Try not to Go Wrong!

[00:00:11][music] Hello. Welcome back to Cracking the Cryptic. Um, I did a liar puzzle last week and uh that was from the previous round of the Grand Prix. I never had time to enter the next round of the Grand Prix after all. It's so annoying. Um, mind you, it gives me a open field of puzzles to do it uh to do from it in the future.

[00:00:35]However, however, um, the liar puzzle that I did, I really was terrified by because every given digit in the puzzle could have been a liar. And it was just brain frying. And indeed well it was a very interesting experience because I found it very difficult until the tipping point after about 20 minutes and then suddenly it was very easy once once you knew where all the liars were it and once you knew where one or two of them were you knew where the others were. It was a very interesting puzzle. This I think promises to be a bit different.

[00:01:12]This puzzle is called rocken turn at Albuquerque and every indication every clue in the puzzle has an error in it.

[00:01:22]And there aren't that many clues. So, it ought to be a bit terrifying, but somehow I don't think it's as frightening. Now, Albuquerque, Albuquerque, I know, I believe I know, is in New Mexico.

[00:01:35]Um, and I embarrassed myself on Wordle uh three days ago by mentioning but think saying it was a city and I thought it was in Idaho and that was embarrassing. Now, someone called Brandon Josie's today, actually, it must have been two days ago cuz Brandon Josie today said, "You should definitely forgive yourself about that. Not many or a minority of Americans would know there's a but Montana," they claimed.

[00:02:04]I'm not sure that's true, but I have less excuse because my parents and I did a big trip around American national parks back when I was 18 or 19 and we we visited a lot of those states um everything around Nevada basically and um we were in but Montana as well as Boise Idaho which I think is the place I was confusing it with. Actually, Boise, Idaho was the one place in America where our accent couldn't be understood for for a moment. Um, which was very surprising. We were asking for what we called salt in a restaurant. And we repeated it several times. Do you have some salt? And nobody knew what we were asking for in that particular restaurant in that particular part of Idaho. Um, and it was only when I eventually tried an sort of more Americanized pronunciation of Saul that it was understood. So, uh, that was a very odd experience. Apart from that, I don't think my accent has ever not been comprehended in the US. But there we or by by Americans, but you can tell me different. Um, anyway, uh, what a what a bizarre reminiscence that is to have at this point. Anyway, this puzzle is not about Idaho or Montana. It is about a rogen turn at Albuquerque. And that is probably a reference to some movie or book that I neither know nor remember. And the puzzles by Dammen who hasn't featured on the channel before. This was recommended by uh Steve. So thank you for that Steve and we will have a look at that. Now I'm going to first of all tell you there is still a little bit of time left to enter the detective pets sedoku hunt that is our Patreon reward for July. Many people have entered it, but you still have time until 400 p.m. on our time on the 20th.

[00:03:56]In Albuquerque, that would probably be um 11:00 p.m. I'm guessing I'd get it in an hour before that just in case. Um anyway, that is on Patreon along with connections, a new connections video today. gridoggram videos, um, crossword videos, including my solve of Sabers's listener and my solve of the monthly club special, which this week was a sort of companion piece to the Friday club special, which we do. Uh, no, the Friday cryptic crossword masterass, which we do.

[00:04:35]Um, not certain if we're streaming on Monday yet. We will let you know. We will post a live um puzz a live link if we are going to we also of course do minute cryptic and word in a minute on the channel. We have some apps as well. They feature thermo and arrow sodoka which are two of the best apps. Do if you were thinking of dipping your toes in the apps do start with one or both of those. They are brilliant fun. um very very good apps and uh you know I think all of them are but there's also the worms on those links uh which are great fun consequential Sudoku and we've got some merch if you're interested in branding yourself with CTC but the first link under the video is to this puzzle and you can have a go at it it's called Rob and turn at Albuquerque by Damon and I'm going to go through the rules now normal Sedoka rules apply 1 to nine will go in every row every column and every 3x3 box.

[00:05:35]Now, the arrow rules are that digits along an arrow sum to the digit in that arrow's circle. The thermo rules are that digits along a thermometer increase from the bulb to the tip. However, each arrow and thermometer clue in this puzzle contains multiple paths from circle or bulb respectively to tip for each of these clues. So that's treating each circle and bulb as a single clue. There is exactly one valid path where all cells obey that clue's constraint.

[00:06:11]So one of the thermo branches in each case and one of the arrows emerging from the circles.

[00:06:17]Cells along invalid paths do not obey their clues constraint.

[00:06:22]Oh, so we won't accidentally get two valid thermos out of one marking.

[00:06:28]And cells shared between intersecting paths cannot both be valid and invalid.

[00:06:35]So that's referring to these cells.

[00:06:39]They're either double on double lying paths or double truththing paths.

[00:06:46]Intriguing, right, give it a try on that first link. I'm going to start now.

[00:06:51]Let's get cracking.

[00:06:54]So up to a point these thermos must be telling the truth and that point is where they branch.

[00:07:07]Oh and the lengths are fixed. These thermos go up one row of the grid each cell and therefore these this thermo is longest. Whichever branch it takes it's eight cells long. So I can pencil mark it with two digits in each cell that are possible until there. Then one of these branches I could theoretically pencil mark 67 78 89. That would just be legal or 6778 89 there but not the other. So I'd better stop there. Now this one I can I need one more degree of freedom because it doesn't go quite so far. Two, three, or four? Three, four, or five?

[00:07:49]four, five or six. Five, six or seven.

[00:07:52]And then I don't know which branch to mark after that. So I'll stop. 1 2 3 2 3 4. Same sort of thing here. If I can get the numbers right, but I have to stop a little earlier. Now look, that has given me triples. 456 in row five. 345 in row four. Uh row six, 2 3 4 in row seven, and one two three in row eight.

[00:08:21]Now, what does that tell us?

[00:08:24]A mad pencil marker would now mark all of these cells as 1 2 6 7 8 or 9. But even I'm not that crazy.

[00:08:35]Or am I? Well, not yet. I might I might end up having to do that. How can we work out? Now, I was looking at this and working out that this could be 678.

[00:08:50]Uh, yes, that won't work.

[00:08:55]That won't work because if this was 678, yes, this is the point about cells shared between intersecting paths cannot both be valid and invalid.

[00:09:09]If this cell was a truthtelling cell, it would be true for both the arrow and the thermo. And it would have to be eight.

[00:09:18]And that would mean this cell would have to be one. But if that cell was eight, look at the thermo. Look all the way back to its beginning. It would have to have a one here and a one here in the same column. So that is a lying. Let's mark it in red as a lying line. And now this cell is a liar. So that's a lying line.

[00:09:39]And now we can mark up six, six or seven, seven or eight, eight or nine.

[00:09:45]Now, can we do the same for this cell?

[00:09:48]Is this a lying line?

[00:09:51]If this Oh, yes it is. Yes, it is. Look at that. If this was a genuine thermosel, it would also be a genuine arrow cell.

[00:10:03]If it was a genuine thermo cell, it would be a six because this thermo, this arrow would need at least three more. One and two there to keep within nine.

[00:10:24]And this six would force 5 4 3 2 1, which would break this cell, which would have to be one or two. Let me let me just paste that in so you can see it.

[00:10:35]That could just be kept down to six, which would allow this arrow to work.

[00:10:40]But the thermo would then go like this.

[00:10:43]And now the one two you'd have to be putting in here to make this arrow add up to a number you could put in there would fail on this cell. So that is not that is a lying cell. And therefore all of these are lying cells. And this is the genuine thermmo. And this is a genuine arrow.

[00:11:02]And now now we are finding the right turns at Albuquerque at least. And I can ignore all these red markings. Now I've got one more wrong or right turn to find. And presumably we'll be able to falsify this cell.

[00:11:21]If this was a correct thermo cell, it would be at least six. Oh, in fact, there's a sort of issue of a a virtual 567 trio in this row.

[00:11:38]There must be a 5, six or seven from here. And then there's a virtual 678 trio. In fact, I can mark this one up, can't I? 6 7 or 8. There's a virtual 67 or 8 trio there and a virtual 789 trio here. And what does that do?

[00:11:57]Now, if this thermo cell was genuine, it would be at least six and it would be a genuine arrow cell and that would be 1 2 or three and this would be 7, eight or nine.

[00:12:12]I don't know. I'm not not inclined to say that's impossible.

[00:12:27]Um, okay. What do we do next then?

[00:12:38]Can I claim I've made a breakin? I don't think so really. I I've found two lying two lying arrows, two lying thermos.

[00:12:58]There's something that would have been wrong about this anyway. Roen, about this. Yes, I know what it is.

[00:13:06]These three cells would have to be different from these seven different cells.

[00:13:12]So, that wouldn't that thermo is invalid anyway. Can I do something about Yes. Oh, that's lovely.

[00:13:22]Right, I'm just going to color these to exhibit what I've just seen.

[00:13:28]And these that is beautiful. This is absolutely beautiful. See if you can see what I'm doing there before I say if you're if you're interested. It's very very clever.

[00:13:39]Uh not of me, but of of Damon.

[00:13:44]And this is an impossible situation for the yellow to be a genuine thermo. By thermo rules, these seven digits would all have to be different.

[00:13:54]But they would also all have to be different from each of these cells which sees every single one of them either in the column or the box. So we would have to have 10 different digits in our Sudoku puzzle. And normal Sudoku rules do not allow for that. So that is not the genuine thermo. That is the fake thermo for that reason alone. For the reason of these three totally unmarked cells which I can't pencil mark at all which I have no idea what goes in them but they prove that this is the lying thermo. Oh, so this is a genuine digit.

[00:14:29]Oh, and I knew that. Oh, it's so silly.

[00:14:35]I didn't need this clever thing at all.

[00:14:38]Oh, that's so annoying.

[00:14:41]Oh well, I didn't need it at all because once I'd found this was a lying arrow. This was a genuine arrow and that cell is a genuine cell, a truthing cell.

[00:14:52]And therefore, this is a genuine thermo which I can mark up. I'm sorry. I saw that totally backwards. But I mean, I think that's still a very interesting finding worth knowing for future puzzles and maybe for the thermo app and other thermo puzzles you might do.

[00:15:13]Literally, this shape is an invalid thermo in exactly those cells because of these three. So bizarre. So bizarre. I love it. I love it. It's so clever.

[00:15:24]Right, let's use some of this geometry.

[00:15:28]Where do these two cells go in column five? Because they don't go again onto their own thermo and they don't go in their own box again. So they must go in these two cells which are selected from 456.

[00:15:43]Now I was thinking I was patting myself hard on the back and going fantastic. We know all the liars and all the truths.

[00:15:51]But I'd forgotten this little spider fell down here who's totally independent of any thermos and we don't know anything about what he's telling at all.

[00:16:00]Now we need a nine in this column.

[00:16:02]That's got to be in one of these cells.

[00:16:06]What's the other digit?

[00:16:10]Oh, yes. Either this thermo is 1 2 3 4 5 6 7 and all of those digits are seen by these cells. So, they're 8 9 or this is 2 3 4 5 6 7 8 and these are 1 nine.

[00:16:25]So, they're either 8 9 or 1 N. Now, this cell sees a 567 triple in its row.

[00:16:35]Okay. So, the other digits are 1 2 3 4 8 or nine. We can immediately this this arrow. What's the minimum it can be? Oh, I was going to say five, but I'm wrong.

[00:16:46]It's four. Actually, if that was one, two, one, that might happen. This is at least four. So, can we rule that out? One, two, one.

[00:17:08]There must be a way. Can you see it?

[00:17:17]Actually, it's not that easy to make up as eight or nine either.

[00:17:22]I don't think it is because look, we've got four, five, six ruled out from these cells and 345 ruled out from this one.

[00:17:31]So none of these digits can be four or five.

[00:17:35]Now we have to we have to allow as in 121 for repeat digits. But how could we make up eight or nine?

[00:17:46]Maybe it has to be four.

[00:17:56][snorts] I just don't know. I just don't know.

[00:18:05]Oh, hang on, hang on, hang on. If that's a four and this is one, these cells are definitely 235.

[00:18:18]There's definitely a problem with that, right? The problem with that is to do with one stepping.

[00:18:26]This set of digits up here are seven, eight, and nine. This set of digits down here are 1 2 and three. The only way we can transition on each thermo between those is by one transitioning to seven in six moves, 2 to 8, 3 to 9, all of them in six moves. And to do that, they must all step by one at each step of the thermo. I think that is certain.

[00:18:53]And that means this can't go 235.

[00:18:56]Basically, it would run into trouble with the other thermos. If that was 235, this would be one.

[00:19:06]Yeah. If that was 235, this digit would be one and this would be three. And this one would have to go three, four, five.

[00:19:13]And there'd be a five clash here. So I've ruled out four from this cell. Now on this genuine ther on this genuine arrow, I'm actually going to paint the genuine arrows green just so I remember.

[00:19:26]Yes, I can mark this one up a bit. That is worth doing. Right, we've ruled out four. Now I think it's quite difficult to achieve eight or nine.

[00:19:36]And the the two cases that I think are worth looking at is three different digits in these cells that couldn't include four or five. Well, you couldn't even achieve eight without including four or five and three different digits.

[00:19:52]You could only achieve nine by having 1 2 6 and the six would have to be here because of the four five six triple in this row. And the one two would have to be there. Now the alternative the other case is that these are repeat digits and they could be a repeat one with a six or a seven here I suppose.

[00:20:26]All right they could be.

[00:20:29]Could they be a repeat two?

[00:20:32]No, because this digit would be four or five to get to the total and we've got the four five six triple. Could there be a repeat three with a two here? No, because three there would contravene this 3 4 5 triple and so would a repeat four.

[00:20:50]So either these are a repeat one or this is a and that's six or seven or this is a one two pair and that's six. I mean that is a quite I don't know if it was worth going through that because I may not be able to use the deductions that that that follow if there are any.

[00:21:11]Feels a bit weird to have even tried that. Now what happens if there's a one here?

[00:21:19]Ah oh hang on. Oh no.

[00:21:27]I think this whole thing might be impossible.

[00:21:31]If there's a one in one of these cells, then this thermo goes 2 3 four five six.

[00:21:37]Ah, well, it's impossible if there's a one in one of these cells cuz that digit is a six. Now, how are you going to Oh well, that's going to break this cell entirely. We've narrowed it down to one and six as its candidates.

[00:21:50]So, if that's a one, this has to be a six and that's broken. So, there is not a one in these cells. They are a definite 8 9 pair. And that means this digit is a seven. There's our first digit in the puzzle after 15 minutes.

[00:22:04]But I think a lot of digits are now going to flow cuz we can go down this thermo. 7 6 5 4 3 2 1.

[00:22:15]Oh, it doesn't resolve this. But we can get rid of ones out of these bulbs.

[00:22:19]Twos. And I mean we can go up these other thermos reducing their candidacies, their possibilities, their um numbers of alternative digits until we get now this doesn't have to be a one stepper because that only applied up to row eight. So this digit is perfectly a liberty to be a nine.

[00:22:43]This thing. Oh, that's seven or eight.

[00:22:45]So this is now one or two. I've got an eight n. Oh, and once once that's seven or eight, this is eight or nine. And now I've got eight nine pairs in these rows. And that's quite interesting. These digits are going to be the same.

[00:23:04]And these digits are going to be the same.

[00:23:12]It feels quite interesting. Yes, it is quite interesting. Right. Let me just show you that with color. These two we'll call yellow. They have to be the same because that's different from both of them. And this pink one has to therefore be there in row two. Now, where's pink in row three? It's in one of these two cells. But pink is not allowed to be Oh, sorry. That that digit then is not allowed to be eight because we've got this 6 78 triple. So, that digit must be nine. And that's pink.

[00:23:46]That must be nine. And that means yellow is eight. And now this digit is a seven.

[00:23:52]And now we can one step down this thermo. 6 54 3 2. So that this one can be 3 4 5 6 7 8. And we've finished we've finished all three thermos entirely. And this arrow with a two. That gives us a two here by Sudoku.

[00:24:15]This can't be six anymore. It never could be. Don't know why I marked it as though it could be. I don't think this can be eight anymore, can it? Cuz now we have the alternatives of 1, two, and a six or 71 and they both add up to nine.

[00:24:35]Wow, this puzzle's great. I mean, it's really clever. Thank you, Steve, for mentioning it. Now five and four in this box are in those cells by Sudoku. And this is a 136 triple.

[00:24:48]This is now 789.

[00:24:52]54389.

[00:24:54]We've got Oh, that digit's a naked single. It sees 267 in its row. So that's a one. That gives us a six here.

[00:25:02]And that means this has to be two. And that's one. And this green arrow is done.

[00:25:09]>> [cough] >> We need a seven to complete the central box. Okay, I'm coming to use spider arrow in a moment. 8 9 here is done.

[00:25:20]That's a three. That's a four. These central rows are being incredibly kind now. Three 8 7 1 and nine here. 8 and two over the other side. Look, we've done all the three central rows entirely.

[00:25:36]digits in this column from four, five, six.

[00:25:42]Even though I've colored these arrows red, I can't stop myself from looking at them and trying to compute them like a numpty.

[00:25:51]Uh, that can't be six. I want to do a bit more sedoku. Yes, eight in this column. Bingo. Then six to seven up there.

[00:26:04]This is a three four pair. But look, I found a four five pair in the top row.

[00:26:08]So, we know the order. This is a 1 five pair.

[00:26:12]Two goes in the corner with a 67 pair above it. This is a 159 triple. We're going to get to that bottom arrow soon.

[00:26:21]I'm dodging it. I am still dodging it.

[00:26:23]That's not six. So, this is now the four five pair gets to work in the top row. That's a two.

[00:26:36]28. These are from 1 135. That one can't be one.

[00:26:41]And that one can't be five. So this must be the five in the row. And that does give us the four and the five. Just what we wanted. And these are from 139.

[00:26:53]And they're not quite finished. But this is a five in the column.

[00:26:58]Then these are from I mean I I know I'm hedging around the problem and not looking at this spidery arrow but I will get there in a moment. 2 5 4 7 no one allowed here. These are from 3 6 8 9 that neither of the top two can be three and the bottom one can't be eight. Okay, now I'm going to look at it. This is possible. Six and six. We'd put a six here.

[00:27:26]This is possible if it was 1 + 8 = 9.

[00:27:34]And this is possible if it's 9 is 5 + 4.

[00:27:38]So I'm ruling out eight from this circle cell because I don't think there's any one arrow that would work.

[00:27:47]And now we might when we get down here, we might have to use the rule that if one of these arrows is right, the others both have to be wrong. And that might weirdly help.

[00:27:59]But I want to do more sedoku. I haven't got an eight in this row anywhere.

[00:28:05]In fact, eight in box eight is fixed as there.

[00:28:10]And now I know where eight is in box seven. It's here.

[00:28:16]This digit in the column is one or four.

[00:28:18]So, they go in. That's going to let me finish the box. And that's going to let me finish the puzzle, I think. But let's just check cuz actually there's there may still be some thinking about, right, this is a liar now because they add up to at least 12. So, one of these is genuine. And whether we put nine or six in, one of those is genuine. So, I don't think this arrow will tell us how to decide that. Actually, this 79 pair will tell us how to decide that it's a six.

[00:28:49]And this is the genuine arrow. And this is the liar. That's so nice. Right. 79 pair there makes this a three and a four in this bottom row. That's a nine. This is seven in the corner. Nine above it.

[00:29:03]Seven pair there. Not many digits left to do now. One and five. That is box two to finish off. and one. Sorry, that's a three. That gives us one three. That gives us 1 nine. And there we go. What a lovely We've taken the right turn at Albuquerque in the end. A time of 2228, which is lovely. And that's a very clever puzzle. Thanks for the recommendation. Thank you for the puzzle, Damon. Um, welcome to the channel. Love to see you guys again tomorrow. Do come back for more Sodoku.

[00:29:36]Bye for now.

[00:29:39][music]