This video brilliantly demonstrates how a simple mathematical constraint can elevate a standard puzzle into a sophisticated exercise in logical deduction. It is a masterclass in turning abstract arithmetic into a compelling intellectual narrative.
Inmersión profunda
Prerrequisito
- No hay datos disponibles.
Próximos pasos
- No hay datos disponibles.
Inmersión profunda
Just What Is "Sausage Sudoku"??!Añadido:
Hello and welcome to Saturday's edition of Cracking the Cryptic, where it's Joe's birthday today. Um, and um, we're going to do a Scojo puzzle. But the reason I'm smiling is this. It's got the most ludicrous title. It's called Let's Sausage. And somehow Scojo's put sausages into the grid. Um, which look remarkably realistic. And uh, anyway, we get loads of Scojo's puzzles recommended to us. Um, but the testers say that this is a very nice puzzle and hopefully um, a good one to do for you, Scojo, today on your birthday. I hope that's right.
The reason I know it's your birthday is not just because um, Logic Masters today is filled with birthday puzzles. um as a tribute to you, but also because I had an email from your fiance Erica um telling me that uh well telling me a it was your birthday, but also telling me that she is going to sort out for you chocolate cake with the correct um ratio of icing to cake today, which is is of course one. So enjoy your chocolate cakes, Gojo, and I hope you will enjoy my solve of Let's Sausage, assuming I'll be able to do it. It's only got three stars out of five for difficulty. So hopefully it ought to be um it ought to be achievable and it's got a very very simple rule to do with the sausages. Um but we'll talk through the rules together in a moment or two's time. Um couple of things to mention before we kick off. Firstly, um Blueprints um Mark and I are back in the Blueprints mansion on Monday evening at 10:00 UK time. We'd love to have your company for that if you're free. I think it's the 44th time we'll have been uh visiting that game.
And uh I don't think we're done yet. I don't think we're anywhere near done yet. Um anyway, I'll try and remember to put a link to that on the screen. Also, um over on Patreon, we have our monthly competition. It's almost halfway through now. Closing date is the 20th themed on Spider-Man. Um let me show you. This is where we were a day or so ago. So, let's uh let's refresh the count. So, we were at 311 solves of all eight puzzles. Um, now, so we click reload. 311 has gone to 47, heading up towards 1,500 souls of the Green Goblin. Fantastic. Well done to everybody who's getting involved in this hunt. The feedback we've had, by the way, um, has been lovely. So, I think you'll enjoy it if you have a chance to have a go. It's over on Patreon along with lots of other bonus content. Uh right now now I must also go to my list of birthdays. It's funny how um birthdays they go in cycles. Some days I have no birthdays to do. Other days are different. And it's not only Scojo's birthday today. There are other birthdays. Well, and other announcements to make. For example, apparently it is American Mother's Day tomorrow. Um and Janet um your son Tony wanted to wish you happy Mother's Day over there in Texas. Um I am assured Janet that Tony is sorting the chocolate cake. So I hope I hope it's properly iced. Of course. Um next. Is this for tomorrow? I can't tell from the list. I think it is. Cozy, are you turning 20 tomorrow? I think you are. Your mom Amy wrote to me. Uh, Cozy got Amy into the channel uh for that.
Thank you very much. Um, and uh, Amy says that she is now hooked. Well, I tell you what, it's not the worst vice to have, I think, solving these wonderful puzzles every day. Um, I think it's good. It's good for us all. Um, but anyway, cozy. Many happy returns. Next, Anna. Anna, you're turning 22 today. I know this because your boyfriend Raphael wrote to me and told me that you've been watching for a while and um and you might like a shout out. I hope that's right and I hope the chocolate cake is splendid. Of course, next.
Andrew. Andrew, you're turning 59 today.
Um your daughter Laura wrote to me and told me that actually 59 is both of your favorite numbers. So, this is a an important birthday for the two of you.
Um, that's a very interesting uh favorite number to have. I'm trying to think if I know anything about the number 59. It's prime. I know that. Um, h, no, I'm not very good at numbers.
It's a twin prime, isn't it? As well, because it's 61 is prime. And I think twin primes aren't terribly common. I think as numbers go up, twin primes get more and more rare. I want to say that.
Maybe that's why. Trying to think when the next tw Uh gosh, no. I'm not going to be able to work. 71 and 73. They're prime, aren't they? Um probably.
Anyway, I don't know. But 59 is Well, 59, your 59th birthday, Andrew, I know that you enjoy coffee and walnut cake the most, and apparently that's what you're having today. And oh, and you're friends of the Peddling Pyists uh family, too.
So, um, well, I I hope you'll see them soon. And Andrew, many happy returns.
Next, one of our younger viewers, Dylan.
Dylan, you've turned what is it? Is it tomorrow? No, it's tomorrow. You're turning three. Your dad, is it Regelio?
Regillio Regelio wrote to me um and told me, Dylan, that they call you Dill Pickle, which I think is very sweet, and that you have watched some of the Cracking the Cryptic videos, and you quite like the rat rum puzzles. Uh although you think the rats are silly.
Well, Marty, I hope I hope you feel told off about that. Make your rats less silly, Marty.
Um, and you're having well, you're having um correctly ratioed uh icing and cake today, but with um the chocolate cake with strawberry icing, I believe.
So, enjoy that. Um, Dylan, and thank you for watching. Um, next, Jess.
Jess, you're turning 20 today, and I know this because your twin sister, Melody, wrote to me. Um, so it's Melody's birthday as well. I can deduce knowledge bomb from cracking the cryptic. Twins share the same birthday.
Well, I suppose they that's not necessarily the case, but it's very likely to be the case. Um, and Jess got Melody hooked about a year ago, so thank you for spreading the word. Um, Jess.
And oh, what does this say? Oh goodness.
Uh, oh yeah, I think Okay, it's Mel Melody. Are you at university at the moment? I don't think you're that far away from home. Um, but you were hoping to send the wishes um over to Jess from university, I believe. So, Jess and Melody, many happy returns. And then finally, Sabrina. Sabrina, your great friend Ben wrote to me to say, "Could we wish you a happy birthday? You've just finished your PhD in cancer cell biology. What an incredible thing." And Ben said, "You are incredibly smart as well." And he told me he's sorting the chocolate cake out. So Sabrina, enjoy that. Many happy returns.
I think I don't think I've missed anybody out. I hope that's true. Shall we have a look at Let's Sausage by Scojo. Let's read the rules together and see what we have to do. We have got um normal Sudoku rules applying. So, we're going to put the digits 1 to nine once each in every row, every column, and every 3x3 box.
The difference between the sums of two linked sausages on a chain must be exactly equal to the number of sausages in that chain.
The difference between the sums of two linked sausages on a chain.
So let's look at this sausage congregation. Why do we the difference between the sums of two linked right? So it is segmented, isn't it? What we're being told there is that that is a sausage.
This is a sausage.
So the sum of the green Yeah. is going to be three different from the sum of the purple I think because there are three sausages altogether in this link of sausages. One, one here, one there, one there. So the difference between green and purple should be three and the difference between blue and purple should also be three is how I read the rule. That is a weird rule, but it's very simple. And that is the end of 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. Let's get cracking. I get three given digits as well. Art vandervatoring style.
Now is is the constraint in this puzzle going to be on short short chains of sausages or on long chains of sausages?
That looks like an enormous chain of sausages. 1 2 3 4 5 that has six sausages on the chain.
So adjacent sausages have to differ in value by six.
Actually doesn't seem terribly useful.
I don't actually think that is useful.
Is it? Is that useful? I know that that domino differs from that domino by six and that domino differs from that domino by six. I don't think that's useful.
Let's try shorter sausage chains. Um, okay. Those two digits share the same parity. They can't be the same because they're in the same box and they're only one cell sausages. So, there are two sausages in the chain. So, they should the digit should be two apart.
How many sausages have we got down here?
One, two, three, four, five. So, this is sort of a German whispers a German whispers sausage collection, isn't it? um in the sense that well yeah except it's it's the sum of yeah you can't really use German whispers logic cuz what we're being told is that those two differ in value from those two by exactly exactly five which is sort of a German whispery constraint without it being quite as productive. I don't understand how to do this. Maybe we've got to use the there's a massive sausage there. Um, don't don't I think there will be ample opportunity for double onto when doing this puzzle.
I'm not I can't I can't think about that. So, hang on. How many? 1 2 3 4 5 six. So, that's a that's a length six sausage. Um, right. So, what's the the minimum sum of that sausage is 21 then?
Oh, some reason I thought that was going to be that was a length one sausage.
That's not a length one sausage. How many sausages are there here? One, one, two, three. I've got distracted. Four.
So, there are four sausages, right? So, we can we can start here.
This is where we start because we've got a length six sausage. We got an enormous sausage here. um the minimum sum of which if we populated that that sausage with the minimum digits we could 1 2 3 4 5 and six that sausage would sum to 21. Now that that means that this domino here or it's not really a domino offset domino but that two cell sausage has to sum to absolute minimum 21 - 4 which is 17. So that's what it must sum to. We can't we can't make this sum to more than 17. So that must be an 8 9 pair and this must be 1 2 3 4 5 6.
So these the digits that are not on the massive sausage have to be 7 8 9.
Now, so we actually know the sum of that sausage because if this this is a maximum sausage, this is the most sausage you can get for your buck on this this sausage. So, it's not possible that this Domino sausage can add up to four more than 17. It must therefore add up to four less than 17. So, this is a 13 sausage.
Um, which is not really doable. I don't pro. No, actually it's not doable doable at all. Can't do anything with that.
Um, and then this is a three cell sausage that either adds up to Can you repeat a digit on a sausage?
Like if that's I don't know if that's a high digit, can you have another high digit on it?
or h what do the rules say? The rules don't say you can't. So, you probably can, right? So, hang on. We've got 21 there.
So, this normally, you see, this couldn't be a 20. If if you couldn't repeat a digit, then the maximum they could be would be 789, which would be 24.
And we could have ruled that out if it, but if it can have a repeated digit, it could add to 25. So, it's either 25 or 17.
But 17 in three cells is far less interesting.
Um Oh, okay. I don't really know how to do that. What about that one then? That sausage is more modestly um more modestly proportioned, isn't it? Now we've got three sausages.
One sausage is a onedigit number. So just a digit.
I don't know. Okay. I don't think that sausage is where we go next. We've got big numbers on this sausage. So the minimum some This is a three three sausage sequence.
Scojo. I'm wondering if Scojo made this.
thinking it would be quite funny to watch somebody solve it. Um, right. That's at least So, it's 15, 16, or 17, isn't it? This top sausage.
Oh, no. Hang on. Hang on. That's going down to a single digit. That's going to be that's going to be massive.
Yes. That this this is the key sausage.
This sausage here. Um, because that what's the maximum that could be? It's a single digit. So it could be a nine, but then we're we're only allowed a difference of three between the sausages. So it's in fact we can see what it's going to do.
It's going to go 9 12 15. That's the only way we can do it because this cannot be bigger than nine. And the difference between each sausage can't be more than three. So it's going to be a nine here. That's our first digit. Um this is uh a 15. So that is a nine in box two.
And these two digits add up to 12 which is well it's either going to be 5 seven 48 or 3 9. So if it's if it's a seven or an eight number there it'll be a four or a five number there. And if it's a nine number it'll be a nine number here and a three number here.
Uh I don't think we can do that. Ah but we've got nine here. Okay. So I can do I can do some sedoku. work. I actually can do some sodoku. That's a rarity. Um, so nine is in one of two cells over here. Eight is in one of three cells over there.
I don't think that can be a nine cuz wouldn't that be a six?
That's a three. It's a three length sausage there. It's a It's a chain of three sausages is the correct way to um articulate the uh the sausage constraint that applies in those three cells. It's a three sausage string.
So we're we're adding or okay, so this sausage acts as a modular line. That might be interesting to think about. What do I mean by that? Well, because the difference between each digit in that string and they are digits on those sausages. They're modestly proportioned shot sausages, aren't they?
So, the difference between each one has to be three.
Um, but you can't repeat a digit. So, it's not like we can go, I don't know, 3. No. Uh, you couldn't go 1 4 1 again.
It's going So, it's going to go if if it does start with one, it would go 1 47.
So, so we are looking at sort of one of the the the vertical slices of a number pad, right? Oh, no. Nearly.
Well, what what that made me think is that this digit has to therefore be a four, five, or a six, doesn't it?
Because it's the middle of a three cell modulus sequence.
Yeah. This this simply can't be nine.
That's that's um that's just true cuz it would go 963.
Um so this is definitely not six by sudoku. So this digit uh it can't be high. So this is a low digit cuz it what we can't do here is go 8 52 or 741. So this is 1 or 2 and this is seven or eight.
And that doesn't do anything. But nine did get placed in row three. Look, we got nine on this sausage.
And what were we there? We were at 21 on that sausage. So this sausage Oh, this is going to be this repeating sausage thing, isn't it? There's going to be two enormous numbers on an enormous sausage.
Um 21. So this could be 17.
Oh, in fact, hang on, hang on. It has got it's actually got nine on it. Didn't realize this, but there's Sudoku available. There is a nine on there. Oh, so it can't, right? It can't add to 17.
It's impossible because it's already got 18's worth of digits on it. And the two options because these add up because those add up to 21 and we're looking for differences of four. The two options for this sausage was 17, which is now ruled out, or 25.
which is now ruled in. So this has to be a 9 seven pair which is that's lovely.
So that's going to fix my my other string of sausages. So this has to be eight. This has to be five. This has to be two. It takes two and four actually out of those cells. Look, eight comes out of this one. So four comes out of this. Uh five comes out of that. So that's nine and that's three.
They have to add to 12. Remember that nine puts nine here.
You see Scojo, I don't do Scojo's puzzles that often, but I've always enjoyed them. I I still remember vividly one that I did um I would say about a year ago which had um is it Rapunzel with the long hair in a tower and the hair came down and it was a beautiful puzzle. Um and this is a bit similar.
It's sort of got some really clever graphics in it.
Um, okay. Now I'm stuck again. Let's Come on. Come on. How do we get unstuck here?
I think uh what was that? That was 13, right?
That's got restricted.
Um the top, right? Let's think about the ways we can make 13. 49. That's not going to work.
Um 67. You can't put seven in either of those places. So, it's going to have to be 58. And that does work. Actually, I was worried that I'd left no possibility. But so, in in row three, this is a 1, three, or a six.
Those digits are going to operate a bit like these, aren't they? That's exactly the same principle here as here. We've got a three a length we've got a sausage string of length three consisting of single digits that can't repeat. So the middle digit is going to be a four or a six or it could have been a five but the five is ruled out. And these digits are going to either be 1 seven in some order or oh they can't it can't be six because one of these would be nine. We'd have to have a 369 triple and nine isn't available. So it's a four in the corner.
which takes four out of these cells.
This cell is no longer a one. So, one is in one of two cells in in row three, which takes one out of a lot of cells in box two. Three can come out of these using Sudoku.
And these digits are 236, aren't they?
We're almost, it's almost looks like it's trying to be helpful.
And we still haven't dealt with this sausage, although there is an eight on it.
Is there Do we know a length three sausage is divisible by three?
Hang on, let me think about that.
I think you would.
No, we don't. We don't. We got to be careful. Actually, I almost I almost said that. Yes, of course we do. But I don't think you do because these are dominoed sausages.
What you could have as a chain of saus on a three on a on a on a string of sausages of length where there are three sausages.
You know, the difference between the values is always going to be three. So we know that whatever the value is of this thing, these two are going to be three different from it. So you might at first blush go ah okay so it's sort of the modular the modularity of this sum.
Let's say that that was 1 mod 3.
These would both also have to be 1 mod 3. But that's not true.
Or is it actually? Hang on. No, it might be true.
No, it is true. I've changed my mind because the thing I've been worrying about just to try and explain is if this was x and these were both x - 3.
But that's fine, isn't it? That's still 3x. And if this is x and one is x + 3, one is x - 3, it's still 3x. Yeah. So the way to think about this is that whatever the sum is of this, it doesn't matter what mod it is mod what its remainder is when under division by three. It'll either be have a one remainder, a two remainder or a zero remainder. The point is that whether you add three or subtract three to this sausage and add three or subtract three to this sausage, these two sausages have the same modulus. So you're either looking at three you're either looking at three sausages all of which have zero remainder three sausages all of which have one remainder or three sausages all of which have two remainder and any version of those is overall exactly divisible by three I'm sure that's as clear as sausage there I've said it so that is so this is okay what's that mod 3 that's zero mod cuz that's 15, right? So, I can use secret.
Yeah. Okay.
Okay.
I've got a three in the corner from a secret. The secret is something I share with only my very favorite people, but if you're watching this video, you're definitely one of my favorite people.
I'm definitely going to share the secret with you if you don't know it already.
The secret of sedoku is that any box of a sedoku because of the rules of sodoku contains the digits 1 to nine once each.
So I know that that box overall has the digits 1 to n once each. The digits 1 to n sum to 45. 45 is divisible by three.
I've just concluded I think correctly that this sausage string contains digits the sum of which is exactly divisible by three. 9 four and two sum to 15. That's exactly divisible by three. So for the box to be divisible by three, this digit is divisible by three. So it's three, six, or nine. Well, it can't be nine. It can't be six. So that is boom. That's three in the corner. That's three in the spotlight. Losing its religion. So now what I'm less confident actually about claiming is that I don't I don't think we do know whether this sausage is in the middle of the values of this sausage and this sausage or whether this sausage could even be lower than both these sausages or higher than both these sausages. I don't think we know that.
But we do know that the digits on this sausage are only ones, sevens, and eights, I think. And that's definitely not a seven.
Just looking at the top row, there's this 25. Oh, there's a 256 triple. The five of which is in this domino. So, we can't put five in either of those cells.
Now, so I know there's an eight on this sausage. So, it's either 81 adding to 9 or 87 adding to 15.
I have difficulty believing it can add to 15. It looks to me like this this couldn't have No, it I can't. It's only there. There's only a difference of three between this sausage and this sausage. So if even if this was it couldn't even be an eight. It could be a seven. The maximum value of that sausage is 7 + 3 is 10. So this must be eight. 8 and one I think which makes this a seven and this a one.
And this adds up to nine.
And the digits we've got left to put in then in just from a purely Sudoku point of view because I'm terrified of the sausage the sausageification um a five six and seven are they five six and seven I think they are 1 2 3 4 5 6 7 8 9 yeah so these digits don't include six now so there are 2 3 4 triple and if this adds up to 9, this must be three less than 9. So that is six and that's 12. So that's nice. It goes 6 9 12 and the logic sort of makes sense.
And the seven and the five can be placed. So five and seven are in two places in column seven.
Si six six I can just place six in box six appropriately enough. um on the giant string of sausages.
Now in column nine, I haven't put in one, four, and nine.
Let's pop some pencil marks in. This can't be nine. So the first sausage on the 1, two, three, four, five. Oh, this was the six sausage string of sausages, including modest sausages and ginormous sausages.
um the first sausage as to seven or 10.
So if it only added up to seven, this couldn't add up to one, could it? So it would have to add up to Well, it Oh, no. No, it can't. That doesn't work at all. If this was a one, we've got seven here. So this sausage either adds up to one or 13. But if it added up to 13 without being able to use 9 8 or seven, there would be no way to make that work. So I think that is a four.
And these digits are a 1 2 3 triple.
And somehow Okay. Well, this is going to have to be 10 - 6 is four. So it's a 1 three pair.
And that puts in a few more digits.
Look, this is okay. So this is a four sausage.
So this can't be a minus2 sausage. So that is a 10 sausage and it's not 37 or 1 n. So it's 28 which might be possible or it's 46 which isn't possible. So it's a 28 sausage here.
Oh. Uh that does put a two in there by Sudoku.
So this is a 10 sausage. to this sausage. Again, it's either a four sausage or a 16 sausage.
Now, ordinarily, I'd rule it out from being a four sausage, but you can put you could put you could actually put three ones in that sequence. So, it could only add up to three. So, it could add up to four probably.
Okay. Um, okay. Hang on. Let's try and do some Sedoku then. If forced, we we'll resort to Sudoku. Uh I don't know. It we did say earlier they had the same parity, but this can't be even. In fact, let's let's do that. What have we got in the row? One's Oh, where's seven in the row? Seven here, one here. So, this has to be two different from seven. So that's a five in the middle of the grid which often happens in variant sodoku. This is a 4 six pair. And in this row we haven't put a one yet. So we get a 1 three pair.
These digits have to be 4 67.
Uh that isn't four. That isn't seven.
So So we've got a four or a six here.
Six is difficult, isn't it? Actually, six is funny. If it's a six, then this sausage has to add up to either zero, which won't work, or 12, which definitely won't work because this can't be a 10. So, that is a four. And this must add up, therefore to 10 cuz it can't add up to minus two. So, this is an eight.
And this is not a four.
So this is 10. So So this sausage in the middle is now framed by two 10 sausages, which doesn't help us to know what it is. It's still either a 16 sausage or a four sausage.
Now, if it's a 16 sausage, these two sausages would they would have to be 69.
Actually, it can't be 69. That's beautiful. Look at this. Right. Look at this domino.
Now either these add to 15 but they can't because 15 in two sudedoku digits is either 7 8 neither of these can be an eight because of this eight or 69. Well neither can be a nine by sudoku.
So this this sausage adds up to four with a one here means these two digits are a one two pair.
Um which is probably useful. He says desperately trying to it is a bit useful in column three. There's a 1 2 3 triple.
So that means that top digit is not two.
That's a 6. 6 3 2 4 3 5 2 4 6 1 6. That was tremendously help. 1 eight.
I've I've done virtually the whole of the top of the grid out of nowhere there. 7 six. What about a three one?
I've done the whole of the top of the grid.
One makes that a two and that one.
So, I've only got one more sausage to deal with or one more string of sausages. I should be more precise, shouldn't I? And in this column, I've not put in four and five.
And in this column, I've not put in two and six. And in this column, I've not put in three, seven, 9. The sodoku does for one. Oh, six here. So, this is a six sausage. And that's a two.
And the difference this Oh, this was my German whisper sausage. So if this is 10 or 11, that should be five different from 10 or 11. So it has to be quite a high number, doesn't it? Cuz 37 is already 10. So we're looking So this has to be massive.
It can't be 37 and it can't be 39. It would it wouldn't be sufficiently different from this sausage. So it must be 7 9 adding to 16 which means this adds to 11 which does differentiate it.
So five four and three in the corner.
That's two threes in the corner. That's three in the corner. That's three in the spotlight losing its religion. That's Maverick flying over.
Obviously intrigued by all this news about sausages. Um, this is a 58 pair, which is Let's check this maths works then. So, I've got 11.
Uh, so this is going to have to be five more than 11. So, this should be 16. So, this is a three, I think.
So, that's a three by Sudoku. Let's get rid of this 57 because we actually know this is 457. The five of which goes there.
Okay, let's try this column. 4 and six.
Lovely.
4 and 7.
179.
Okay, we're going to need the sausages to help us there. Let's keep going though. Uh 28. Yeah, we can do that.
That seems okay.
Four comes out of this cell.
Seven comes out of this one.
One comes out of this one. Do we need Do we need the sausage? We probably do, but I'm not certain. All right, let's try and do sausage logic. So, we've got 16 here. So, this has got to add up to 11.
It can't add up to 21 or whatever it would need to. So, that's got to be a seven. That does 7 9.
Oh, okay. And we're still left with a deadly pattern. But this, so we've got 11.
Um, this can't add up to 17. So it's not 17. Hang on. Be careful, Simon. It's getting confused between all my sausage differences. No. Get get your head in order. Stop thinking about sausages.
Right. 11. Five different from 11 is 16 or six. Okay. Well, that's good cuz six would work. So that's one. That's one.
That's nine. That's nine. That is a brilliant puzzle. Very, very funny.
Quite difficult to talk through in any sane way. Sco, but I did enjoy it. We sausageed away. I should have said, not let's get cracking. I should have said let's get sausage or let's get sausaging. Um, but very amusing. Very nice puzzle actually.
Just really I mean it's quality, isn't it? It's quality. It's not complicated.
didn't require, you know, 600 paragraphs of rules and yet that gives us much joy and in you know it still it wasn't trivial at all. Um there was some quite interesting modular maths going on some triangular numbers bit of a secret very enjoyable indeed. Let me know in the comments how you got on with it. I enjoy the comments especially when they're kind. And we'll be back later with another edition of Cracking the Cryptic.
Videos Relacionados
A Number Plus 5 Is 12
MathGirlTutor
101 views•2026-06-03
Olympiad Mathematics | Indian | Can You Solve This One?
PhilCoolMath
650 views•2026-06-03
Escaping the Fog
LogicLemurGaming
760 views•2026-06-03
H2 Math June Holiday 2026 Intensive Revision | H2 Math Tuition by Achevas #singaporemath #h2math
AchevasTV
304 views•2026-06-01
A Brutal Radical Expression Made Easy! The Shortcut Changes Everything.
tamoshop
112 views•2026-06-02
V : jee main /advance class 11 mathematics : Binomial Theorem class-1 ( 29 may 2026 )
dcamclassesiitjeemainsadva9953
125 views•2026-05-29
Is This Pentomino Tileable?
3cycle
241 views•2026-05-30
This Sudoku Has Many Lines!!
CrackingTheCryptic
2K views•2026-05-29











