Make Sure This Has Exactly TWO Solutions!?!

[00:00:00][Music] Hello and welcome to tonight's edition of Cracking the Cryptic. We've got a really strange puzzle for you today.

[00:00:22]It's called Shrodinger. It's by JT. Um I think that's James T. I don't know what the surname is, but this has been recommended to us by none other than Dying Fletchman, who some of you might remember is an absolutely phenomenal setter of very interesting Sudoku puzzles. And Dying Flutchman wrote a special email to us saying that we simply had to have a go at this. Um, and so we're going to we're going to believe him. Um, it the why do I say it's strange?

[00:00:55]is because we have to finish the puzzle and then once we finished it, there are going to be a pair of digits in that finished solution that were to exchange every instance of them.

[00:01:12]So, exchange one for the other across the whole grid, the puzzle would still work.

[00:01:20]And that is a strange concept indeed.

[00:01:23]Um, I love the idea of this. So, it's I love the title as well. So, it's presumably punning on the fact that you're never quite sure whether the cat is alive or dead until you open the box.

[00:01:34]And here, we're not going to be quite sure um what what the correct finishing solution is because it's sort of going to have two possible states, I think.

[00:01:43]Um, but yeah, I'm intrigued. I've got no idea of the difficulty of this either. I found it on Logic Masters and it's only been solved seven times. So, who knows?

[00:01:53]Who knows? Um, but I will read you the somewhat strange rules. I think this is definitely a de debut for JT in a moment or two's time. Now, what can I tell you about? Well, we've had a request actually for me to read um an old poem, not not that old, but must be hundred years or so old. Um, so I will do that at some point. And but before that, I will make a quick appeal. If you do enjoy the channel, please do like, please do subscribe. Um, we'd really appreciate it, and it it helps to keep the algorithm in check. The puzzle we never seem to be able to solve is the YouTube algorithm, and we'd love to give a wider audience to these wonderful, wonderful puzzles that we get to do every day, and you could help with that.

[00:02:37]If you enjoy the channel and you're not subscribed, please do subscribe. We'd really appreciate it. Um, now, now, let me Oh, there we go. There you can see the title of the poem that I'm meant to be reading, The Soldier by Rupert Brookke. Um, I'm not I'm looking actually at the dates. The date that Rert Brookke died was in 1915. So, I'm not sure I'm not sure if if this then applied to him. I don't know if he died in in the First World War, but he could have done and that would make this an awfully poignant poem. Um anyway, this is Robert Brooks, the soldier.

[00:03:20]If I should die, think only this of me, that there's some corner of a foreign field that is forever England. There shall be in that rich earth a richer dust concealed, a dust whom England bore, shaped, made aware, gave once her flowers to love, her ways to Rome. A body of England's breathing English air, washed by the rivers, blessed by sons of home.

[00:03:51]And think this heart all evil shed away.

[00:03:55]A pulse in the eternal mind no less gives somewhere back the thoughts by England given her sights and sounds dreams happy as her day and laughter learned of friends and gentleness in hearts at peace under an English heaven.

[00:04:18]It's very very nice and so yeah thanks well you know who you are. Um, thanks for the recommendation to read that. It was it's a poem I I think I did at school originally. Um, and I haven't visited it very much since, but it's it was nice to spend some minutes in its company today. Um, and I hope you enjoyed it. Anyway, with that said and done, let's let's have a look at Schrodinger by JT and I will read you the rules to this puzzle. We have got normal Sudoku rules apply. So we've got to put the digits one to nine once each in every row, every column and every 3x3 box. Then it says in this puzzle there exists a pair of digits where if you were to swap all the final positions of the two digits in the finished grid, the puzzle would still reach a solution which satisfies the conditions set by all other clues. The special pair of digits, the swappable digit pair, is two distinct digits which add to 10.

[00:05:17]Okay, so that prevents them both being five or something. Two distinct digits which add to 10. We're either looking at 1 n 28 37 or 46. Um the swappable digit pair is a discoverable, persistent and necessary component for solving this puzzle.

[00:05:37]Oh, hang on there. No, I thought that was going to be it. I was like, hang on, we can't we must know more than that.

[00:05:41]And there are there is another paragraph. It says, okay, digits along an arrow sum to the digit in that arrow circle. So those three squares, if that was 1 2 3 1 plus 2 + 3 equals Oh, tried to type six and missed. That would be how that arrow could work.

[00:05:57]Um, digits can repeat. Oh, digits can repeat along an arrow if allowed by other rules. Right. So that's allowing these two cells to be the same. I think digits in a killer cage must sum to the small clue in the top left corner of the cage. So those three add up to 11. Those three to 22 etc. And digits cannot repeat within a cage. So we can't make that sort of double seven eight. That won't work. It would work by stoodoku but we'd have repeated the seven in the cage. And that's too naughty for words.

[00:06:29]We mustn't do that. Um and pairs of digits with white dots in between are consecutive. So those two cells are consecutive. So if this square is a three, that square is either a two or a four in order to be consecutive with three. And they are, let me check, they are all the rules. Do have a go. The way to play is to click the link under the video as usual. But now I get to play.

[00:06:53]Let's get cracking. I get four given digits today. And I mean, one thing that occurs to me is that one of these given digits must be a strange digit, mustn't it?

[00:07:04]because we're looking at a pair of digits to be swappable that add to 10.

[00:07:08]It's either 1 9 28 37 or 46. So, one of these digits is a naughty digit.

[00:07:15]That 8 cage uh can't be 26. So, that's either 1 7 or 35. A 22 cage must contain a nine. Uh do I fully pencil mark it?

[00:07:28]All right, I will. I will. There's definitely a nine in that cage. It's either 589 or it's 679. Two options. 14 cage has two options. 59 or 68.

[00:07:41]Uh a three cell arrow. We looked at the minimum which would be a 1 2 3 triple on this arrow. Uh sums to six. So this square is quite a big old digit.

[00:07:51]So there's quite a lot of big real estate in column six.

[00:08:00]Um, right. Uh, not seeing anything at the moment.

[00:08:07]This cell's even, but lit literally, yeah, literally all the options are available. It's even because this is odd and across a consecutive pair, we'll always find there's an odd and an even digit.

[00:08:22]No, what I was about to say, it's nonsense. I was about to say, where's one in this box? You can't put one on a white dot because it would have to have a two on it with it. There's a two here.

[00:08:32]So, one Yeah, I thought one was more restricted, but it isn't. It's in one of three places.

[00:08:41]This is weird, actually. So, what exactly am I meant to do?

[00:08:48]It can't be to think about this.

[00:08:54]I mean, how's this puzzle going to work?

[00:08:57]Is it to think about that?

[00:09:03]So, so there are two digits that sum to 10 that have to be Oh, I see. Yeah. Okay. I sort of dimly see.

[00:09:17]Yeah. Okay. Here's here's a here's a point and it's only a point, but I will make it. Imagine this was a nine and imagine one appeared on that arrow.

[00:09:28]Then I can see that that would be impossible because uh sorry and that's if one and nine are the naughty digits.

[00:09:36]But if that was the case then then we're meant to be able to swap the nine for the one. In other words, this three cell arrow which contain a nine would sum to one. That's not going to work. Now, that doesn't that doesn't mean anything more than I've just discovered a thing about the puzzle. I understand something.

[00:09:56]So, there must be some reason.

[00:10:02]Yeah. Yes. Okay. Okay. I've got something. So, nine is definitely definitely in that 22 cage. So if one and nine were swappable in the finished grid, a one would flip into this 22 cage and there would be no way it can work.

[00:10:19]So 1 and nine are so one is a natural digit. Let's have a color for a natural digit.

[00:10:27]So it's either 28 37 or 46.

[00:10:31]You see I think it might be 46.

[00:10:33]Actually, the reason I say that is that you could use white dots to sort of because a white dot with a five on it could have a four or a six on it.

[00:10:50]That's quite an isn't it? So maybe it's got to be 4 six.

[00:10:57]Yeah. Okay. It's not 37.

[00:11:01]It's not 37.

[00:11:05]No, it really isn't. I was I was just looking at this cage. I'm just I'm just checking my logic sound. I think that's right. If it was 37, that's going to break this eight cage because if this 8 cage is 35, I'm going to swap a seven into it. And 75 doesn't add up to eight. It adds up to 12. And of course, if it was one seven adding up to eight and then I swapped the three in for the seven, it would only add up to four. So that doesn't work. So this digit is also natural.

[00:11:38]This is very odd but quite interesting I have to say. So if my hypothesis is right, I want to disprove 28.

[00:11:49]How am I going to do that?

[00:11:54]Where have we? We might not have an eight in there. So, we can't use that to do it.

[00:12:06]Ah.

[00:12:11]Well, okay. Here's here's a different point.

[00:12:15]Can that be 68 now?

[00:12:18]I don't think it can. Can it? Because whichever is the naughty pair, 46 or 28, we'd swap a low digit into this 14 cage.

[00:12:28]That would make the cage total wrong because either 64 or 82 is the naughty pair. So that's 59, which means this isn't nine. That means there's a one on this arrow now because even if it's an eight here, we'd have to have a one because 2 + 3 + 4 is equal to 9. So there's definitely a one on this arrow.

[00:12:52]There's definitely a one down here. Can that be actually that can't be a one?

[00:12:58]This cell here because this cell would have to be a two and this cell would be unfillable because it couldn't be one or three. So one is relegated in column nine.

[00:13:17]Um, right. How do we do this then?

[00:13:24]Right. That can't be seven because if that was seven again, I'd then have to swap a high digit in here because if this is seven, this arrow is 124 and I don't know which is the naughty pair.

[00:13:37]But if it's 28, I have to swap an eight onto the arrow. And if it's 4, six, I have to swap a six onto the arrow and it won't add up. So that's that's not going to work. This is not seven. This is six or eight. Now, if it's six, okay, it's not six because that's really clever. It's very good setting actually because if it's six, I hadn't real I could have done this right at the start.

[00:14:04]We could have said this couldn't be six at the start because what that does is it makes every single type of naughty d of naughty pair appear on the arrow because whatever the naughty pair is it breaks doesn't it? If this is 612 3. If it's 64 that's naughty. This becomes a four and it doesn't add up. If it's 91 a nine appears. If it's 28 an eight appears. And if it's 37 a three a seven appears. So some way or other this was always broken. So this is an eight now given it can't be a six. And that must mean well we can't swap a two into this cell. So 82 is natural and 4 six is naughty. There we go. We found something. So this is so this now can't be 134 because that would swap a six onto it. Um so this is 125.

[00:15:00]And all of the all of these need to be completely pure as the driven snow, don't they? So this is 59. That must be pure.

[00:15:11]Now, now what do we do? I don't know. These must both be natural.

[00:15:20]So four and six are naughty whenever they appear.

[00:15:27]Uh, I don't know what to do. What What can I do with this new knowledge? I Ah, I know what I can do. This can't have six in it anymore cuz that would swap a four into the cage and it wouldn't add up. So, this is not 679. It's 589.

[00:15:51]Um, now It's intriguing actually, isn't it? I don't know what to do.

[00:16:00]Um, is this obvious in any way at all?

[00:16:10]Ah, well, hang on, hang on, hang on. Yes, here is here is a a very very strange point, but I'm going to make it. Um, could you put a naughty digit? So, naughty digits are four and six. Could you ever put them on a white dot in a box where the five couldn't join them?

[00:16:35]No.

[00:16:36]And what do I mean by that? Imagine this was four.

[00:16:40]Now, this can't be five. So, it would have to be three. But now, in the finished grid, that four is going to become a six or has we have to analyze the grid as if it becomes a six. and the three and the six would not be consecutive.

[00:16:54]So the five being trapped in the 14 cage I think means that well four is in one of two places and six is in one of three places I think right here. So here we can do a little bit of um I can say fatuous things that actually have a consequence. Um, no jokes about how many things I say.

[00:17:22]Facuous. Um, right. A white dot, it always contains an even digit. Well, four and six are not available for these two white dots. So, these have two and eight on them for their even digits.

[00:17:37]Now, eight can't go with nine. So, one of these is a 78 pair and one of them is a two with a one or a three.

[00:17:52]So, that can't be one. So, that can't be two.

[00:17:57]No, that's not true. It could be two if that's a three. So, be careful.

[00:18:05]Right. So these digits are the four and the six that we know can't go on the white dots. And whichever of one and three are not used on the white dot that has the two on it.

[00:18:20]Oh, bobbins. Okay. So that hasn't actually hasn't done it, has it?

[00:18:30]Both.

[00:18:32]Okay. Um, right. I mean, can I put I'm really skeptical about my ability to be able to put a naughty digit on this arrow.

[00:18:55]If that has say say that had a six on it and then it would become a four, I'd have to correct that somehow here and that just doesn't feel very possible to me. The only way of correcting it would be to have the opposite effect. So for example, if this was I don't know how to make this work, but if that was a six, that could become a four. And if that was a four, that could become a six.

[00:19:22]Now, that would preserve the total for the arrow in this cell at 10, but that's not a possible total there. Yeah, there's no other way of doing it. You have to you'd have to correct the total.

[00:19:44]What about if No, it just doesn't work.

[00:19:46]You can't muck about with this. that won't work cuz that in one case that's going to decrease by two or increase by two and you're going to have to have the same effect on the arrow to make it add up and this cell sees both of those cells. So that that can't work. So I don't think that can be four or six. So this ah well that's good because that means those two oh this is very good actually because according to that logic this is four and six and I know the order. So that's four, that's six.

[00:20:19]They are both naughty digits.

[00:20:25]Now, what on earth does that do?

[00:20:32]Is it doing something here?

[00:20:38]Yes. Oh, I see. Yeah, this is lovely.

[00:20:43]Yeah, this this is lovely. Oh my goodness. This is very clever. Look at this box. Now, now this five up here, which I was very interested in for stopping fives being on these white dots, also stops a five being on this white dot. So, I can't put four or six on this white dot because it won't have five on it. And therefore, it would be incorrect once I swap the the other digit, the other of four and six onto it. Now, that means where are four and six in this box? And the interesting thing I think is that at least one of them has to be in the 11 cage which means that in the finished grid we have to be prepared to swap the other one. You know if this was four and became six how are we going to reduce the value? It's going to have to have both of them in it. So I think that's so this is four and six. This is one. This is sick. This is really clever.

[00:21:42]Now, oh, this is this is very clever because now this white dot has to have an even digit on it and that's going to have to be two and it can't have a one on it. So, that's a 2 three and this is a one.

[00:21:54]And now, okay, I don't quite know what that's doing, but it does mean that these are 2, three, and 78 in some order. This is a one by Sudoku. So, that's a two by Sudoku. So, this isn't two, so that isn't three. And that does feel like it's logical.

[00:22:12]What are those digits? 1 2 3 4 5 7 5 seven perhaps.

[00:22:22]Um, okay, that's good.

[00:22:30]If Oh, no. Okay, look. Look at column four and imagine that this top pair was 78.

[00:22:40]Where are we putting two and three in the column? I think we've only got one cell available for the two and the three. And obviously, although this puzzle may be called Schrodinger, it's not a puzzle with Schroinger cells in it. Not really anyway. So, this can't simultaneously be two and three. So, the two three must go at the top of the column. This is now a 78 pair.

[00:23:08]Um, oh, bobbins. I don't know what that means. I'm sure it means something. I can't I just can't see what it is. Oh, three. Three in column five I can place.

[00:23:21]So, three.

[00:23:25]Why haven't I got Oh, yes. Okay. So, three.

[00:23:30]Three is in one of these.

[00:23:35]And if if three is on the dot, it's going to have to have a four the other side. Oh, which is a funny digit. How can that be?

[00:23:45]That doesn't work, does it? If I put three here, this would have to be four because it can't be two. And again, this is going to become a six in the correct solution or in the alternative solution. And the white dot won't work. So it's it's the same point we saw before. So this is three which means this is seven which means this is not four. That's all we get from that.

[00:24:11]It could be six or eight if this was seven. Uh this is a one in the corner.

[00:24:17]This is a one over here by Sudoku. So let's double click our ones and see if we can do better.

[00:24:23]One is Oh yes we can. One in box one is actually placed. I think now I mean some something I'm seeing is that seven Oh, it's it's broken. Oh, no, no, no, it's okay. No, it's okay. Seven in this box is on a white dot. I don't know which one, but it is. And that seven can't go with six for the same reason the three couldn't be on the white dot and go with four. If we put the seven with the six, once we think of the six as a four, it split personality will break the puzzle.

[00:25:03]So seven has to go on with eight, which means this square is not an eight. One of these is a 7 eight pair.

[00:25:12]And eight is now in this domino, which means that that square is an eight. And that Whoops. And that squares a seven which does nothing really. I don't think it's doing anything.

[00:25:32]Okay.

[00:25:38]Oh, okay. Right. Got it. Okay. Look at this box again and think about four.

[00:25:46]four is on a white dot. Now, we've already learned that if we're doing that, we have to partner up with the five. So that when we split switch switch the four for a six in our minds, it'll still work. So these are 7 8 and 45, which means this is nine. These squares are now 58, which means this is nine. This is this column's done. We need to put nine in it.

[00:26:11]These squares are 4, six, 7.

[00:26:16]And this digit is available to us.

[00:26:19]That's a six, I think.

[00:26:22]Oh, which is which is naughty. So, let's put that in.

[00:26:27]So, this column hasn't had 589, I think.

[00:26:31]Let's put that in. That's definitely not eight.

[00:26:38]Six comes out of this one.

[00:26:42]Um, we might be about to get um a little bit of noise off off off camera. Hopefully off camera. I can't tell, but I can hear things that suggest there might be about to be an interruption. I'll keep going.

[00:26:57]Um, now let's see. Come on, Simon. We must be We're not a million miles away. Seven in row four is in one of two places. It can't be in any of these.

[00:27:14]I haven't really thought about this white dot sequence.

[00:27:20]What else have I not thought about? Can I do some sedoku somehow some way?

[00:27:26]I've got this funny arrow here.

[00:27:30]I mean, is this is this arrow under any pressure? If this was this digit can't be one or two, can it?

[00:27:40]Now, if it was three, this would be a four. That definitely won't work because then it would become a six. And that the maths wouldn't work. So, it's not a three here. And if it's a four here, it becomes Yeah, it can't be a four actually by Oh, hang on. Hang on. What is this digit? Sorry, I didn't realize this. It's seeing four and six, which because I've made them red, I'm not sort of scanning properly.

[00:28:02]So, this is a big digit. Oh, it can't be seven because that would be eight. So, this is this must be eight. Oh, sorry.

[00:28:09]So, that's eight. This is nine. That's that's that's relatively straightforward.

[00:28:14]This is five. Now, so this is 7, eight or nine because it's got to be consecutive with a great big digit. And that means eight is in one of these two cells. Uh which doesn't do anything. Nine has to be in one of two cells in box six, which means nine is placed actually in box seven.

[00:28:37]And We can probably do some other magical things. And those things are going to include putting six as a pencil mark into one of those. Six as a pencil mark into one of these. Four as a pencil mark into one of those.

[00:28:54]Actually, I've completely I've completely messed up doing my coloring, haven't I? I'm not sure. Is it serving terribly much as a purpose?

[00:29:05]Maybe it could be. Maybe I should be a bit a bit less cavalier about not making things green because actually, you know, when you got four and six in a row like we have there, or four and six in a column, we can green things. That can't be four or six. One is definitely not four or six.

[00:29:27]One and nine are not four and six.

[00:29:30]Is this doing anything useful?

[00:29:34]Probably not. Um, let's think about it.

[00:29:43]F. Oh, nearly. Actually, it's nearly interesting. You nearly have to put six on that, which of course would mean five has to go on it as well.

[00:29:57]Five could be down here, I think.

[00:30:05]I'm not sure.

[00:30:08]Maybe I'm not sure where to look actually. Can I put five on that dot?

[00:30:19]I think maybe I could. I'm not certain I can't. So, I'm going to have to hunt around, I think, for more more logical things.

[00:30:31]Now where where do we look then?

[00:30:37]I might have to do some pencil marking which I know is totally anathema.

[00:30:43]I mean okay the that digit is even. I think that might be wrong but it it it it sees 139. It sees five and I've got a seven pencil marked up there. Yeah. So that's an even digit. Okay. Okay, that that that's going to help a little. It's not eight, it's not two. Oh, so okay, that's important. So that's a naughty digit.

[00:31:09]Now, we've learned already, haven't we, that when we put the naughty digits on the white dots, they have to be next to five, which means this is also a naughty digit. I don't know if it's the same one. I Oh, that's that's a horrible question.

[00:31:25]I I would tend to think it can't be, but I'm not sure.

[00:31:29]Now this okay so five is now in one of these two cells which means four must be above it on its white dot. So we can take four out of these two 5 78 triple in row thingy.

[00:31:43]So seven is in one of these which means eight is above it. So we so this has become a 48 pair. This has become a 57 pair. Therefore this is an eight. This is a five.

[00:31:58]Now, does that help us?

[00:32:02]I don't know. That can't be seven anymore. So, that's that's a naughty digit.

[00:32:10]This can't be four anymore. Doesn't Oh, we should be able to Oh, no. Hang on.

[00:32:15]What's going on? Yeah, that's good.

[00:32:16]There's a four in one of those. So, that is a six. This is a seven. This is a four. This is a six. A four gets readyified down here.

[00:32:28]This is a four by Sudoku of all things.

[00:32:31]I mean, that's an outrage making me do Sudoku in your Sudoku puzzle, JT. Right, these are 278. That's not Oh, this is a naked single. That's a seven. It sees eight and it sees two on the arrow.

[00:32:46]So, in this column, we can't we must put the four here.

[00:32:51]So, this digit uh we need to put a six somewhere, don't we? And what else do we need? Is it a three?

[00:32:59]Three and six. So, yeah, if this Well, I've got a six pencil mark, which I'll trust there. So, that's three. That's six. That gets readed. That gets greened. These Well, let's do the three digits there in. Oh, whoopsie. Um, those three digits are 257.

[00:33:21]which I'm not sure if I can do. I can do a little bit. That's not five.

[00:33:30]Okay, this column has a four and a six in it.

[00:33:34]So everything else is of course green.

[00:33:36]That's there's a four and a six in this box. So one of these is a funny digit, but I don't know which one it is.

[00:33:47]Uh, apologies if you do.

[00:33:51]Nine in this box can't go on the white dot because it would be a 98 pair.

[00:33:55]That's going to break that cell. So, nine is in one of Oh, bobbins. I thought it was going to be here, but it's actually not, is it?

[00:34:06]No, I think it's got three possible position. Oh, no. Hang on. I've got a Oh, no. Hang on. I've got a nine down there. So, it is there. 98.

[00:34:17]This is not an eight in the corner. Now that's odd.

[00:34:22]Nine is here apparently using the power of Sudoku. Let's double click nines. Can we do more with nines?

[00:34:32]Nine is in one of two cells in box one.

[00:34:39]Oh, bobbins. I don't know then. Um, I've Oh goodness. I've got to put a four or a six into one of those. But I don't know if it's that one. But if it No, hang on. It can't be this one. We've We've Gosh, when will I learn? You can't put six on a white dot unless it's next to five. So, this is a two. This is a one. This is a seven. That's been available for ages. You've been shouting at me about that. And I deserved it. I deserved it. So, don't feel bad. Oh, look. This is This is finishing it. Is it? I shouldn't have said that, but it might be. Um, this is now a four or a six, which is definitely a red digit.

[00:35:22]This is a two.

[00:35:25]We don't quite know, do we, whether five is five is in one of two's places. So, it definitely could be on this dot.

[00:35:36]Um, we might be able to do there could be some sedoku going on here as well because that was a flurry of activity that we haven't really had before.

[00:35:52]I can't It feels like there must be something there, doesn't it? Maybe maybe row five. What do we need in that row?

[00:36:00]We need three, four, six, eight.

[00:36:05]Can we do something with Oh, we can't put eight on this dot because this couldn't be seven or nine.

[00:36:13]Okay, I'm going to pencil mark it. So, 3 4 6 8 now. That can't be eight. I've just discovered if it's three.

[00:36:24]No, it it's not three because now this would have to be four. And we've learned that's impossible because once it gets switched to a six. So this is this is it. There we go. That's the naughty digit which means everything else in this box is now a nice digit. A nice kind digit. It means we have to put five here which means that's five. That's seven.

[00:36:47]That's eight. That's four. That's Oh, this is going to do things. Look. Look.

[00:36:52]Yes.

[00:36:54]Six must go there. That's a sedoku point to emerge from the the the shroing of fog.

[00:37:03]Um, three has to go there by Sudoku. That is eight by Sudoku. So, this is 8 8 2 7 two five pair. I don't know if that's resolved by something I can't see.

[00:37:21]Right. Let's Let's do all of Oh, careful. Do all of the greening. A little bit of reading. That's now got to be a red six, not a red five. So it's not standing by. And okay, all of the fours and sixes are done. And hopefully we're just left with a little old patch of sedoku to finish. Seven in that column. It goes here. So seven two nine in the corner. 95 52 23. Three there by Sudoku. Three there by Sudoku. If we haven't made a ricket, that's a seven.

[00:37:58]Now before we click anything, we are going to just stare at this and make sure.

[00:38:05]So it's very well it's not very easy to see. Let's do the let's highlight the sixes.

[00:38:11]Now if those sixes uh which color let's make give the So imagine those sixes all became fours in the in the alternative solution.

[00:38:26]I think interestingly the only place that matters is here really where the white dot saves it is still correct. Now the fours on the other hand if they don't know what to highlight them to make them clear. I'm trying to find a good color and I Oh no no no no. Let's make them light blue. Now if they all became sixes that would work. These two would swap positions. So that's fine.

[00:38:55]This would work. This would work.

[00:39:00]It's It's brilliant. It's absolutely It must be correct, mustn't it? I mean, gosh. Oh my goodness. It's really old. I didn't I thought it was a new puzzle.

[00:39:08]Well, never mind. Um, that was fantastic, JT. What an interesting idea.

[00:39:15]What an interesting idea. That is That's I think that's going to cause quite a lot of comment actually. The swappable digit pair. Very cool. 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.

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