Getting Between a Solver and his Sandwich

[00:00:11][music] Hello. Welcome back to Cracking the Cryptic and uh we're looking at a sandwich sedoku today and also between lines. So, this has been recommended to us by um Grime, I think it was, who solved it on Logic Masters Germany. It's by the Scrass, who's not a name I know. Um anyway, I do like Sandwich Sodoku, so I'm looking forward to it. We have apps featuring our first ever one was Sandwich Sedoku.

[00:00:47]um a name coined by Alex Bellowos when he was writing an article about our channel back in the very early days for the Guardian. Um and we were saying that between 1 and nine Sedoku was rightly very popular and uh he featured a puzzle in the paper and called it sandwich sodoku. It's brilliant name and it's stuck. Um and there we go. That's a little bit of history for you. Um, yes, we have apps including Sandwich Sodoku and Classic Sudoku 2 and the worms and they are all very good value. They're on the links under the video along with what else have we got? We've got um our merchandise as well. And uh that features the Rat Run merch including mugs by Marty Sears and lots of other Cracking the Cryptic um goodies that you can get your hands on. and we do at last have a reliable deliverer of that stuff.

[00:01:46]Now, uh we've also of course got Patreon. Yes, today it was the deadline.

[00:01:53]Today was the deadline for the um Detective Pet Sudoku hunt, but there'll be another one out on the first of next month. There are of course gridoggram connections and um crossword videos including Sabers's Listener and the Times Monthly Club special for amongst the cryptic crosswords. So loads of content there to keep you happy if you're into puzzles and of course we've got this puzzle today. It's called Sandwich Between Sudoku for obvious reasons. Uh it's by the scrass and I'm going to go through the rules. Now you can play it on the first link under the video. I don't know its difficulty but I am going to try and solve it. Let's do the rules. Normal Sudoka rules apply.

[00:02:35]That means 1 to nine will go in every row, every column and every 3x3 box.

[00:02:41]The a clue outside the grid indicates the sum of the digits between the one and the nine in that row or column. So in this column, wherever the one and the nine are, if you add up all the digits between them, they sum to 18.

[00:02:56]And the digits along the gray lines must be between the digits in the circles.

[00:03:03]Uh so do have a try. Um I noticed that Rocky Row had praised the puzzle on Logic Masters Germany and that's always a good recommendation. But give it a try. I'm going to start now. Let's get cracking.

[00:03:18]Um right there there are some trigger points in Sandwich Sudoku. Any clue over 31, you know quite a lot about its um [clears throat] its sandwich size and where the where what we call the crusts go. any clue over 21, you can determine that the middle of that column or row is not a crust cell. We don't have any of those today. We have a few zer which obviously mean that the one and the nine are next to each other in those rows and columns.

[00:04:00]But I think we're going to have to work on some interaction between the between lines, which is quite surprising.

[00:04:09]I don't know what it's going to be. Um, is this right? There must be at least five different digits separating these digits in circles um, numerically. So they could be 2 3 4 5 6 3 4 5 6 7 or 456 78 at a minimum. There there could be more, but I think that means these definitely come from the family of 1 2 3 7 8 9. It's Why do I feel I'm not making enough deduction from that? I really do feel that.

[00:05:02]I don't know. It feels to me like there aren't very many sandwich clues here in a way.

[00:05:12]It's tricky, isn't it?

[00:05:15]There's this one as well, which als No, it doesn't also have five necessary digits. It only has a necessary maximum of four.

[00:05:30]And all that's telling me is that five doesn't go in a circle.

[00:05:37]Wow. I don't know. I should be learning.

[00:05:40]I should be understanding something about this line. Obviously, digits can repeat on between lines.

[00:05:51]Maybe I should consider the the overlapping zeros.

[00:05:57]What's going on with those? [laughter] I don't know at all.

[00:06:09]There are sometimes considerations about columns together and rows together. The fact that these two have zeros might mean that one nine are confined within a box. Oh, right. I've remembered a very important thing that that is absolutely blooming obvious and it's taken me three minutes to remember it.

[00:06:36]Uh and that is that one and nine cannot go on the between line cells because the they you couldn't make them between two other digits. So these can all be painted green immediately. Those are not cells that contain crusts one and nine.

[00:06:54]What I'm looking to do is coat the grid in red crusts dotted around green.

[00:07:00]Now that must help. Look, that tells me, look at that. All of these digits can't be across one or nine in this column because of the zero clue because they would need the other one to be next to them. So, they're all green.

[00:07:17]That is a definite red crust going either with a one or a nine above or below it.

[00:07:23]And now these two must be green because we're going to have the two reds in the box in those three cells. In fact, all of these are green. The two reds in column six are there. Now, we've got a red in row seven and that's a part of a one nine pair.

[00:07:40]So, lots of green. Green in this box because there's only two reds in any row, column, or box here. I'm not sure in this row. Now, we've still got a zero row to deal with here. Oh, look. We've only got two potential red cells left in box five. And then we then we use the zero row and put a crust in there. And that really has changed the game. Right, I've only got two red potentials left in box six. Now I've got my two in column seven. So everything else in that column is green.

[00:08:17]I've got my two in row five.

[00:08:22]Now, in a moment, I'm going to be able to use the clues with numbers in. Well, I can here. These two can't be read. In fact, all three of these can't be read because the sum of the sandwich in this column is 18. You can't put nine in a sandwich because nine's always a crust.

[00:08:40]So, 8 and seven is the minimum two cell sandwich. And that means the 18 cell sandwich, the 18 sandwich is at least three cells and it doesn't go north. It must go south. That's a crust. These are green. These are now the two remaining crusts in the column. We've had all the crusts in row two.

[00:09:04]Uh we've got a 16 in this column. And that's going to stop this being red and this being red because obviously actually the sandwich is at least three cells for 16 or 18. So that goes red.

[00:09:17]That's the second one in the row. We're going to have all the crusts completed in a Well, maybe not. Yes, here's the second one in box four. And this column needs a sandwich of 18, which is at least three cells. We've had the two crusts in this row. So there's the remaining crust in box one. That's a crust and that's a crust. And there we go. So I'm now going to get rid of the green. All the reds are our crusts.

[00:09:45]They're all ones and nines. In fact, let's fill them all in as one nine pairs.

[00:09:55]And now we can maybe we we've dealt with all the zeros obviously.

[00:10:02]We've got 16 here.

[00:10:07]Uh there are a number of ways that can break down. 8 6 2 8 53 7 6 3 754 are the four ways. Here it's a four cell and that's different. Oh that digit can't be one or nine anymore. That is 2, three, seven or eight. Oh, this sandwich row is eight. So, I can fill in my first digit in the puzzle after seven minutes.

[00:10:39]Three of which were just not realizing the absolute basics of between lines.

[00:10:45]Now, eight there.

[00:10:50]This is quite interesting because the circles can't be one or nine.

[00:10:55]So, the closest they can be together is 2 and 8.

[00:11:01]And these three, four, five, six, seven are available. In fact, I'm going to pencil mark those.

[00:11:11]Ah, neither of those circles can be an eight because of where this is. That is a very elegant elegant um bit of setting. So I think the maximum difference between those circles occurs if they are two and seven and then everything on the line is 3, four, five, and six. And since we know there are four on the line in this row, that must be what happens. So this is a 27 pair in this row. Now eight is in one of these cells and the other digit from two or seven that one.

[00:11:47]Yeah, that's nice. I like that. Um, haven't quite understood how we're going to figure out any of these 18 sandwiches yet. Even this one, which is just three cells, this long line would be a lot easier if it was like this and couldn't have one or nine in any circle, but clearly it can do what's left in box eight. Perhaps we've had three from 3 4 5 6. We've definitely have have had eight used here. These can include one digit from 2 and 7 and one digit from 3 4 5 6. So I think they're either a 2 six pair with 345 here or a 3 seven pair with 456 here. I think that is right. These are either two 7 or 38.

[00:12:59]And that means this is a 2 3 78 quad and these digits are 456.

[00:13:07]So weird. I think that's right though.

[00:13:14]Now those are quite interesting digits.

[00:13:16]Four and five are here along with either three or six. What's going to go here?

[00:13:35]What I'm trying to get at is does this now have to somehow be two or eight?

[00:13:40]Yes. Uh, no. I was going to say whatever that is must go here. That might not be true if it's a three going here in the case that this is a 27 pair.

[00:13:55]Yeah, that was close. Um, but I can't make that grand presumption.

[00:14:12]I'm feeling a bit tempted to start coloring these digits by high and low. I it might be quite difficult to do though.

[00:14:31]Do I know anything else I can do? And the answer to that is probably not.

[00:14:40]I'm finding it very difficult to think of a way of getting to the nub of what is high and what is low in this puzzle because I mean I'm not really getting any. I suppose this digit sees both the two and the seven and also eight and one nine pair. So that is from 3 4 5 6 as well.

[00:15:03]That's slightly interesting.

[00:15:12]Oh, there we go. Sorry. This 2378 pair has got a very big clue. Three is in one of these cells. And we said these are either 38 or 27. So, they are 38. No, no, that's not right.

[00:15:35]No, no, no. I've got this all wrong.

[00:15:37]I've got this all wrong. Bother. When I filled in these, I think correctly, I knew that eight was down here, but I never marked that. So, these are either 37 with those being 456 or 26.

[00:15:58]I mismarked them, didn't I? That's why it's not as easy as what I was just doing.

[00:16:07]These are either 2 six or 37.

[00:16:10]So between those cells and those cells, two and seven are going to be used up.

[00:16:14]But they are not a quad. And three doesn't have to be in this group.

[00:16:21]And if it was in this pair, this would be 37.

[00:16:29]And that would be fine. Right? I'm going back to my mark my my coloring plan.

[00:16:33]Let's make this green. Now, that could be high or low. This is the other color.

[00:16:38]So, I'm going to make it pink because one of these is high and one of these is low. Now, the green digit from 27 is in one of those.

[00:16:51]And the pink digit from 27 is in one of these cells along with a digit that I'm going to call light blue. that is not that is the same polarity, the same high or low as green, but is a different digit. So if green's a seven, the blue digit here is a six.

[00:17:12]If green's a two, the blue digit here is a three.

[00:17:19][snorts] And I don't quite know how I think this is going to help me, but it might do.

[00:17:24]Pink is in one of those cells. This light blue could be there or here. So now I was going to look up at this and go this can't be green 2 or 7. So if it's light blue it's three or six. [snorts] But if it had to be ah th this cell's interesting in this row these cells sorry these cells are all inside the relationship between these two digits and this is the only one that isn't one or nine that's outside that relationship.

[00:18:18]Yes, this is this is very important. So if that's a one, this one is a seven and that digit is eight.

[00:18:31]And that won't work because that would need a nine in one of these circles and they don't have it.

[00:18:43]Am I wrong about this? I might be wrong about this. I was then thinking I am wrong about it because it also doesn't work the other way round. That's really interesting actually. So if that was a nine, I was saying this would be a three and that would be a two.

[00:19:02]But that doesn't work either because you can't put one in these circles. So I've I've misunderstood. But that's okay because it it allows me to see what I've misunderstood. This is a quite extreme digit. It's either green or pink.

[00:19:16]And that means that this doesn't have to be outside.

[00:19:21]It could have been inside. It could have been one of the between digits because there are six of them. That's how this can exist since we know it's not two or eight. I mean, we literally know that these digits aren't 2 or eight because they couldn't have the the requisite 1 or nine in a circle. They are from 3 4 5 6 or seven. And I think therefore naturally they have to be inside this relationship.

[00:19:52]And therefore this is extreme as extreme as it can be which is to make it two or seven. And now we can color it as pink.

[00:20:03]And that means this sees both two and seven and can't be a seven.

[00:20:10]No no no no no. Two and seven not the extreme digits. Mark, two and eight are the extreme digits and we can't color it. Two and seven are different things that happen down here. Not to see eight.

[00:20:23]They're not equivalent. Right. That is two or eight and it's much less helpful except that we do know where it goes in this box. Now that's brilliant. It goes here. I can't color it at all because I don't even know which of green or pink is a two and eight I haven't even assigned a color.

[00:20:50]Okay, but I'm back on track a bit now.

[00:20:54]These are so oh whatever that digit is can't be on its own line here.

[00:21:02]So, it's in one of those three, which I could have worked out from the fact that it's in these two cells.

[00:21:14]I I know I am so dense at this. It I wish I wasn't as well, but there we go.

[00:21:30]Well, in a way, eight has become a digit of interest. And maybe I should start thinking about this short 18 clue.

[00:21:39]Could it avoid having an eight in? The answer is yes. If it was 765 here in these cells, that's the only way.

[00:21:58]And the trouble is I just don't know if that if that is the case or not. I mean I could say green is in one of these two. I haven't said that before but it is. And therefore these digits can't involve two or seven. They do involve eight because that eight is looking at those cells and we've got these to think about.

[00:22:22]But they don't involve two or seven. So the other possible digits here are from 3 4 5 6.

[00:22:33]Now we worked out that these include four and five.

[00:22:38]So these cells definitely include seven, which is something rather unexpected.

[00:22:48]they include the other digit from 2 or 8 that isn't this one.

[00:22:55]So these have to be from 3, four, five, and six.

[00:23:03]And either three or six is in this group with seven and the other digit from two and eight.

[00:23:12]That can't be seven anymore. This digit here can't be seven. Now if that is seven, eight is going in one of these circles.

[00:23:26]Ah, this group. Yes, this group adds to 16. I don't think we can put an eight in it because the other three cells would have to add to eight. And you can't do that without a one. So this digit is a two. There's my second digit in the puzzle, which has taken even longer than the first digit took. That's now where two goes in box two. Uh, box five. One of these is a two. This is not a two down here.

[00:23:56]This is a nine because two and one won't work. So, that might unwind all my red cells and vastly populate the grid with digits that I didn't have before.

[00:24:11]It's great. It's great. It's unwinding all the reds. Look at that. Absolutely beautiful. They're all done after that.

[00:24:21]Uh, and are any of them in circles? No.

[00:24:25]Only that one. So, it doesn't achieve anything else for the puzzle. But that two is now looking at this cell, making it a seven. Green is a seven. This is a two. This is not a two. This pair is seven and eight.

[00:24:41]That two is looking at Oh, sorry. I wasn't trying to hit enter. I was trying to get rid of a two from that cell. One of these is a two.

[00:24:52]There's a seven in one of those two.

[00:24:54]This 78 pair has determined this pair.

[00:24:58]There's no seven in them. So, they are two and six. So, that these can be three four five.

[00:25:05]And now these group the these cells are six seven eight that takes six out of the other cells in the row.

[00:25:15]Ah this is good. Now six has come off this line. These digits are 3 4 5.

[00:25:25]One of these what was pink? It's a two.

[00:25:32]Seven is looking at that cell as well making it very suggestive that seven will end up in one of these circles but that that's not given at all. Now these add up to 16. So in the column as a whole 16 there plus 9 and 1 is 26 + 7 is 33. That's going to leave these two in the column to add up to 12 because I'm sure you know the secret that every row column or box in a sodoku adds up to 45.

[00:25:59]For these two to be 12, they can't both be sixes. They can't be 57 because we've already had a seven. They can't be 3 9 because we know that's not a nine. So, this is a four and that's an eight. And they're just done.

[00:26:14]This is now not four. That four comes out of these which are 356 triple 3562.

[00:26:25]Let's just check they add up to 16 in our head. They do. That's definitely right.

[00:26:33]This is a 26 pair as far as I can see by Sudoku. I'm going to get rid of the colors I was using I think cuz I mean it's they've done their job.

[00:26:46]This is a 35 pair in the row. This is a 47 pair. I've somehow never written this in as a two. I thought I did earlier.

[00:26:55]Maybe maybe I went backwards after I clicked the tick or whatever I did. That is three or five four seven. So this is a 345 triple.

[00:27:09]This is a 345 triple as well.

[00:27:13]So this digit can't be 2 or 8 because it's circle can't be 1 or nine.

[00:27:22]Can't get outside it. So two is in one of Well, this can't be two or eight. So it's six or seven.

[00:27:31]If it was seven, eight's in a circle.

[00:27:37]Um, now we've got an 18 clue here. Oh, let's add up. 18 + 10 is 28. These three add to 17.

[00:27:57]That's quite high. Is it 872?

[00:28:01]No. There's quite a lot of possibilities.

[00:28:08]872 863 854 764. Those are all the possibilities, right? That two is looking at this cell.

[00:28:21]I was going to get rid of these colors.

[00:28:22]Don't know how that failed. Right.

[00:28:24]That's a six. That's a two.

[00:28:29]Six is looking at this cell. That's a 78 pair. This is three, four, or five. So that is the low end here on on this between line. This must be the high end.

[00:28:40]Must be seven or eight. But we've got eight looking at it. So that's a seven.

[00:28:44]That's a six.

[00:28:46]And now we found six [snorts] in the central box.

[00:28:52]Um, this group adds to 18. If that was a four, this would have to be a 68 pair.

[00:29:04]Oh, can this be a two?

[00:29:07]No, because these two would have to add to 16, and we can't use a nine. So, that's not two. This is now two.

[00:29:14]One of these is two.

[00:29:18]Four does work there. If it was a seven, I'm sure we can make 11 here with either 65 or 83.

[00:29:32]Still got this sandwich. We've got this sandwich to do, which I haven't really spent any time thinking about yet, but it seemed to have a lot of possibilities when I was thinking about it earlier. So, I'm not thrilled. We're okay. This column six and 345. The four in this column is in one of those two cells. So, this isn't a four.

[00:29:57]These include two and either seven or eight.

[00:30:08]Uh maybe I should think about this which can't have a two in a circle and therefore it can't have three on its line.

[00:30:20]That's good. That's a bit good. One of these two digits in this row now is a three.

[00:30:32]One of these circles is either three or four at the low end and the other one could be six or seven or eight at the high end. That's not so helpful.

[00:30:53]278 triple. That's quite good fun. Uh 6192 I don't know. And there's this between line that I haven't looked at at all. I mean, it just looks frankly a bit scary. Oh, maybe it's not. Maybe it's not. This digit can't be 2 or 8 because of the between line and it can't be 76 or 9. So, it is 3, four or five.

[00:31:27]Now there is a lower digit in one of these. Can that avoid being two is my question.

[00:31:37]If it was three, the lower digit here, this would be a four, five, six triple, we'd have 278 to fit in amongst those cells and the higher one here. And actually, yes, I think that is doable.

[00:31:53]But maybe this is going to play with. So what did I say? I said those added up to 28. These add up to 17. And we've now got a three, four or five here. If that was a three, these would be 68 and that would be two.

[00:32:15]And these would be broken.

[00:32:19]Right? My calculation of this column is that the green cells add up to 18 cuz that's the clue. The reds add up to 10 and the light blues add up to 17. If I was to put a three in the corner here, my only chance of three in the corner in this puzzle, these digits to add up to another 14 to make the 17 total would have to be 68. And that would break these cells. So, that's not a three and and that's not that's not quite as useful as I wanted it to be.

[00:33:00]But but let's let's carry on with the possibilities. If that's a a four, these add up to 13, but they can't be 94.

[00:33:15]They would either be 67 or 58.

[00:33:30]Yeah, I I I can't I can't say they're not I haven't I haven't got enough information.

[00:33:39]Oh, bother. Okay. [snorts] >> [laughter] >> I'm gonna have to think about this one again, maybe. Oh, it's so weird.

[00:33:54]Right. What's going on on this? One of them is low, but that could be 2, three, or four. One of them is high, but that could be six, seven, or eight.

[00:34:08][snorts] Neither of them can be a two.

[00:34:10]that much we know and I've used that already.

[00:34:21]Sorry, I don't know what to do next. Um, this 18 sum, right? If that was a four, ah, there'd be nowhere for seven in the column. Oh, that's really interesting. If this digit was a four, these would have to add to 14 and be 68.

[00:34:42]And now that we've got that seven and we haven't allowed a seven here, there'd be nowhere for seven in this column. So that is a seven and it is indeed the seven in the column. Now one of these two digits is a seven by sudoku. But more importantly perhaps these add up to 11 and they can't be 74.

[00:35:00]They're either 65 or 38.

[00:35:06]If they were 65, this would be a three down here. And this would be 248.

[00:35:14]And this would be a ah they there is a three in one of those cells. That's what we established. That's what the three in the corner means. So these aren't 38.

[00:35:23]They are 65. This digit down here is a three. And now we're getting quite a bit done down here. That five gets placed in the middle box.

[00:35:36]Yes, that five sorts out the 65 that we just got. Now that has to be a three four pair. This digit is a five. I was going to say that makes this a six. It doesn't do that at all. It stops this being a five.

[00:35:53]This is now a 78 pair in the box. That's become a five. I hadn't noticed that.

[00:35:58]This has become a three. Yes, this has done a huge amount. It was this group that I saw early on. That's a 248. This is a 35 pair.

[00:36:12]9521 1 9526.

[00:36:18]These are from 3 478.

[00:36:24]Little bit surprised this is all going to get unwound. Five is looking up to the top cell here which is therefore three or four.

[00:36:34]In this top row we have 2 3 4 5 8 all to place. Okay. Maybe I'm going to have to come to this line. I mean five didn't really help me.

[00:36:56]I don't know.

[00:36:57]So, I've done the 18 clue here. Now, it was 567.

[00:37:02]I've done the 16 clue here. This green 18 clue I've not done at all. Ah, this 16 clue. Let's make it pink. I have not done that. If this digit was a three.

[00:37:16]Yeah, that doesn't work. We would need another odd digit and an even. In fact, after this digit, which is odd, we need one more odd and an even. So, that must be odd cuz this one can't be. So, we've got seven there.

[00:37:33]These now add up to nine. And it looks like 54 is the only way they can be. And that's really useful. That's two. That's eight. That's seven.

[00:37:44]87. Right, that is done. And that is very important.

[00:37:49]This is three or eight by Sudoku.

[00:37:54]These are from 2368. I'm not going to get overwhelmed with working out what they are. These are done. Eight and two.

[00:38:03]That is not done in this row. This has become a five. That is the most unhelpful digit possible. That's four though. That's seven. This does look like it's beginning to be helpful in this column. Yes, three and four are done. And that now is an eight. And this is a five. And that's a three in the box, which is finished. And this is four in the corner. That's an eight.

[00:38:27]And these are a 2 three six triple. So six now has to be in one of the circles to justify this. So that's a three. And now the circles are a two six pair.

[00:38:39]We've also got two six pair in column one. Oh, but these blues had to add up to 17 to make this column work. And we've got 11. So that's a six.

[00:38:51]That gives us this two six pair down here. This has become a six by Sudoku. These three five are done. This is a 38 pair that I can't resolve. I must be able to resolve this pair.

[00:39:06]I can't. And therefore, oh, it's this circle. I can resolve that. That was an eight. So this is a three.

[00:39:16]That does get everything else done.

[00:39:18]Otherwise, it would have been a deadly pattern. Okay, let's get rid of the coloring of those clues cuz job done.

[00:39:26]And indeed, job done on the whole puzzle. Lovely puzzle sandwiched between Sudoku by the scrass and I have enjoyed that a lot. That's a very very good one.

[00:39:37]Thank you for watching us on the channel as always. Pleasure to have you with us and do come back for more tomorrow. Bye for now.

[00:39:45]>> [music]