secret. 45 from the perspective of this puzzle is odd.

[00:13:30]Well, 45 from the perspective of any puzzle is odd. But do you know but so but I know that row overall sums to an odd total. But I know that line sums to an odd total and this line sums to an odd total. So those eight cells sum to an even total because two odd totals sum to an even. So that digit must be odd to make the parity work.

[00:13:57]So actually this row or within those within these two lines we know exactly what the even total is because the even digits in Sudoku 2 4 6 and 8 sum to 20.

[00:14:18]Oh no, that's No, this is not easy actually.

[00:14:26]So, okay, I don't really know how to use that because we because we need to know whether each line whether the odd numbers are bigger than the even by one or the even numbers are bigger than the odd by one.

[00:14:44]Because say that the odd number was bigger than the even here. And then the even number was bigger than the odd there.

[00:14:51]Then the odd numbers overall would sum to the same as the even, which would be 20, which would make this a five because you'd have 20 lots of even, 20 lots of odd, and then that would be a five.

[00:15:05]But it could it could be in both. If if the evens were always greater than the odds, then the odds on those lines would sum to only 18 and the evens would sum to 20.

[00:15:21]So this would be a seven.

[00:15:23]And if the odds are bit bigger than the evens in both cases, that would be a three because we'd have 22's worth of odds and 20's worth of evens. Oh, this is this is not easy, actually.

[00:15:43]Um ah hang on. So I'm wondering if it's in some ways I can I mean okay let's think about a three-digit line then. So a three-digit line must have an odd number of odd digits on it. can't have three odd digits because it would it would have no even digits at all and that would be a concept so ludicrous it would be like a redigulator or something. That won't work.

[00:16:14]So, and we can't make three odd digits add up to one and then say ah well they are only one different from the even total on the on the line because three different odd numbers will add up to at least uh nine 135.

[00:16:29]So, this has got one odd number on it and two evens.

[00:16:36]So, has that one. Any any threedigit line has one odd digit on it.

[00:16:46]What about Okay, let's try a fivedigit line. What's that got on it?

[00:16:51]So, could it have only one odd digit?

[00:16:54]No.

[00:16:56]Because even if that was a nine, four even digits would we know would add up to 20 in that instance. Maybe if there was a five-digit line that crossed box borders though you couldn't maybe maybe it gets more complicated then.

[00:17:12]So could all four of those be even? 2 4 No. 24 that would still add up to 12 which this couldn't get within one of.

[00:17:26]Yeah. So I I suspect unless there's a very strangely shaped five-digit line and I'm not seeing anything that's sufficiently strangely shaped. A five-digit line will have three odd digits and two evens on it. And what did we say?

[00:17:46]Oh, hang on. Oh, okay. Hang on. Box two is like like the bottom row. That's really weird.

[00:17:57]Have I Have I miss just miscounted that?

[00:17:59]Have I just done the What I'm saying is that that dog leg thing there has to have three odd digits on it and therefore two evens.

[00:18:14]This line has two evens on it because that we know the nature of any three cell line is two evens and an odd. So that uses up all of the four even digits in this box and that cell is odd.

[00:18:30]But I it's like it's like and it's just not it's not even remotely enough is it to actually do anything with that.

[00:18:45]Am I being am I being so dense here?

[00:18:59]I've got no clue what to do.

[00:19:07]It must all of all of the lines differ by one from each other.

[00:19:15]I missed a mathematical principle here.

[00:19:22]Okay. What about a four cell line? Well, that was a four cell line.

[00:19:27]That's a four cell line.

[00:19:32]It Yeah, we worked that out. It could be even or odd.

[00:19:43]Okay. What about then?

[00:19:52]Right. Okay. What about that thought?

[00:19:55]Does that do anything?

[00:20:02]Oh, you. I am so dumb sometimes. I am so dumb. Oh, good grief.

[00:20:18]Oh, I've Okay, the right. Oh, this right right.

[00:20:24]that I don't know what this does, but it does occur to me.

[00:20:36]I'm going to have to actually I'm going to have to think this through carefully, but the right um leaving out this box, every single digit in the puzzle is covered by a line.

[00:20:53]Now the nature of sudoku digits in in any box or any column or any row is that the odd digits are five bigger than the evens.

[00:21:05]Um because the odd digits sum to 25 1 3 5 7 9. The even digits sum to 20 2 4 6 8. So the natural the natural um balance of the puzzle is very much in favor of the odd digits.

[00:21:25]But I it's really it's really very much in favor of them.

[00:21:36]And yet the odd digits on any line could only be one greater than the even digits.

[00:21:47]Yeah. Okay. So what is the total of all the odd digits that are not in the in the in a sedoku that are not in box five?

[00:22:00]They are going to be 25 * 8 because there are eight boxes and the odd digits in any one box sum to 25. 25 * 8 is 200.

[00:22:10]And the even digits are going to be eight lots of 20 which is 160. Yeah, it's massive. It's a massive difference.

[00:22:17]160.

[00:22:28]I've done it. That That is That is sick.

[00:22:32]That is absolutely sick. What an What an idea.

[00:22:38]Okay, I apologize if you've all been yelling at me. I could well understand it. I just did it didn't occur to me to think about the natural imbalance that exists in the puzzle and how how the lines could correct could deal with it at all.

[00:22:58]So, so what's happening here is that we have got a difference of 40 um uh all of the digits, these digits here, everything that's in this puzzle that is not in box five, the odd digits in all of those cells are 40 bigger.

[00:23:25]But on any one line, the maximum they could be bigger than the evens is one.

[00:23:31]Now the puzzle says it's called 20 almost balanced lines. Now I think there are going to be 20 lines then. But I haven't actually checked that. So let's do that. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20. Yeah. And and that's that's what I expect because because can you see what's happened here?

[00:24:00]How does this puzzle possibly work? How can that difference that ingrained difference of 40 be catered for within 20 lines? 20 lines can give a maximum difference of odd digits versus even digits of 20. If if on every single line the odds were bigger than the evens, these these lines could deal with a difference of 20. Yet the difference is 40 outside of this box. So what we have to do is we make those cells even.

[00:24:33]So they're going to be in some order 2 4 6 and 8. So that's 20.

[00:24:38]Now the difference on all the lines between the odds and the evens is exactly 20. And that that the puzzle can just cope with by making sure that the digits on every single line that are odd add up to one more than the digits on every single line that are even. So on any one line the odds are just going to edge it and then the puzzle can work and it's the only way it can work. It's it's just lovely. It's absolutely lovely.

[00:25:12]It's lovely and it hang on. So, let's just make those all odd now. So, we've nearly got all our odds in row column five.

[00:25:23]Oh, it's that is that's a that's as good an idea behind a puzzle as I've seen in a long time. I love that rocky rower.

[00:25:36]So, right. Well, now I can do the bottom row, can't I? Because now we know I know that there's 20's worth. Yeah. That I know there's 20's worth of evens and I know on any line the odds are one greater and there are two lines. So the the odds add up to 22 in those cells and the evens add up to 20. That's 42 which means my first digit. That's three in the corner. That's three in the spotlight losing its religion. A this is sick. It's absolutely sick. Um yeah. Okay. So that's the same, isn't it?

[00:26:24]Yeah. The the box two is the same because what you've got is four evens in it on the two lines. It works exactly the same way as this row. Those four evens will add up to 20. There are two lines, so the odds are two greater cuz on each line they're one greater. So that's a three as well.

[00:26:46]So three in the middle box is in one of two places.

[00:26:53]Now what does that mean for these two cell thingies? If the two cell thingy can't have a three on it, it can't have a two on it either because we know we know that the nature of all of the two cell lines now is that the odd digit will be one greater than the even digit. So two in this row. So that's a weird I mean that's a weird point. Two is in the wings of um oh well no I'm going to change two is in the wings but I've just realized there's a basic parity point on each one of these lines these two cell lines there will be an odd and an even digit and the odd digit will be one greater than the even.

[00:27:38]But the point is that those seven cells therefore include all five even digits from row five.

[00:27:45]um cuz that one's got an odd and that one's got an odd and there are only five odds in the row. So these two are even.

[00:27:51]Now how did three cell lines work? Uh three cell and that's a nine. Three cell lines have to have one odd digit. So one of those is odd. One of those is even.

[00:28:06]Now we can we know the parity of those parity of those is even.

[00:28:23]I can probably get the parity of this one I think.

[00:28:29]Yeah, that must be true, mustn't it? So these two digits add up to an odd number. Any line individually adds up to an odd number. So these two digits must sum to an even number to make the parity work. So those two sum to even. Those three sum to odd. So we're now on the correct odd total, which means these must sum to an even number. But overall this line sums to an odd number. So that digit is odd which is presumably important somehow.

[00:29:15]Um I don't know what to do now. Um, that line has got three odd digits on it. So, how many odd digits are on that one?

[00:29:32]It can't be.

[00:29:35]Oh, it could. It could be all. Oh, hang on, hang on, hang on, hang on. Let me just write this down because I'm forgetting. So, this line has got three odds and therefore two evens.

[00:29:53]Now, this line has to have an odd number of odd digits on it. Well, that can't be three now because that would put six odds in the box. So, this has only got one odd digit on it.

[00:30:08]So, it's got So, it's got one. So, this string contains one odd and two evens. That's all the evens for the box. And this cell is odd.

[00:30:22]Sort of pinching away at some of these points.

[00:30:26]Now, now hang on. Now this one.

[00:30:31]Well, this is really weird because now these three digits we well we've got one odd, which could be enough because we know that if these three were even, the line overall would add up to an odd number. But if those three are even, what's the can't be all be even. I mean, straight away there'd be five evens in the row.

[00:30:52]So there have to be more odd digits on this line, but there have to be an odd number of odd digits on the line. So this string is one even and two odds.

[00:31:10]Now, so this is one even, two odds.

[00:31:15]Let's just write that in. One even, two odds into those cells.

[00:31:22]So the three odds on if this was a one, then you could repeat a one, couldn't you? That's That's annoying. I keep thinking that maybe these lines are not they're like killer cages, but they're not.

[00:31:42]Maybe this can't be a five. If this was a five, it can't be a three.

[00:31:47]Then the other odd digits could be one and three adding up to nine. Only the even digit could be eight and eight and is that's going in the right direction, isn't it? The odds are bigger. We've al also got to make sure the odds are always bigger than the evens, but that would work. That's so actually I don't maybe this can't be seven then that's got to be 1 or five cuz if it's seven the even digits are going to the odd digits sorry are going to add up to 11 and we can't make the even digit add up to 10.

[00:32:20]So this is one or five and that's a real pencil mark.

[00:32:28]There are two. So there there's an even on here, an even here. That's two evens.

[00:32:35]Three evens. There's one even in there, which means there's one even in there.

[00:32:41]One even in there.

[00:32:45]Oh, I see. And this is one even and one odd to make the count work for the row.

[00:32:50]Two odds here. Three, four. So there should be one odd here.

[00:32:59]Um, wow. Okay.

[00:33:07]What was this line? Do we now know what this line? Yeah. Odd. Oh. Oh, this is one odd. Okay. One odd. Sorry, I should write this down. One odd. Whoops. One odd.

[00:33:20]Two evens in there.

[00:33:24]And the odd. Okay. And the odd has to be bigger, doesn't it? I.e. the odd has to be bigger than the two than the three evens on the line.

[00:33:36]Okay. So, this definitely can't be eight. It probably can't be six. No, it can't be six cuz two and four would take us to 12. Does this have to be two?

[00:33:46]Maybe. Yeah. Ah, sorry. That's been available forever. Yeah, this has to be two because if it was four, by the time we added at least two and four to that, we'd get 10. And although we could get um the balance to be within one by putting in the odd digit as a nine, the odd digit would be lower. And we know that on every line the odd digit is one higher than the sum of the evens or the odd digits are one higher. So this has to be two.

[00:34:19]And then if this had anything other than two and it must be two and four here.

[00:34:25]And then it's 2 49 is what it is. That's the only way it can be constituted. So the evens add up to eight and the odds add up to nine and therefore a one bigger.

[00:34:38]Okay. Well, that's that's great news.

[00:34:43]Oh, okay. So, I'm going to be able to work this out, aren't I?

[00:34:47]Because now I now I know that this line contains six and eight, which is 14. So we know that the odd digits on here add up to 15. So they're going to be 357. And this is a one.

[00:35:03]There we go. Oh, but we didn't really want that to be a one, did we? Because one gave me all sorts of flexibility here. I wanted that to be a five.

[00:35:15]These are not twos anymore.

[00:35:20]This is wonderful. This is quite wonderful. Rocky Row, you are a complete legend. Um, now, but I need to be more of a legend and I need to solve this, don't I? So, how do we do that?

[00:35:39]I know how we do it.

[00:35:42]Oh, well, hang on. This line, this line's a problem now, isn't it?

[00:35:58]No, it's okay. It's okay. We can make it work. It's got one odd digit at the moment. Well, that's not going to work.

[00:36:06]it would make the parity of the overall line correct. But this is a three and it should be greater than the sum of all the evens if there's no more odd digits.

[00:36:15]So both of those need to be odd. We need an odd number of odd digits on any line.

[00:36:21]Now this digit can't be lower than five.

[00:36:25]So it's at least a five. So that the sum of the odd digits on this line is a minimum of nine. And yet they have to be one greater than this digit. So, it must be an eight there. And now I've got a 4 six here.

[00:36:42]Now, now what does that mean?

[00:36:53]Oh, yeah. I should be able to work this out. Maybe this has been available forever as well because again, it's the same point, isn't it? The even digits here sum up to 20 and there are two lines there. So the odd digits on these lines must sum up to 22.

[00:37:18]But the odd digits that are available in box one are 3, 7, and 9, which sum to 19. So this has to be a three by maths to make the maths add up. So we get 22 overall.

[00:37:33]Now, maybe this is doable now.

[00:37:37]Oh, no. Three.

[00:37:41]Okay. Where where's three in box one? It can't be the only odd digit on here because it wouldn't be greater than the even digit or even digits I should say that would populate the line. So, this is a three. We can color it in.

[00:38:00]So three is in a domino at the top of or at the end of row one I should say um and this line here has got seven or nine on it as its odd digit and seven would go with two and four and nine would go with two and six. So there is a two on that line.

[00:38:33]Doesn't seem to do anything, does it?

[00:38:38]Three. Three. So there's a three in one of those cells.

[00:38:46]Okay. Right. In this string of digits, we've we've notated look that we've got two odds. Now, we can't use three as one of the odds. So if it didn't have a one in there, it would be a five and a seven and a one, which would add up to 13. And that would require the even digit to be a 12, which it can't be. So there is definitely a one to come on here.

[00:39:08]And then either either five. Oh, we can't. Oh, hang on.

[00:39:13]We can't put eight as the even.

[00:39:19]So the highest even I can have in there is six. So it must be six. It must be six with a 1 five pair. And then the odds add up to seven. The evens add up to six. And it works. And balance has been achieved. Now in the rest of row four, then I need 47 9. Oh, hang on. I need four. I do need 479. But four is not an odd digit. So four is over there.

[00:39:48]This is 7 or 9.

[00:39:51]This is 1 56. So this digit is 2 4 or 8.

[00:40:00]And that thing which doesn't have three.

[00:40:04]How does how do I'm still not very good at working out how these sort of two cell thingies work. The odd digit is one greater than the even digit. So the odd digit can't be seven on there now because that would need a six with it.

[00:40:21]So, it's nine. It is nine. 98 is the only way it works, I think. I'm I'm going to double check that, though. It can't have one on it cuz one's in the box up there. It can't have three on it by Sudoku.

[00:40:34]It can't have five on it. If it had seven on it, it should have six because the odds need to exceed the evens. So, it must be 98, which means this isn't eight.

[00:40:48]It means nine is in one of two places in box five.

[00:41:00]Um, now so that could be 76.

[00:41:08]You can never put one now on a two cell sequence because there were because the odd digits are meant to exceed the even.

[00:41:17]So where's Oh, where's one in row five?

[00:41:19]I didn't think of that, but it's it's got to be in one of those three cells.

[00:41:29]Ah, right. Four is in this domino in row four. So what what can we not put on this domino? We can't put five on it because it would have to accompany four.

[00:41:40]So five is in those cells. This these are actually 135.

[00:41:47]This is seven or nine.

[00:41:51]So now this needs an odd digit. That's got to be a 67.

[00:41:56]Uh school kids everywhere rejoice.

[00:41:59]Um this is 49 now by Sudoku. That's seven. That's nine.

[00:42:07]And now this. Oh, where's where's four in row five? It's got to be at the end. It's got to be there. So this digit is a two.

[00:42:20]And now we know what those three are, which is 58, which is lovely. So that's eight by Sudoku. This is a five pair.

[00:42:32]And now these digits are now known over on this side of the grid. We need 7 2 and three. 237. That looks right from a sedoku perspective.

[00:42:46]Now this can't be a one. We just said we can't put a one on any two cell sequence. So that's going to be five with a four, which does the four and the n. This is so good. It's so good. Um, now there is a five down there. Look.

[00:43:05]So, we can probably work out this line, I would imagine.

[00:43:10]Well, where's the parity got to so far?

[00:43:13]We're on an odd digit cuz we're on 15 for the odds. So, we don't want any more odds. So, we're on 15 for the odds. That means we need 14 for the evens. And at the moment, we've got four and two.

[00:43:26]Um, so we need an eight. That's got to be a 58 pair.

[00:43:32]And now 02 we can put in in this box at the top. And the other digits we've got to place are 6 79.

[00:43:45]So we need another even on this three cell string. That's now going to have to be six. So that so in order for the odd digits to exceed the six and the two, we're going to have to accompany those with nine. This becomes a seven.

[00:44:00]Um, this is not a five look by Sudoku.

[00:44:04]This line needs two even digits on it which are four and eight. Let's check the maths on this. So, we've got 12. So, we should have 13. And we do the odds and it sort of works. Um, eight here means this is a four.

[00:44:22]That's an eight.

[00:44:25]So, that's a six. Oh, this is still going. It's still going. It's just a delight. Uh oh, that's a nine. It sees two and four in the row.

[00:44:37]So, that's a nine. That's a six. No song for you because it's double the song creator.

[00:44:45]Um, let's try row three. We need 2 4 9.

[00:44:53]Nine is definitely on one of those.

[00:44:58]That can't be two. Look, this one we don't know.

[00:45:07]Okay, we might be about to get stuck, which is which is a distressing thing indeed. That can't be a three. Remember, every three cell line only has one odd digit on it. And that odd digit has to be one greater than the two even digits on the line. So, in fact, oh no, was a bit I was going to say we know what this is, but we don't. Cuz if that's seven, that could be a two. And if that's two.

[00:45:31]Oh, that's a seven. So, this is always a That's weird. That's always a two seven pair, which means I don't know what that means. It probably does mean something for is almost restricted in in column thingy. Column eight, the technical term. Oh, I've got a nine here. So, that's a nine. That's an eight.

[00:46:01]Nine is in one of those three. Can we put nine in the corner? It would have to go with eight here. Maybe we can.

[00:46:09]Oh, if this is four, that would need to be five. Uh, that also appears possible.

[00:46:15]That's distressing. Um, do we need do we need those to be odd is a question we could ask.

[00:46:28]I'm think yeah, we do. It's certainly having one odd digit on this will not work if that odd digit is a three. So, we've got to have an odd number of odd digits. So, they're both odd.

[00:46:41]That's I should I I probably should have kept going with my parity, shouldn't I?

[00:46:45]Let let me how how can I do that? Simply I'll just double click blank fours sixes and eights and make them blue.

[00:46:56]And then I'll double click blank nines, sevens, ones.

[00:47:03]When I say blank, I mean uncolored.

[00:47:06]Threes.

[00:47:09]Okay, that's that's that's tidied up my coloring. Now these are both odd. So that one is 7 or 9 by Sudoku and that one is 7 or 9 by Sudoku.

[00:47:27]So it's going to depend on what this digit is, isn't it? If that digit is a four, we've got 12, which means these would have to add up to 13. They could be 1 N bother. If that's 14, um, these have to add up to 15. So these have to add up to 12.

[00:47:48]That doesn't work.

[00:47:51]So I don't think this can be a I'm just going to double check that as well.

[00:47:54]Sorry. So 14 14 for the evens means 15 for the odds. You can't do it. So that's four.

[00:48:01]That's six.

[00:48:04]12 here required these to add up to 10.

[00:48:06]So they are 91 in in a specific order.

[00:48:13]This digit is six or seven by sudoku.

[00:48:16]These digits are two six or seven by sudoku and hope. All right, we got a six here which we didn't have before. So maybe this horseshoe is now how how is the horseshoe working?

[00:48:34]The horseshoe is working.

[00:48:37]Is it? The horseshoe could be terrible, couldn't it? Couldn't it be?

[00:48:46]Oh, no. No. No. The horseshoe is beautiful. The horseshoe is beautiful because how can it have only one odd digit on it?

[00:49:01]Even if that was a nine, the three even digits would because one of them is a six and let's make the other two as low as possible so they could both be two.

[00:49:11]That would add up to 10. But the odds are meant to exceed the evens and they couldn't. So this has got three odd digits on it adding up to seven. So it's got to be three. This is absolutely perfect. 33 has got to be that. There's no other way to do it now. Oh yeah.

[00:49:29]Okay. That does give me a one here.

[00:49:32]That's definitely an odd digit.

[00:49:35]This is now not a three cuz I've got a 27 thing going on.

[00:49:42]Now, what about this column then? 567 into the into the gaps.

[00:49:50]Oh, nearly then nearly got something going on in the bottom row.

[00:49:57]Um, that's two or seven. Can we do anything with that? Oh, we can probably we probably know what the odd digit is on there, don't we?

[00:50:09]Well, yes, actually I do because it can't it's got to be five or seven. If it was five, we know it would beat the four on the line, which it can't. So, because four four is impossible on the line. So, it's got to be 7 six again.

[00:50:25]So, this is two. So that's two, that's seven. Let's let's check this. That line does work. That's now even. That's even.

[00:50:35]The seven six is actually resolved, which I didn't see. So that's good news for me.

[00:50:46]So this row has got five. This is a This is not a nine. This is five or Whoopsie.

[00:50:52]It's five or eight.

[00:50:59]Nine is in one of those. Can that really be nine? 98. Would that be okay?

[00:51:09]Don't know. It might be.

[00:51:16]I probably am meant to think about this domino. The two cell dominoes are much more powerful than I'd realized when we started the puzzle. And so the odd digit on here, if it's nine, it has to go there. Sorry. If it Yeah, if it's nine, it has to go there. It's not one or three. Now, it could be 54, couldn't it?

[00:51:38]But that would have to be four here, five here. And it it can't be 67. Oh, it can't be 67 for lots of reasons. It would break these to make both of those five, but it would also break that cell.

[00:51:52]So, there are only two ways that can work.

[00:51:58]Yeah, that's fine. That's fine. Right.

[00:52:00]So, now look at these two cells.

[00:52:07]It's not possible that these have a five in them cuz this would be eight and then you couldn't fill this. This is either 8 n or it's four five. So if this is five and that's eight, there's no valid total for those. So this this is 67. I've now got a six seven pair in row nine. So that's a two.

[00:52:28]So this is a five and that's a six.

[00:52:33]Five is odd. Six is even. Knowledge bomb there. Um if this is 67 So this digit is three, four, five or eight.

[00:52:53]Oh, this must be doable.

[00:53:00]Do I know?

[00:53:06]I don't I'm not sure. I'm sorry. Um, if that's seven there's Yeah, there's going to be a way to do this. There's Oh, okay. There is a two on this line.

[00:53:26]So, if this is six, that's going to go with a two and we're going to have to partner that up with a nine. So, it's going to be 92 in that order. If this is seven, then the two is going to have to go with a four. And that's going to be a two four pair. And that's going to have to be in that order. Two here, four here.

[00:53:53]If this is seven, oh, and there's a six seven pair I've not seen in row row eight as well.

[00:54:10]Seven in column six has to be up there.

[00:54:15]This can't be a four by Sudoku.

[00:54:20]So nine is in one of those cells.

[00:54:27]I'm not sure. I'm not sure. Oh, three. I can do three in the middle box. I hadn't noticed that.

[00:54:35]I don't think that's going to be the helpful thing that's going to get us home, unfortunately.

[00:54:41]Um, if that's nine, those two have to be two six in some order. Does that fail?

[00:54:51]Probably not. Do we have to have a two on there, don't we? Cuz four and six would add up to too many. So, there's definitely a two on this line.

[00:55:01]That's not Yeah, that's not news. That doesn't help me.

[00:55:05]Um, eight can't go on this line with two cuz it'll get too big.

[00:55:15]So, eight is on this other line here, this dogle leggy line.

[00:55:21]again. That feel like I'm close to spotting something, but I haven't quite got the final piece of this figured out, have I?

[00:55:32]Um, what about I've got no idea where I meant to look here. Three in row eight is in one of two places.

[00:55:50]Okay, that's probably not it either.

[00:55:55]This line 1 2 3 4 5 six. That is a length six line.

[00:56:05]Um, now sorry if I've no doubt you've all spotted what I meant to be spotting and I'm just being just being my brain's being recalcitrant. naughty brain.

[00:56:21]Or is it going to be that line?

[00:56:27]So this line is going to contain whatever is not on there, isn't it? So let's say that was four, five. This line would have 8, 9, and one on it. So this has always got one on it as one of its odd digits. It's always got seven on it.

[00:56:45]So, it's got 17.

[00:56:50]Yeah, but that Yeah, this is all sort of just working that I don't think that is how you do it. I don't think we're getting any extra. Oh, I've got a 29 pair in column four. That could do it.

[00:57:01]So, I need 156 into the gaps.

[00:57:06]Okay, let's see if that helps. 156.

[00:57:13]The two nine pair means this isn't a two.

[00:57:18]This is one. This is one, five, or six.

[00:57:21]Does that stop that being anything? Oh, it's not six.

[00:57:26]So, six is up here.

[00:57:31]Oh, that's good. So, six can't be there.

[00:57:34]Look. So, six is on this line. So, this line is 6 2 9. And the nine, we know where it goes. Lovely. That's a relief.

[00:57:43]I was getting I was getting stuck there, but I think we might have just got unstuck. So, nine being here makes that two, which seems to make that four, which makes this seven. This six, that's seven, that's six.

[00:57:57]Okay, that's good. This isn't six.

[00:58:01]That's what we learned earlier. So, the digits that we haven't put in, let's have a look. 58 into column column five. Can we do anything clever with that?

[00:58:16]No. No, we can't. Um, nine is in one of those two.

[00:58:25]If that's nine, that's nine. That's eight. That would be a one five pair.

[00:58:30]Would probably Oh, where's Oh, no. I've got it now. Where's four in the bottom row?

[00:58:37]It's got to go there. So that is four.

[00:58:40]That's five. That's eight.

[00:58:43]That's seven. 57.

[00:58:47]587. So that's three. Oh, that's another Is that another three in the corner?

[00:58:52]That's three in the corner. Three in the spotlight, losing its religion. Um, that's 584. So this is a three.

[00:59:01]That's eight. That's five.

[00:59:05]That's six. That's seven.

[00:59:08]We probably just have to do a little bit of math to tidy up this this last line.

[00:59:13]Let's check whether it works. We've got um 16 on it at the moment. And 12 in the odds. So we need another five to make that work. So that's one, that's five, that's five, that's eight, that's eight, that's seven, that's one. One, five here, eight here, and something. Nine.

[00:59:33]Probably.

[00:59:36]The sedoku is probably okay. Let's I haven't checked some of these lines.

[00:59:41]That line works. Um, here we've got 12 and 13 is beautiful. It's I mean, it must be right. There's no way this come.

[00:59:49]The fact it's sort of 24.

[00:59:53]24 and 9 is 33.

[00:59:55]So, that's going to be a 17 and a 16.

[00:59:58]And it is a 17. It must be right. Yes.

[01:00:01]And it is. Hardly anyone has solved this.

[01:00:06]Isn't that fantastic? It's taken me an hour. Um, and I could just do some double clickage and make the puzzle completely consistent regarding its parity shading. So 2 6 8. Let's make those even. Eights. Threes in the corner. Go on. And that is the total the total answer. Let that's brilliant.

[01:00:32]Rockya absolutely incredible puzzle.

[01:00:35]Fantastic. Loved it. Loved every instant of it. It is world class that one with the most amazing breakin. Let me know in the comments how you got on with the puzzle. I enjoy the comments, especially when they're kind. And we'll be back later with another edition of Cracking the Cryptic.