Simple Arithmetic? Well, Yes, But ...

Added: 2026-05-20

[00:00:14]Hello. Welcome back to Cracking the Cryptic and uh a puzzle with some arithmetical symbols in the grid today by Valdronius. A new name to the channel. Welcome Valdronius. And I'm going to have a look at this in a minute. Um, I am going to tell you it may still just be time to get your entry in for the Spider-Man Sudoku, which is our hunt for the month and is available on Patreon where we also have um some tough crosswords. Simon has a go at Oscar Johansson's this month and later in the month it has been postponed. My um monthly club special will be coming. Um, and there are also gridoggram and connections videos on Patreon. It's great fun. Loads of good stuff. We've also got apps which feature um Domino Sedoku and Classic Sodoku too and the worms including Blobs's Worm. That's fabulous. We've got uh what else have we got? We've got a bit of merch as well.

[00:01:15]So, check that out too. All good fun.

[00:01:18]The links under the video will take you to all of that as well as to this puzzle, Simple Arithmetic by Valdronius.

[00:01:24]I'm going to go through the rules in a moment. What I'm going to say first about the symbols is that we're not going to sit here and complain that they're quite big and black and will fill the cells and obscure some of the numbers we're we're using cuz that's choice and Valdronius is the creator of this puzzle and has worked very hard to give us a sedoku we can solve and it's up to them right the rules are these normal sedoka rules apply one to nine will go in every row column and 3x3 box.

[00:01:56]Any cell marked with a plus, minus, times star or divide slash is the sum, difference, product or quotient respectively of the two orthogonal cells either vertically or hor horizontally beside.

[00:02:14]So this star is either the sum of those two cells uh sorry the product of those two cells or the product of those two and this plus must be the product of those two because it doesn't have a horizontal pair. All such cells have been marked except where a cell qualifies for two marks and in this case only one mark is shown. Well, I'm the only one, Mark, who's going to be trying this puzzle in front of you. I understand those rules. I hope you do.

[00:02:46]Let's get cracking.

[00:02:50]So, I think the cells within the center of the puzzle are harder to use than the ones on the perimeter.

[00:03:00]So, I'm hoping to start with those because we know where the where the pairs are. So for this star, right, we can't use a one as a factor on one of the in. So these two yellow cells must multiply together to give this star digit because it doesn't have a vertical one obviously. Now we can't use a one there or the other two digits, the yellow, the remaining yellow and the star would be the same digit and that would break sodoku rules. So we must be multiplying two by either three or four otherwise we're going to get out of sodoku range and 2x 3 is 6 2x 4 is 8 so that's what we must be getting there. Now this star is very similarly multiplying 2x 3 or 2x4 because the same strictures apply to not using ones for that one. However, we don't know whether it's those two cells being a two and a three or a two and a four or those two.

[00:04:07]We do however know that the output, the result, the product is another six or eight. So, we have a pair and yeah, I don't know.

[00:04:25]Okay, one of these cells is going to be a two. That's not very interesting information, is it?

[00:04:39]Yeah, it's definitely easier to Right.

[00:04:41]Let's look at the divide that's on the perimeter. So, I think the same stuff applies. We can't use a one because that would make a digit repeat in this divide sum.

[00:04:56]So again it's 2 * 4 is 8 or 2 * 3 is 6 but this time well the product the the the quotient the result of the division is 2 3 or 4.

[00:05:12]Ah that's harder it's not as useful because the factor and the other divisor are or the the multiple and the divisor are selected from 2 3 4 6 8. So, I know that one of these digits is a two. I mean, I suppose I know that one of these yellow cells is a two, but that doesn't really help much with this plus.

[00:05:38]Yeah, this is weird. It's difficult to get started. Valdronius, well done. I thought this would be just, oh, we attack it and we find some things and we we get going. It's not. It's quite hard to start.

[00:05:53]Okay.

[00:06:00]Is there something about even digits down here? These two cells are definitely even.

[00:06:13]So, the only remaining even digits I have left that could be involved in this plus are two and four.

[00:06:27]Right. The plus is not where I said that around this 6 or 8 there must be a two in one of those cells in this box. It's not there because that would then be the result of 1 + 1 and that would put two ones in the same box and column. So the two in this box is in one of these three cells acting to create this 6 or 8 uh product.

[00:06:57]That means that the only even digit available for this sum is a four. Now this is very significant or it's a bit significant because we need an even digit in this sum. We can't have two odds added together equaling odd. So there is a real parity issue here. We must have four in this group and it's either odd plus odd equals 4 and we could work out how that would work or it's odd + 4 equals odd.

[00:07:30]But it means this digit is not four.

[00:07:32]Now, it doesn't mean that this doesn't have four in its factors cuz it could be four there and two here giving eight and then this would be 3 6 2 and that is possible.

[00:07:52]In fact, if Oh no, that is not possible because if we had four there giving eight and two here, we would need a one three pair there. So we could not have three here. So this is not the four. The four unsurprisingly is one of the addends here. We're adding it to something else and getting an odd total that is 5 7 or 9. We're adding it to 1 3 or five and getting five 7 or 9 there.

[00:08:25]This is where it's a little difficult to read the candidate numbers because of the the thick black lines, but that's fine.

[00:08:34]Um, now now we know that this is a product of 2 * 3 cuz it doesn't use the four and the 2 * 3 can't be that side.

[00:08:45]So, it must be up and down. Two and three there gives six here. This digit is now eight. So, these have to be two and four. And that one is two. And this one is four. That is a lovely beginning actually. That's really neat. So we've got started now.

[00:09:02]Now maybe we know more about this cuz we're not using three in it now. So 4 + 1 = 5. We're not going to get a seven in the center. That's the point of that.

[00:09:13]We're either going to get four and one here or four and five here adding up to five or nine here. And seven's going to be in one of those cells.

[00:09:22]Now, this plus is the only one where we know in this bottom row where we've obviously I'm going to mark off as orange when we've actually done um a sign cell. This one we haven't done.

[00:09:40]4 + this equals this. We've only got one even number. Oh, look. We can actually place four in box what's it? Box seven.

[00:09:51]So, oh well that's good because now that has revealed that this is not 4 + 1 equals 5 because then we couldn't fill in this cell.

[00:10:02]It can't be there can't be another even number involved here or we'd need two of them and we've only got six available.

[00:10:09]So, this is odd and we've just discovered it's not one. It's three or five and this um sum is seven or nine.

[00:10:23]I'm utterly scared to move on to something like this because I'm just going to look at that four and go, "Oh, we have to add something here to get that." We don't necessarily because this could be adding side by side digits and and I'm very scared of just botching which way round the sum is.

[00:10:49]But I am running out of actual information or anything I can do. There is clearly a six in one of these cells.

[00:10:56]Oh, so therefore there's a six in one of these cells.

[00:11:03]Um, that's not as Oh, six would. If it's in a minus, it's going to be surrounded by either 93, 82, or 71 in one direction.

[00:11:22]Yeah, that isn't easy.

[00:11:26]If six was here, this plus would have to be taking the digits side by side.

[00:11:34]because four and six equals 10. So that wouldn't be giving this sum. Oh goodness. I don't know. Oh, okay.

[00:11:43]Right. There's this overlap here, isn't there? So, one of these divided by the other gives that. But that or that one of those is subtracted from the other to give this.

[00:12:02]I might have to work through all the possibilities. So no, I mean that's that's very interesting straight away. If I wanted to make this digit a four, these would be eight and two to give the right division.

[00:12:22]Now, if that was a four and this was an eight, this just doesn't make sense. You can't subtract four from something or something from four to give eight.

[00:12:33]So, if that's a four and that's a two.

[00:12:37]Oh, bother. You could put a six here.

[00:12:39]Oh, I thought I'd ruled out four.

[00:12:42]I haven't. If that's a four, this is going to have to be two. And this could be six.

[00:12:54]Okay. Well, that's possible. So, it would go 8 4 2 6 in that case. If this is three, this has to be two or six.

[00:13:04]If it's two, that could be one or five. If it's six, this could be eight.

[00:13:15]H I haven't ruled anything out. And if this is two, I suspect there are lots of options.

[00:13:23]H not so many. But I think 8 2 4 6 would still work. Yeah, I don't know. That is not what I'm meant to be doing next.

[00:13:32]That's horrific.

[00:13:35]I find this very difficult. Maybe I need to go to these divide signs, which must always be like this one. It doesn't matter whether they're going vertical or horizontal. They must have two, three, or four on the divide sign. And they must then be flanked in one direction or another. Oh, that one can't be four.

[00:13:59]Um, but it could be either. Well, this sum uh it doesn't have to be vertical. It could be horizontal.

[00:14:08]If it was vertical, these digits would be 6, three, and two.

[00:14:19]Oh, then what about this? Then we couldn't that would be nine with a five here or five with a one. I don't know.

[00:14:33]Oh, this puzzle's hard. It's going to be about using things that are next to each other or something.

[00:14:43]Wow. I do not know.

[00:14:46]I do not know how this puzzle is meant to function at all. Even though I've done some digits and got a start.

[00:15:00]Is it about par again? I mean, is it?

[00:15:03]No, because I'm looking at this row and just assuming they're all vert horizontal horizontal maths and that's just not necessarily right.

[00:15:19]Oh, there's the negative constraint.

[00:15:22]All such sums have been marked.

[00:15:26]Oh man, I didn't think about that yet.

[00:15:30]And that's terrifying.

[00:15:33]How am I meant to be using that?

[00:15:38]Surely not yet.

[00:15:46]Oh, this is going to be terrible if I have to think about stuff like the negative constraint throughout.

[00:15:59]I mean, this isn't ruled out on this sum. I don't think at all.

[00:16:08]Gosh.

[00:16:16]I suppose look, this can't be a one. Oh, this can't be a seven because that three would have a minus sign. Oh my word, this is going to get hard in a hurry.

[00:16:30]Right, this can't be one as I just said both for that sum and for that sum because there is a relation between them.

[00:16:39]So it's five or nine and this is the only place for one in the box and this digit on the plus becomes five and that digit becomes nine and we've suddenly finished the box and we've done that five sum.

[00:16:52]Oh, this is going to be Oh, I'm horrified by the puzzle now. Right, this plus if it was a horizontal sum, we'd have a nine here and a two here or an eight here and a one here.

[00:17:10]If it's a vertical sum, right, this digit has to be more than seven or four, whether it's horizontal or vertical. So, it is 8 or 9. If it was eight, we've definitely got a one here because 4 84 is not allowed.

[00:17:25]So if it's eight, we've got a one here.

[00:17:27]If it's a nine, we've either got a two here or a five here.

[00:17:41]Oh, this this plus can't be going vertically because of that nine. So, it's definitely adding those two cells to make it.

[00:17:53]Um, right.

[00:17:55]That's I mean, this is interesting, but my goodness, it's still terrifying. This digit, for instance, can't be nine because of that grouping. And nor can this.

[00:18:09]Oh, well, nine can't go on a minus, actually. Well, those those are really important facts. Suddenly this this can't be nine cuz that would be a minus.

[00:18:18]This can't be nine cuz that would be a minus. Nine can't go on a minus cuz it can never be one digit minus another. So by sudoku suddenly and and that bit of rule. This digit is nine. And now this is well these two add up to nine to make this minus work. And they're not 54 and they're not 18. They're either 36 or 27 where I don't I don't know which is larger and which is smaller.

[00:18:55]Oh, the negative constraint. I mean, this is going to be a beast of a puzzle, isn't it?

[00:19:02]Well, of course it is.

[00:19:06]But it's interesting to note that nine can't be on a minus because there's quite a few places where that matters in this.

[00:19:14]Um, well, I don't know. Maybe I ran out of them quite quickly there. Okay. If this digit is a nine, that's a five, this is eight, that's one.

[00:19:31]Then this is three by Sudoku.

[00:19:34]And then these are 2, six, and seven.

[00:19:37]And we can't make this minus work. So this is not a nine. This is a seven.

[00:19:43]That's a three. We've done this cell.

[00:19:48]That's crazy. But now nine is in one of these three. But much more importantly, five and six are in this pair. And this digit must be in a sum with five and six. So they now have to be 1 56 in which the middle digit is not six.

[00:20:08]Oh, this is crazy. This is I mean that's really clever, right?

[00:20:14]These cells now are part of a 289 triple.

[00:20:19]That eight or nine is either being con completed by a five there or a two here.

[00:20:26]And it can't be eight, I don't believe, anymore. So that's a nine.

[00:20:32]But I don't know whether this is a two or that's a five. I can't tell that.

[00:20:39]Unless there's some way I can tell.

[00:20:41]Okay, this can't be a five because then this group of cells is either 583 and we'd have a plus here or 523 and we'd have a minus here. The negative constraint is massive. I did not expect that.

[00:20:56]Look at this. This can't go 187 or 527.

[00:21:03]So, it's either 12 or 58 here.

[00:21:07]Oh, that's crazy. Oh, this can't be 326 or 321. 326 would get a divide here and 321 would get a minus. So, that digit's eight. This is two. This can't be five and is one.

[00:21:24]This must be six by Sudoku. now. And that's a five. And now this is done either way. It's a plus either way. That crazy cell, right? This has been done.

[00:21:38]Oh, I messed up. I messed up big time.

[00:21:43]I assumed this was a horizontal minus sign. Right. Right. I noticed that I messed up at least. Let's go back.

[00:21:54]Yeah, I went back all this way, didn't I? I In fact, that's how I decided this was seven. I said if this was nine, this is three, this is eight.

[00:22:09]This must be one to complete the eight.

[00:22:12]4 9 5 8 1 have gone by Sudoku. That's a three. And then I said this can't be 267 because I was assuming this was doing a horizontal sum. that is not available to me as a method. So I have to be much more careful. Okay.

[00:22:31]But these these negative constraints, they're huge. This digit can't be a six because that would have a plus in it.

[00:22:38]So one of these is a six.

[00:22:42]I mean that's positive positive constraint is barely any use with these interior ones. Ah, it's such a difficult puzzle now. I realize that now. I'm getting it. Vronius gradually I'm getting it but it's difficult it's difficult to get it right five six seven I mean this is hard so I'm going to briefly think about this seven problem again if that was a seven no if that was a nine This is five. That's eight. This is one.

[00:23:29]This is three by Sudoku.

[00:23:33]So we've got 8 1 3 in that hypothesis.

[00:23:44]A nine here 95 813.

[00:23:50]So these would be 267 that that couldn't be a 27 pair because 927 would create a s an equation.

[00:24:02]So this would have to be six.

[00:24:06]It would be sitting between two and seven.

[00:24:09]But it would be sitting above a one and that would be six. This would have to be seven and that would then have to be getting it sevenness from a sum to the side. Oh, this is so complicated. I mean, I'm looking ahead a long way there and it's just difficult. It's difficult to achieve it.

[00:24:46]Okay, this digit can't be 9, 8, or 7, but it's the sum of two cells. So, it's 3, four, five, or six. And these ones are low. They're from 1 2 3 4 5 on this side. Must be 1 four or five. On this side, 1 2 3 or five.

[00:25:06]Now, this cannot be that times that because it just can't be big enough.

[00:25:16]on these divides, we've got to have a six or an eight on one side or the other.

[00:25:22]So that's on this side. This digit is Oh, no, no, no. There's me assuming that this has a vertical sum. That's not known. Oh gosh, that is not known.

[00:25:44]I It's It's weird that I was able to predict the problem I was going to have with this puzzle and then I've been constantly having that problem of looking at these interior signs and assuming I know which way they do the math.

[00:25:59]I just don't.

[00:26:01]Okay, let's come back here then.

[00:26:05]I mean, I've got nothing. I've got nothing. There's a six in one of those cells. I've got to use this negative constraint incredibly hard. I really have got to.

[00:26:20]But I don't I don't know what I can do with it. There's a six in one of those.

[00:26:25]There's a four in one of these.

[00:26:30]This trio uses either six or four.

[00:26:47]This digit can't be the complement of 3, four, five, and six in a nine sum.

[00:26:53]No, it could be. Oh, that's weird. That Yes, that trio. Then we'd have the situation where only one mark is shown in that cell. So, it can be in fact. Oh wow.

[00:27:08]I hadn't allowed for that.

[00:27:13]Oh, I would quite like to Yeah, that's that's strange. I would quite like to say that this digit can't be six or eight because that would at least make one of these two six or eight. But this might be able to be six.

[00:27:37]This would be a 23 pair if the if the sum went horizontally there.

[00:27:49]I'm sorry if you if you understand how this works and you're getting wildly frustrated with me.

[00:27:56]Well, there we go. But I have to I have to get through it at my own pace.

[00:28:00]Otherwise, I just don't get through it.

[00:28:02]So there's no real apology available, right? There's an eight in one of these two cells. That's quite a big deal. That eight, wherever it is, has to be between 9 and one.

[00:28:24]It can't be in this cell I'm in because you can't put 91 there or there.

[00:28:30]So the eight is not there. This is the eight. Now it's either going to put a one there or a one here and a nine there. So one of these two is a one.

[00:28:41]That's what we learned there. This cell now can't be a one.

[00:28:46]And this plus which I have to be adding across is going to require a five or a six sum and one or two in this cell.

[00:29:00]Uh, this digit can't be eight anymore by Sudoku.

[00:29:08]Now, there's a one in one of those cells to deal with this.

[00:29:18]Now, negative constraint. That's what I should be thinking about a bit.

[00:29:27]For this to be a two, this has to go 4 6 2 that would be three. H I always think I know that that means what this is, but I don't.

[00:29:45]eight minus that is that I know that eight is the biggest number in these in this trio because nine's gone. So these two do add up to eight in some means by some means. Um I don't know how eight on a minus sign. That's a powerful thing, isn't it? I mean, it just is.

[00:30:24]Right.

[00:30:26]Let's just keep going. Um, I've got a nine in one of these cells.

[00:30:34]It might have to be here if this was a one.

[00:30:46]Okay. Interestingly, if this was a one, this digit couldn't be four because of this trio and no symbol there. So, it would be five.

[00:30:56]And this would then be six. And this would be one. Over here we'd have one, five, six. This would be a two, seven pair. These would be three and four.

[00:31:12]I don't know. It's not impossible, I think. But it is interesting.

[00:31:19]I'd know. Uh, no. I wouldn't know the order of three and four based on this not being a minus because it's a plus.

[00:31:29]I would know the order of three and four based on these two adding up to eight actually.

[00:31:35]Oh, that'll be quite interesting.

[00:31:41]Right. If this is one, this has to be five by the negative constraint. Then we get a six here. We've got two seven pair over this side.

[00:31:52]This is three and this is four. This is five. This now can't be using the five. So, it must do a horizontal thing and it must go 428.

[00:32:12]That feels like it's not impossible, but it would be quite powerful one way or the other, wouldn't it?

[00:32:23]Goodness me, this puzzle. This puzzle is going to do my head in badly.

[00:32:38]This digit is a minus thing.

[00:32:42]Ah, it can't be going up and down because that would either be a four four pair or there'd be a three there and three there. Is that right? Yeah, it is.

[00:32:52]It is. Uh, yes. So, this isn't going up and down. This is going side and side.

[00:32:58]So, those two subtract one from the other to get that.

[00:33:04]I mean this may not particularly help but it's worth noting that we have got a relationship between those three digits.

[00:33:20]Oh my goodness. This is crazy hard.

[00:33:25]I did not expect this workout from this puzzle. It is insanely hard to understand how to do it.

[00:33:36]98.

[00:33:38]Um, we've got an eight in one of these cells.

[00:33:47]I mean, there is a whole bunch of negative constraint in this puzzle. Wow.

[00:33:51]It's incredible how much there is.

[00:34:00]I do I do want to get through. I do want to understand it. It's going to take ages. This is going to be a very long video. What are we half an hour in already to the solve? Oh goodness.

[00:34:11]Right. Can this be a seven? The answer is no because it's surroundings would either have to be an 81 pair or a 29 pair and that's not possible with them having gone. So this isn't seven. So the seven in the box is in one of these two cells which we know add up to nine. So now we know they're a 72 pair. And that gives us a 368 triple up here.

[00:34:38]9827 3 is now in one of these two cells by Sudoku.

[00:34:52]This is the subtraction of a two or a seven.

[00:35:00]Well, if that was a two, clearly these two add up to that. But that can't be anything bigger than six.

[00:35:11]So, this would either be 2 46.

[00:35:15]It can't be 213 because that would break this cell. But it could be two. Oh, it can't be 235 either because that would also break this cell.

[00:35:24]So this would have to be 2 4 6 and that breaks these because they both become five. So I actually think this can't be a two now.

[00:35:38]Right, let's go through that again.

[00:35:42]This is definitely doing a horizontal sum. It's the it's the minus of one of these light blues versus the other.

[00:35:50]If that was a two, this is not the highest digit in the sum. This is So those two add up to this. They can't be 213 or they break this. They can't be 235 or they break this.

[00:36:05]They must be 2 4 6. But that breaks this pair which both become five.

[00:36:14]They couldn't be 257 because if that was a two, 7 8 9 would be ruled out of that cell. So this is not two. This is seven.

[00:36:22]This is two.

[00:36:25]Seven is now the highest digit. It's the highest digit in the box available for this sum. So these two add up to seven.

[00:36:31]And they don't use two.

[00:36:34]So they're either 43 or six.

[00:36:44]Okay.

[00:36:49]What's that tortoise?

[00:36:56]If they were 43.

[00:36:59]Ah, goodness me. I was going to say that would be five. That would be six. We'd have 369 here. No good. But it is good.

[00:37:10]It's fine because there'd be a plus there because there couldn't be a minus.

[00:37:18]Wow. And that's if it was six. This would be four, five. This digit would be a three.

[00:37:31]That would definitely be a five at that point. Okay. What if it's 43 here? Then we've got 56 and that's a one. So this is either one or three.

[00:37:42]Right? Let's have a little think about this minus sign.

[00:37:51]It's either created by an eight there and a seven here, which would not be contributing to this sum.

[00:38:05]Or it could be a three here and a two here or a six. Now if this was six, that would be 5 4 1 3, right? In that case, we'd definitely have a five here cuz six three can't leave a six, a three or a nine here. Okay. So if that's a six, this is five. If this is a three, then this is a one.

[00:38:49]And this might be a seven, but it might be a two here instead. Oh. Ow. Right.

[00:38:56]This can't be a 3 six pair because 369 would form a minus here. So, one of those is eight and that's not eight at the top. I mean, this is absolute negative nonsense that I'm trying to do now. But there we go. If that was a one, I was going to say this couldn't be a seven or a nine, but this sum would be irrelevant because there is a minus in the middle cell. That is such a hard rule to get used to.

[00:39:29]Oh, if this was a four, this would be a one. And that would be a problem here because there'd have to be a plus here. So, it's not a four. Ah, it's simple when you see it. It's not simple till you do.

[00:39:43]Now, I filled in all those by sodoka. I can even fill in that and this by the yellows being added up. Those two sums are both fully done.

[00:39:53]This eight is done by 91. That one is going to be done by either a seven here or a two or a four here. That's quite a lot of optionality. This two can't be north south. It must be east west. This digit is a six.

[00:40:11]And that one's done now.

[00:40:14]Right. Well, that was a bunch of progress. These remaining cells in the row 1589.

[00:40:21]Now, here's me immediately assuming, oh, we have to have an 8 91 group here. But this could do could be going north south.

[00:40:30]1 126 that can't be a one in the same box.

[00:40:35]This is a minus sign, so it can't be a nine.

[00:40:40]Um, if it was an eight, it would have to be surrounded by 91 either there or there. Neither of those are possible because of this. So, that's a five.

[00:40:51]And this digit if that was an eight. Oh yeah, it would be surrounded by 91. Ah, right. Let's look at the five.

[00:41:00]Oh, that could be 61 or 4 9 3. I mean, there's all sorts of possibilities for that. Five.

[00:41:13]I just wanted to prove this was a one first. Oh, I could look at this now.

[00:41:22]that minus.

[00:41:26]Look, it could go 369.

[00:41:29]Oh, I thought at least I could rule out the higher digits from here somehow.

[00:41:40]2 3 69. That's so possible. It almost No, it's not. Okay, here's why that's not possible for this to be a six.

[00:41:52]This has to be okay. I was going to rule two. I am going to rule two out of this cell because this needs a two around it or to be a two because the the sum that's acting either there or there to give this quotient needs a two. It's either 2 48 or 236.

[00:42:19]And if that's a two, none of these cells can be a two. So that's not a two. This sum does need a two. So the two is now in one of those cells.

[00:42:35]So this sum is using a two. This sum that's giving a minus number here is using a two. It could be 3 2 1.

[00:42:47]If this was 8 or 9, I think the only way you get too close to them. So it could be 268 or 3 2 1.

[00:43:01]We must use a two here for this calculation.

[00:43:07]So I think those are the only possibilities. 2 6 8 or 3 2 1. And I'm going to leave them as the only possibilities left.

[00:43:20]This is now a 1 eight pair. And this digit is a nine. This five is now getting its sum from north south.

[00:43:29]This is done whichever way round this 18 turns out to go.

[00:43:36]I mean this puzzle is mad and I could I could be making logical errors occasionally. I just cannot legislate for that entirely. I'm doing my best.

[00:43:47]This is a 98 pair by Sudoku and nine can never be on a minus sign. So that's an eight and that's a nine and that is indeed 9 minus one. So it's been done.

[00:44:00]This now has to be 9 - 4 to exist.

[00:44:05]These are a three and a seven. Yes, sure. I could put three here and it would be 7 - 4.

[00:44:12]But if I put seven here, oh no, I can't put one there. That would be the wrong way around. So I'm going to do that. Three and seven.

[00:44:25]And that's done. This is now done. 8 - 7 gives the one.

[00:44:31]These cells are 256.

[00:44:34]I've got to look out for the negative constraint in a moment. These are 3 47.

[00:44:39]That works very nicely for this as long as it's not seven. But it could be a north south minus sign.

[00:44:53]Are these not tidied up yet? A four. No, five is now in one of those two. Oh yes, this becomes a three thanks to that five. That does tidy it up. We get a seven here. We mark it as orange.

[00:45:07]That doesn't sort this out. But nine is now in one of these two cells.

[00:45:14]If that was eight, we would need a one here. That's possible.

[00:45:26]Five is now definitely in one of these two.

[00:45:34]These are from 1278. I mean there is we've got okay two has to be amongst them otherwise this would be a plus or a minus in a sum of 178. So there is a two there. That means that one of these two is a two.

[00:45:57]Okay let's go through the possibilities here. If that's eight, this is one. If that's nine, either this is two or that's five or both.

[00:46:08]Oh, six is looking at that cell. So, that can't be a six. This one couldn't be a six because of that trio. So, we've placed six here. Now, that is not doing an up and down minus. So, it's doing a left to right one.

[00:46:23]Let's mark that yellow. Get rid of these other colors that I've used.

[00:46:29]Right? That is doing a left to right sum. It's either got 71 left right or 28. This digit is one or two. And this one is the high one. Seven or eight. That's now a 1278 quad. And this digit is five which remains in the row.

[00:46:52]Yes. It couldn't be 5 61 cuz the minus would be the wrong the wrong ruling.

[00:46:59]Right.

[00:47:00]This could be a one horizontally.

[00:47:04]It can't be a two in either direction.

[00:47:08]So I'm writing a one in there. And in fact that has now been done.

[00:47:16]And this six is therefore needing a seven here.

[00:47:21]And the six is therefore done.

[00:47:25]Now this is not done yet, but I don't think it can be eight anymore because that doesn't work north south and would require a one east west. So that's a nine and it is done north south. It doesn't really matter now whether it gets done east west. But by sudoku we do find out what those digits are. And this nine actually works both north south and east west.

[00:47:47]Wow. Okay. This is going good. Now, this is going well is what I mean. I'm very sorry for the poor grammar. 345 there.

[00:47:55]This minus Oh, I feel like it's an 835, but it could be north south. This is a 569.

[00:48:03]Oh, soon I'm going to be able to come to things on the perimeter, which is marvelous. That's where I can do actual work.

[00:48:11]This minus must be a north south one.

[00:48:14]So, these add up in some way.

[00:48:18]I don't think that can be three because you can't get a difference of three between any two digits either side of it. I don't think it can be four for the same reason. That's true. That's a seven and it must be surrounded by a 1/8 pair. So now we found two here and that's eight and that's one and this is eight.

[00:48:44]Right? That's seven's been done. North south and now this has been done whichever way around the 3 four works.

[00:48:51]That's fine. This digit is a minus. So this can't be six anymore. This is two.

[00:48:59]This is three. This is six. And both of these perimeter values are done along the perimeter. That was my last perimeter set. So I hope it gets easier now. This digit can't be three. And I don't think it will. This can't be six.

[00:49:15]So we've got 459 left in the column.

[00:49:18]This can't be three in the box anymore.

[00:49:22]That does well. Also, this is now part of a 2 48 sum either. Oh, these digits are 127. Oh, look. We can just fill in a lot of these. Four, five. A lot of triples anyway. 368 there. 2 4 here.

[00:49:38]368. We've already had 179 there.

[00:49:44]Now, no two in those cells.

[00:49:47]Now, which now is Oh, that was done ages ago. I should have made it orange. We've only got four sums left to uh create the rest of the sudoku here.

[00:49:59]So, quick I think I don't know right this one cannot be working horizontally because three four and five no two of them can add up to give the other. So this one must be working vertically with a two subtracted from not nine.

[00:50:24]Either six to give four or five to give three.

[00:50:32]Now that's a three four pair and that's a five six pair. And everything else in the column is 1 7 or 9. That can't be nine. The only place for nine in the final column is at the bottom.

[00:50:46]17936.

[00:50:48]Ooh, this can't be involved in this sum.

[00:50:53]One is not allowed because it causes a repeat and seven and nine are not involved. So, this is a vertical sum of 248.

[00:51:03]A vertical well, but when I use the word sum, I'm sorry. I think it's British.

[00:51:07]That can be a mathematical problem, an equation. is probably what I should say.

[00:51:11]Anyway, that makes this a five. This becomes three. That's four. This is three. This is not three. Oh, I don't like my pencil marking down here. And now I have to go back because I botched it.

[00:51:29]I botched it back here.

[00:51:32]Now I got Well, okay. Let's just see when I did the pencil marking because I It's not a 345 triple at the bottom here. It's a 134 triple. I just misread the row there.

[00:51:49]134. And I mean that's going to make this very available for a horizontal version. Okay, I'm really sorry.

[00:51:58]I just thought I was cruising to a finish there. Now that's 569. Let's get it right this time.

[00:52:06]Yeah, these mistakes do happen. Now, this though, that can't be. It could still be six.

[00:52:14]No, it can't. If that was six, this would go 268. And that cell would be impossible. So, that's a two.

[00:52:22]And then that is the difference between 1 and three. And now this must be a six to make this division work. And those are both done. I think a lot of this is going to be the same logic as I was trying to do. Oh, this has become a four. That's a seven.

[00:52:41]This is not six. We've got a 59 at top and bottom. That can't be a three. And we can't put sixes in any of those cells. So, this is in a 2 48 triple somewhere. We've taken four out of those. And this has actually done. Now, I worked on this being north south. It certainly doesn't have to be because it's done east west.

[00:53:03]This is done.

[00:53:06]This is done east west. Whatever digit it is, that's an eight. That's just sedoku.

[00:53:16]And it's done. Those aren't twos.

[00:53:20]So now I don't have all these things going on up and down as I thought I did.

[00:53:24]And I have to do a bit bit of better work. That's not a nine. So we have got a 56 pair in this column. A 97, right? For this to be part of a 248 sum going east west, a 248 equation going east west, that would be a two. That would be a four. And this would be impossible.

[00:53:48]So it's not. So this is part of a 2 48 equation going north south. Can't be 2 36 because of the position of that. So these are 2, four and eight. That is a triple. And now 3 4 1 3.

[00:54:05]This doesn't work east west. So we've got to make it work north south by putting a six in there. That gives me 56 here.

[00:54:16]These are from 1579.

[00:54:19]And this is done north south. This is done. When we get 824 in here, it will be done north south.

[00:54:32]Okay, this is good. Um, that can't be a four or this would have a minus north south.

[00:54:39]Got to still look for these.

[00:54:42]Oh, that these these negative constraints. That can't be a nine or this would be a minus between nine and three. So, that's a five. That finishes the bottom six rows. You would think we were close to a finish, wouldn't it?

[00:54:55]You'd hope we were close to a finish, right? I can put in my triples up here.

[00:55:00]Try and not get them wrong.

[00:55:03]459 there. That makes this minus all too easy to fulfill.

[00:55:12]368 there. Okay, this is a 245 triple.

[00:55:16]This is a 179 triple. I can take five out of there, six out of here, three out of there.

[00:55:25]Okay. So now this can't Oh no, that has got a sign in it. So I can't rule on that.

[00:55:33]I'm trying to compare sort of three cell pieces up here. But again, there's a sign there. Oh, I haven't colored this in. There's a little minus sign hiding behind this four. I can color that one in. This one though is not working horizontally.

[00:55:52]So that is going to have to be either a nine or a one. That must be one. Well, that might be quite helpful. We can take one out of a couple of cells which are now a 79 pair. There's also a 68 pair in the row. That digit is two. That gives me four and eight up there.

[00:56:12]Now, that takes four out of a couple of cells. Eight out of one cell. There's a 36 pair in the row.

[00:56:24]H. Doesn't that do anything? Okay, let's go back to this 68 pair. That can't be two anymore. There's a 79 pair, so that can't be nine.

[00:56:36]Now, this can't be nine. It doesn't matter whether it's horizontal or vertical or running rings around a carousel. You can't put a nine on a minus sign. So that's a five. And that is going to do I mean the five is done immediately north south. But that's fine. In fact, that's the last sign we had to fill in. So hopefully the rest of this works by classic Sudoku because if it doesn't, I really haven't got any more shots to fire. That's not a seven, right? Uh, no. No, I've got the negative constraint to fire. That is a big shot that I do have left to fire. That can't be nine.

[00:57:19]This can't be seven. Yeah, it doesn't work by classic sedoku. We've got clear deadly patterns there and there. So, we're going to use the negative constraint and say that this can't be a three between the five and the two or it would have a minus sign on.

[00:57:39]And that does one of the deadly patterns. And then this can't be a one between the three and the two or it would have a minus sign on. And if this is not the solution, I'm going to break down in tears right now. Let's see. Done in under an hour. Oh, nobody's done this one before. That's brilliant.

[00:57:59]What a puzzle. What a what an annoying backtrack I had to do late on there.

[00:58:06]That is so clever and so devious and so surprising.

[00:58:11]I think the rule set will be used again by someone and I expect it'll be someone who can watermark it a bit better so we can see all our digits. That is a very clever puzzle. Well done, Vronius. Great fun.

[00:58:28]Thank you for doing it and thank you guys for watching me. It's such a pleasure to bring you these incredible constructions uh by geniuses every day. I'll see you again soon. Bye for now.