This video masterfully demonstrates how a simple arithmetic constraint can elevate Sudoku into a sophisticated exercise in deductive reasoning. It is a brilliant showcase of how minimalist rules create profound logical depth for the seasoned mind.
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The Dance Of The Sudoku Mushrooms!Added:
Hello and welcome to Tuesday's edition of Cracking the Cryptic, where on a cold windy day here, we're going to be having a go at a puzzle by an old friend of the channel, Florian Wartman, um has created a puzzle called Mushroom Dance.
um presumably because these are a little bit mushroom shaped. Um and it's just a normal region sunline puzzle, but lots of you have written to us to say this is wonderful and not too difficult. It's got three stars out of five for difficulty and uh very much looking forward to having a go at this. I haven't done a puzzle by Florian for what feels like at least a couple of months. Um, and uh I think Florian's been making puzzles that we've featured probably since co times. So I have no doubt we're in for a treat with this one. Uh, as I say, lots of recommendations to have a look at it. So we'll read the rules together. It's just simple simple inverted commas region some lines and we'll read those rules in a moment or two's time. But before we kick off, a few things to mention. Um, firstly, thank you so much if you joined us last night for what I think was a pretty um pretty interesting blueprint stream. So, Mark and I were in the Blueprints mansion last night. Um, we never have great expectations as to what we're going to achieve, but I think we did um we did manage something. I'm not exactly sure what it was last night, but we did definitely do something. Something quite unexpected. Um, so I'll try and remember to put a link to that um to that video on the screen in case you're uh in case you missed the live the live stream and you can catch up on the VOD uh as Maverick flew over as you probably just heard there. Um, and uh well, let us know in the comments what you think of what happened, which I think was um yeah, it it feels a bit surreal. But anyway, um, uh, very much fun was had that. That's important to note. And we'll certainly, I think, be back in the mansion next Monday evening.
Um, so look out for theuling of that stream. Other than that, over on Patreon, couple of things to mention there. Firstly, we've got the um, uh, the Spider-Man Sudoku hunt for the month of May. Our competition that runs until the 20th. chance to come on to the channel and um solve a puzzle. If so, if that might appeal, do get involved. Only eight puzzles to do. And remember, if you do get stuck, you can go over to the Discord server, the Cracking the Cryptic Discord server, where there is a Patreon only dedicated chat channel. Um, and over there you can find hints and tips as to how to get yourself unstuck. It's very friendly bunch over there. So, I do recommend it if you are stuck. Um and but but there's also a bit of a bonus over on Patreon. Um because um especially if you enjoy our crossword content, uh we released uh a new video last night um in which I solved a puzzle by Oscar and and Oscar uh it was Oscar's first ever cryptic crossword construction and he sent it in to us and Mark tested it and thought it was so good that we should we should have a go at it in a video. So, I did that and it was very good. It's an astonishing achievement really to make your first cryptic crossword construction any good at all because it's so difficult to write the clues precisely, but Oscar did do it. Um, and um, so if you're if you're into your cryptic crosswords, you might enjoy that. That's over there on Patreon right now, too. Um, now let's do some birthdays.
Heath, you've turned 78 today. Um, you ca you came to the channel for the sedoku, but you've stayed for the word games. Um, you enjoy I think you enjoy all the word stuff we do, all the cryptic crosswords, Mark's word in a minute, the connections and gridoggrams.
So, thank you for watching all of this stuff. I know that you taught language arts for 46 years. Um, so perhaps it's not surprising you gravitate towards the word the word puzzles in the end, but Keith, I hope you have a great birthday today. Many many happy returns.
Oh, the next the next one is not a birthday. It's just we had a very kind email from Australia from Zach and Bri um who watch daily and have been getting into the minute cryptic videos. Um but anyways, it was a kind email. So, thank you both for that. But you wanted to know how many emails we receive daily.
The answer is well, it's certainly hundreds. uh many hundreds and some days I'm sure it will go over a thousand. So it's a lot um and um in fact in fact yeah I mean I've talked a bit about this in the past but probably I would guess 80% of the emails can be dealt with incredibly quickly. So it's sort of a glance and then move on. It's the 10 to 20% of them that that you know that are more difficult. you know, the the 80% might include people trying to sell us stuff or people trying to ask us to sell their stuff or simple spam. Um, you know, it's that sort of thing. Um, but the 10 to 20% and and yeah, they're the ones that where you have to think, sometimes you have to write a reply, sometimes you have to do something.
Those are the ones that take the time.
And actually, a lot of the time I think that Mark and I spend around the channel is on emails. So, it's not like we just record um record a video and then and then get on with life. This this very much for both of us is our lives. Um and it's great. I mean, it's a great privilege. I mean, who who wouldn't want to solve puzzles as a job? Um but certainly, yeah. So, so the short answer is hundreds if not thousands. There we go. Anyway, thanks for the email, Zach Bri. Another birthday though, Charlie, your best friend Maria wrote in. Um, and Charlie, I think I remember that you wrote um you asked for a shout out for Maria, if I remember rightly, and you'd composed a poem for her, which I know uh I know she was incredibly touched by. Um, but she wanted to sort of respond in kind, not with a poem, but she wrote some very lovely words about you. I know that you're a beautiful, kind, and loving soul, a wonderful writer and storyteller, and you inspire her every day. Um, and she says you're a great cat daddy to Willow. So, Charlie, I hope you have a great birthday today. I do hope there's some chocolate cake in store.
Um, and then finally, last but not least, Stefania over there in Iceland.
Stefania is turning 16 today and has been watching since co. So, Stefania, thank you so much um for watching for that amount of time. I know your mom doesn't understand why you enjoy the channel. What I mean, that's ludicrous.
Ludicrous.
Um but anyway, Stefania, many happy returns. I hope the chocolate cake is good and good luck with the driving lessons/test.
Um but that's all the news. Shall we have a go at Mushroom Dance by Florian Wartman? Uh the rules are not going to take long to read. Let's see what we have to do today. We've got normal Sudoku rules applying. So, we're going to have to put the digits 1 to 9 once each and every row and every column and every 3x3 box. And then the 3x3 box borders, divide each blue line into segments. And along an individual line, those segments must have the same sum.
So, let's do this one. Um you can see as the line so the line only spends one cell of time um in box five and then it crosses this border then it spends a few cells of time in box six and then it exits and goes up there.
So what this rule means is that these three digits, the three purples, you sum them up and you'll write that digit into the yellow cell and the green cell actually because these are going to have to have the because every segment along line has the same sum effectively. That means those two digits will be the same.
But that's how region sum lines work. 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 mean, I think Florian's been quite kind here, hasn't he? Because it certainly looks like most of these lines, if not all of them, have a three cell segment versus certainly all of those. So if we just study those cells for a moment on each of the each of these segments must add up to at least six because the minimum we could populate those digits with is a 1 2 3 triple. So that means that well it means those two digits. Okay.
Yeah. Let's use colors. So, we'll make these two cells green cuz they must be the same cuz they're going to have the same segment sum as whatever those three sum to. So, they they've got to be at least equal to six, right? And these two can't be they must also sum to at least six, but they can't be green because these two are in the same box. The same is true for that one.
Let's make that one orange.
That's got to be at least six. And it can't be green and it can't be purple.
And this one is quite pretty as well.
Let's make that indigo. And we know that this must be another flavor of 6 7 8 and 9 because it sees purple, it sees orange, and in its column it sees green.
So these are the digits in some order. These are the digits 6 7 8 9. Now what's this one?
this. Uh, no. I was going to say, no, I don't I don't quite know. Yeah, I think I will know. Let me just have a look at this. So, let's have a think.
The this obviously this digit, whatever it is, is at least six and it can't be green and it can't be orange. So, it's either indigo or purple.
Um, if it's that doesn't work. I don't know then.
Um, oh, bobbins. I don't know. I don't like leaving loose ends, but I can't see immediately what that is.
Okay, I've seen something else, though.
Um, green. Green is restricted in box two because green can't go in its own column and it can't go in its own row and it can't go on its own region sum line because imagine this was green then in order for this segment to sum to green those two cells would both have to be a zero and that's not going to work. So green in this box, we don't quite know where it is, but it's in one of two places.
And it nearly it nearly has to be on on the line at the bottom, which would be very powerful because it's quite difficult to put high digits on three cell region, sum lines that add to a single digit total. Because imagine green was 7, 8, or 9. it then couldn't go in these cells because if imagine it was seven well we'd be adding at least a one and a two to seven and that would give us 10 which couldn't be accommodated within the orange digit. So the only way that green is on this line here in either of these cells is if it's six and if and that would make orange into have to be a nine.
Um yeah but but this this pattern is the same here, isn't it? Where's orange in box eight? Orange is in one of two cells. So orange is also it's it seems to be trying to get onto this green line. And again the only way it can be on the line is if orange is six.
Uh ah oh. Oh sorry. Good grief. Right. Look look at per Where's purple in box six?
That's a good question. It can't go on its line. So, we don't quite know where it goes. But that purple is looking at the purple indigo cell. So, that's got to be indigo now.
So, we've got Right. So, now we've got four. Look at that. We've got four indigos looking into the middle box of the puzzle. So, where's indigo in the middle box? It's got to be in the middle of the puzzle. Exactly in the middle.
Right. An indigo in box one is now in one of these two cells.
Indigo nearly indigo in box seven is quite close to being placed. What about indigo in box 9 again? It can't go on its region sunline. So one of two places.
Ooh. Ah right. Here's something then. So this line here uh let me just highlight all the cells on it for a moment. those cells. We can see indigo by Sudoku has been forced onto the top side of this line.
So, h I thought I was going to get the color of this one. I can't Well, um I Okay, I now know indigo is not nine.
Um because if it was nine once we added a digit to 9 this digit would be at least a 10 and that's not going to work.
So and this digit is six. Well no it's not six. This digit is 7 8 or 9 and it is the sum of which is per No it's not purple. Be careful Simon is not purple.
It might be well it might be purple but it doesn't necessarily have to be purple.
Um, so purple is in one of those three cells.
Oh, bother. Okay, that was nearly it, wasn't it?
So, so this line contains an indigo digit and and then presumably a very low digit. So, it must have a 1, two, or a three on it, plus indigo to equal that digit, which I I can't get out of my head that this looks like it's purple, but I don't think it has to be. It could be orange.
Um, okay.
Sorry. I'm not seeing what I have to do now. I don't think it's that line, which probably means it is that line.
Um, right. Here's here's a point. Where is purple?
I don't know how I'm going to pencil mark this, but where's purple in column five?
And the answer is I haven't got a clue.
But but it's not possible. Now, if we just focus on those two cells at the top and bottom of column five, they can ac Yeah. Okay. The way to think about it is that these three digits in the central box, so green, orange, and purple, if we think about where they go in column five, I can't put all three of those digits in the top and the bottom cells. So, one of those digits must be on a line.
And therefore, one of those digits is a six. And it will add up to it'll be a 1 126 triple adding up to nine.
So, so one of these has to be a six. Which means this indigo is not a six. So, indigo is not a six. Indigo is not a six. Indigo is not a six. Indigo is not a six. Nori. Now, whichever one of these is six is therefore going to be either on that domino or that domino cuz we we can't possibly put a higher digit into those four cells than six. And that's going to mean either this either green or orange is a nine. Um and and their their segment is going to be a 126 segment.
So So purple is now not nine.
Ah uh hang on. What does that do to this one then?
Oh no. No. Careful. I've done it again.
Sorry. Goodness me. I've I dodged one there. I I I said purple is not nine and then took it out of this cell. But I don't know that that's purple.
Um, I would really like to know whether it's purple. Oh, indigo is seven or eight.
And indigo is on. So, this can't be seven anymore.
So, this has to be either 1 or 2 + 7 or 8 for the indigo digit in order to give a single digit total. So, this can no longer be seven.
And that's feels like that's really it's very interesting, isn't it? It's it's I I love the way that these constructors can keep coming up with innovations in with just using the simple region sumline rule.
Um, so if that was purple, there's something there. Isn't there? If that's purple, where is because what what this line establishes is that indigo is indisputably lower than this digit. So if this was purple, it couldn't go on this line, which adds up to indigo.
So it would be purple plus something equals indigo. Whereas this is indigo plus something equals purple. If this is purple. So if if these are purple, purple would go there now.
Would that matter?
you'd actually get a lot of purple placed around the grid, I think, if that was the case. Because then in column five, where would purple go?
Um, and and it cuz if if purple couldn't be in here or here, and purple would would in that instance be eight or nine. It couldn't go there.
So this it would go there there. It would basically you'd almost you you'd almost get all the purples.
So maybe this has to be purple for some reason.
It's got to be okay. It's got to be a color.
So it's either it's it's either orange or purple just by Sudoku cuz it has to be a 6 seven eight or nine. It's got to be one of these colors and it can't be indigo or green.
So, what does that mean?
Uh, I'm not sure. It's It's the honest answer.
Is there some way I'm meant to know?
We've always got an issue here though actually. Whatever this is, don't we?
I'm just thinking even if this is orange.
Oh, it's not. No, actually, it is different. It's different. This can't be orange. Ah, that's really clever. That's really clever.
Okay.
Okay. It's a similar point to the one I was asking about about whether this could be purple, but it's subtly different. Let's make this orange just for a moment. If this is orange, how does it work in column 8? That is the question. Obviously, it can't repeat in its own column. And it can't be on a line that adds up to itself.
And it can't be on this line for exactly the same reason as purple couldn't have been if this was purple. because this this line here is telling us that orange is the result of s summing indigo with another number. So we can't put orange on this line. So orange which it couldn't also be here which wasn't the case for purple because of sedoku. So orange would have to go there, but then orange is on this line, but orange is 8 or 9, and you can't put an eight or a nine on a three cell segment that only adds up to a single digit total. So this is not orange and has to therefore be purple. Um, so now, so now purple is eight because it has to be a digit that's in common between this cell, which is 6, 7, or 8, and this digit, which is 8 or 9. And so the only thing that works there is eight. So those are all eight, which means indigo actually um is going to have to be seven, isn't it? Because we're adding a digit to indigo, which can't be six for some reason. I can't remember. But yeah, I think it was cuz six had to be one of those three colors in order to appear on one of the lines in column five.
And so, oh, we can just fill some of this in now. So, sevens can go in the grid.
Eight is over there.
The um the other two colors, green and orange, are now six and nine.
So, this one is six or nine.
Everything that adds every three cell sum that adds up to seven is a 1 124 triple. Ah okay. So on this one we can place the one and eight we can place in column 8.
Certainly can't put eight um on this line in box eight. So eight is eight's going to get placed.
That's going to do it, isn't it? Let's just check that. Is that really true?
Yeah. So look at eight in box eight. I think it is in one of those two cells, which means by sudoku, it can't it can't go on this region some line. 8 + 1 + 2 is 11, which these can't be. So 8's going to get placed at the top there.
Look. But that pushes orange onto this line. And that tells us that it's the orange that's the six and green that's the nine.
So this So six goes here. Green is nine.
This is now well we certainly can't put nine on on this um on a line that adds up to six. That six line is going to have to be 1 2 3.
Six is in one of those cells. Six is on here. And this is a 1 126 triple adding up to adding up to nine.
So in column five, we haven't put four and five in and they're going to have to go there. Which means in box five, we've got a 1 2 3 triple out of absolutely nowhere.
In box eight, this one is is ploning a one into column five. So now this is a 2 six pair on the nine arrow at the top and this becomes a one and now this becomes a one by Sudoku.
This becomes 2 three and this becomes 2 six. So now I've got a one three pair on my six arrow and I've got a two at the bottom of the grid.
It's just it's it's really clever how that all unwound. Sort of quite magical actually that you could get to the bottom of the color of this cell.
Now an yeah an eight arrow must have or not arrow but the these three digits must include a one because if they didn't the minimum they could be would be 2 + 3 + 4 which is 9. 9 is bigger than eight. There's a knowledge bomb for you. So, so this is a one by Sudoku.
These two digits add up to seven and that digit is not two or four. So, this digit is two or four and this digit is three or five because you're always going to need a two or a four in some sum that adds to seven uh if you can't use one six, which you can't um without repeating the one which would be too naughty for words.
Right? This is a 124 triple in box one.
So there's a one in column two there and three is in one of those cells.
So four five four five oh 9 is in one of these. Is this nine? If this is nine, these add up to nine and they're not 8 1 or 27. So that' be 3 six or 45.
Uh that might be okay. Don't see a problem with either of those to be honest.
Um let's try and do more Sedoku in the Sudoku puzzle. Okay. Okay. So, there's a seven there and there's a seven there and there's a seven here.
Don't know a great deal about nine. Do Oh, yes. Okay. Yes, I do. Where's nine?
In box nine.
This is There's actually a seven pair.
Look in box box nine. And that's going to place nine for me in box six, which is going to give me the opportunity to pencil mark a nine in box four.
Um, in column 8, what do we need? 3, five, and six.
So these digits are from 3, five, and six as Maverick does another another pass over the flight tower. Oh. Oh, that's 3, five, six as well in box 9. Ah, but six can't be in the corner. So six is in one of those cells. So six is now not on this. If this is a nine, it's not on there. So this would h if this is nine, this has to be four. Five. Now that would be a two.
That would be uh I don't know. Uh no. Okay. Maybe that's maybe that's possible, right? So, what do we do?
Okay. Where's the digit that's two or four here?
There's a two or a four in one of those cells that has to go in the top row.
Where's it going to go? Can't go in its own box. So, it's going to have to go in the corner.
That's about as useful as a chocolate teapot, I think.
That doesn't stop this being four, five, either. Um, maybe it's this one, then. Maybe there is something we can say about this one.
We can say that we're only adding up low digits there to come up with this digit because these can't be high digits. They can't be 6, 7, 8, or nine.
But just they could still be four, five adding up to nine, couldn't they? Oh, what about the bottom row? Three, three, four, five.
Seven. So, is it 7 8 and nine in this column? That can't be 7 8 9. That can't be. That can't be. That can't be. They can't be. Oh, that's weird. I couldn't see that at all. Where is 7, 8, and 9 in column two?
The answer I think is there for one of them which is not seven.
Not here. These two 7 8 9 and seven is definitely down here.
Okay.
Um, okay. So, I do I do at least know.
Oh, wait. Hang on. I did Oh, so so sorry. I didn't realize this. This that's a two cell segment adding up to a one cell segment. So, this definitely can't be nine.
But this digit is huge. This digit is the sum of two digits, one of which is a seven or an eight. So that's got to be a one or a two. So this is an eight or a nine.
Right? In row seven, there's a 789 triple.
The eight, right? That's lovely. The eight of which in this 789 triple in row seven there. The eight in that triple is is over in box seven, which means this digit is now not eight. That's going to have to be seven.
So, this is an 8 n pair, which means this is a seven. This is a nine.
And that's probably important for reasons that we'll have to work out.
Right. This This is definitely green.
This is definitely indigo. That's indigo. This is Well, we don't know yet.
This is um a purple green pair.
So those two digits they well they can't include a one. No way. Because one we'd have to be adding at least a seven to a one in order to get to eight or nine. So that digit's not a one. So this digit is a one.
Now, so one of these digit one of these digits is a one. I don't think I know which one.
And if I put two here, that won't work, will it? What would I add two to to come up with an eight or a nine? I need at least a six.
So two in two in row now this is massive that's a massive point because now two in this row seems to have to be in row six column 9 and that's going to fix that those are a 43 pair to get give me get me my extra seven that was due to add up to the eight that we needed. Now this is a two that's a three.
This is not a three. So this is a five or a six.
There's a five six pair now left in column eight and three. Three is on this line. So this is three.
Oh, so it's it's a three plus a Well, it can't be 3 + 4, can it? That would only add up to seven. So it must be 3 + 5 which is means this one is eight. So we've got eight here, one here by maths, nine here, eight here.
Let's let's tidy up our colorings. Make sure that we're all on the same page there. So these are not purple anymore.
This is now definitely green.
35 makes this a four. This a five. This a five. This a six. In this row, we've not put two and four in. Oh, okay. I thought I've made a mistake. That's okay. That is okay. This is a two four pair, but that gives me a 1 124 triple in column two. So, that's not a four.
And now I've got a 35 pair. So, the digit I haven't put in is six in column two, which makes this a Oh, I could have got that a different way. Oh, but that's three in the corner. That's three in the spotlight. losing its religion.
Um, okay.
So, how does this help us? What do we need to complete? We still need to put six in. Oh, we need to put six into box um into box four. This has probably been a available for ages. I just didn't see it see it at all. But six is now. Let's go to colors and make sure they're all orange. That's definitely a green nine.
And and well actually that can't be a nine arrow anymore because it can't be 45 which was I think the option that I narrowed this down to. If this is nine, can't be 1 eight. Can't be 27. Can't be four five.
So it would have to be 3 six. But that would make both of those have to equal five. And that won't work. So this is not green. It's not nine. And that is So that's nine. It's green. That's green.
It's nine. This is not.
I don't know what. So this is quite a low digit now. It's No, it's got to Oh, wait a second. It's It is a five because the minimum this can be is 2 + 3 and the maximum that can be is also five. So that that's where the equilibrium lies.
And that's now a four.
So this is a two. This is a two. This is a four.
Now what can we do with this? We're going to get that digit. Three. That's a six.
We've got another three. Another three in the corner. That's three in the corner. That's three in the spotlight.
Losing its religion as well. This is now five. This is a four.
So this is a five and this is a three.
Right? What do we need here?
Two and three. Okay, we can do that. Two and three. Three and one. Two and four.
Those digits are what? Three and four.
So in this column, these digits are eight and five.
must be resolved. It just must be. This is four. That's four and six. Now that I can do that seems to be resolved. 4 65 58.
And this is eight by Sudoku. So 8 7 1 1 4 4 3 2 six. And if we haven't made a ricketet, that's a five. Now, I haven't done my coloring very well there. So, let's try and fix that.
That one's got to be indigo. That one's got to be indigo. Don't think ones ever got their own color. Sixes did, though.
So, sixes all want to be orange.
Fives don't deserve to be purple.
Uh, that doesn't deserve to be orange.
So, I should have four colored cells in each box.
And I think I have. I think I have. Yay.
Lovely. Absolutely lovely. What a beautiful puzzle. Um, I really liked that the logic around this cell and what color it had to be. Um, very beautiful ideas going on in the central column.
Florian, as always, just a quality constructor of a quality puzzle. I hope you enjoyed your mushroom dance. Let me know in the comments how you got on. I enjoy the comments, especially when they're kind. And we'll be back later with another edition of Cracking the Cryptic.
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