A masterclass in deductive reasoning that transforms chaotic constraints into an elegant display of pure logic. It proves that even the most daunting complexity is merely a sequence of inevitable steps for a disciplined mind.
Deep Dive
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Deep Dive
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Hey, how's it going? Welcome back to the channel today's puzzle, which is called neon star. It is very neon starified.
It's by web the third.
So let's just dive into this and see what we've got going on cuz I think these are all very standard rule sets.
So it's digits on a green line differ by Well, it doesn't say normal Sudoku, but there's normal Sudoku. So every row, column, and 3 by 3 box will contain the digits 1 through 9 once each. Digits on a green line. Now this inner star is our German whisper green line. The outer star is the region sum line. So on this inner star, whatever you are, you have to at least be five away. You have to at least be five away from that one and so on and so forth across these things.
And then digits on a blue line are divided into sets with equal sums by the box borders. So like I said, the outside star is the region sum. So these three digits because they are in a singular region and on the same line will add to some value. That value is going to go across the entirety of this line. And these three cuz they are in a separate region must add to that same value. These three in a separate region on the same line must add to that same value across the board all the way around.
And then finally we have digits in a cage do not repeat must sum to the number in the top left corner. Killer cages. So these two will add to eight, these to eight, these to seven, these two to six, etc. etc. Lots of groupings here we can do some work with. So those are all the rules.
Not expecting this to be too difficult, but you never know. Sometimes we get hung up on these.
Anyway, link's going to be in that description. Let's get at it. Let's have some fun.
Okay, so the first thing I wanted to look at was some of these groupings of killer cages cuz I think we might be able to start working on values mathematically here. So that's a 25 right there. So these have to add to or 20 in some fashion. Now these are going to have to be the high digits. So that's going to get us onto our German whisper immediately.
Cuz obviously you can't make both of these low and then still have a way to get to 20. So highs in fact every single one of these here in the the groupings of these rows and columns are going to be all the high digits. So then we can put all the low digits and then we'll start to uh really jump into what some of these I'm not going to color everything. I'm just going to do those because we got there.
So uh let's start thinking about the the possibilities of highs and lows and that might start to translate over to our region sum.
Now you could be one, two, or three.
Obviously you can't put a four here. If that's one, two, or three, you could be seven, six, or five.
You have to be one, two, three. You could be a four though.
Hm, not great. Well, let's go to the high here. I didn't even notice the seven's in over the high digit. We might also have some values there we could work with, but this is a seven and it's on it's a seven cage, but it has a high digit. So you have to just be a six and a one. Then you will be a one and you will be an eight.
Now eight uh if I can read these 17 uh 23.
So these will add to 22 in their totality.
We already know one of them's a six, so we're now down to 16. So that has to be a 9 7.
That was some You could also instead of coming from the direction I came from, you can just do that as well to know that these were all going to be high digits or very close to it. You probably wouldn't have known it because of this eight, but you get the point.
Uh this six can no longer be a 1 5, so it is a 2 4, which means you are the three No. How did I screw that up?
Oh, I was thinking this was a 10. I don't know why [clears throat] I had that in my head. I was like that has to be a 3 7. No, it's a 3 5.
Easy enough, right?
And that all works. Good.
Now do we want to keep going down the line? I think we probably do.
Uh this is going to be low.
Again, it could still be two, three, or four.
That will leave you to be three, four, or five. Now we also can start to jump over to our region sum if we prefer to do that. But let's actually go over this five cuz I think this is going to be better cuz we can't do the two three version. So it will be the one four version, which means you can't be a one, you can't be a seven.
>> [clears throat and snorts] >> And can we think about the 12?
Eh I think there's multiple ways we might be able to do this. It obviously can't be the eight four, but it could be a nine three or it could be a seven five. And I think both of those are still possible.
Uh what about these guys? We might as well just start putting some of this in.
Trying to find a keep going kind of around the thing here and find what we need to do, but >> [snorts] >> ones, twos, and threes, sevens, eights, and nines.
You will be from uh you could be anything really. Six, sevens, eights, nines, not fives. Haven't thought about the fives yet, but I don't know if there's much there to really worry about at the moment. One, two, three again can't have the four. So we're going to be looking at six, five, four here.
And do we I guess we're going to have to start getting over to here unless I can find something else that's going to help me a little bit better.
Hm, I don't know that any Or or we can do some more math maybe and see what these could be.
Cuz again we're looking at that's a 15 24. That just means 21. That's not all that helpful.
4 21. So these have to be 24.
Okay, that is helpful. That's a 9 8 7.
Although does it really tell me anything? I don't know if it does.
Uh It doesn't It doesn't really tell us too much on these either unless there's maybe some restriction now because we can't put the seven on the eight. So it's either the six two or the five three.
Uh is either option going to break the seven?
The answer's no.
You will be from one five or two four.
Eh I guess you could Maybe it's just the combination of all those together that might work. If I don't find anything here in the next few seconds I'll move on, but it's worth a a look, right?
Probably just have to start thinking about high and low on these, but I'm going to give it like I said one more second here.
Can't [snorts] do seven one. You could do the six two which would leave the one five, which would leave the four three.
Or you could do the five three, which leads the two four and the six one.
Yeah, there's multiple ways that can work. Okay, let's move on.
You I don't think we're going to get anything more on these either. So let's try to figure out if we can work out the the region sum, the basis for it.
We know there's an eight in it. There's a minimum two three. So that's at least 13 total.
So let's think about these two first.
The least this could be would be six. So this has to would have to at least be a seven.
The most it could be would be a 10. So it had be at least a three there.
Eh I don't know if that's telling me anything to be honest with you.
Okay, um What else? What else? What else? What else? We have to have something in here, right?
See if we can find another restriction.
Let's just put some of this information in. Six, sevens, eights, and nines.
There's not much really correlating back across just yet.
So that's where the little rub is. You could be anything. Well, sevens, eights, nines can't be a six.
Okay.
Yeah, it doesn't really look like it's telling me what I need at the moment.
Okay, let's find something else.
Let's see.
Where aware do we have a good look at something? Guess we know one of these will be a four, but that doesn't tell me too much either.
One of these will be a one. That doesn't tell me very much.
I don't think we can limit some of these.
Cuz in every case we could always put like eights and nines unless that disrupts the the values, but I don't think it would cuz again we were at 24 here. So we had to be 21. So we put a three here and we have an eight and a nine.
Oh, we'd have to do would put a What? A five with it to get to that 21. That's not a problem.
You couldn't be a one by the way. You can't be a six then. Didn't notice that one.
>> [snorts] >> That means you have to be five, three, or four.
Eh you are one four or um two three two three four. We're starting to push.
Eh, not really a five into one of those, but I'm not really getting in our region sum yet. So, if you I keep feeling like we have more work we need to do before we really get into that one.
So, where is that other? We've got two highs here. We know one of these has to be high.
You don't have to be high. You could be the mid and this could be the last of the highness.
Mm, I don't know. Let's go nine three.
Um, again, can't do eight four.
I could do the seven five. I want to try to push as much as possible if I can. I guess that means No, it doesn't. I like I said previously there was a one there, but yeah.
So, um, no. Again, trying to find some sort of nice easy in here and I'm not finding it.
Okay.
That's the way we want to be. That's the way we want to be.
So, let's try to find something else.
Some other concept we can work with.
Like, can we put fours in some of these positions? Can we put six? So, you can't be a six.
Sevens, eights, nines, all that I think can work.
Right? Cuz if I try to put a three on this side, we're looking at an eight nine.
This would be either a one or a two.
You could still be the two three or the four, so that's not doing a whole lot.
Uh, no, cuz then you could still be a seven five. I was trying to think about those options there and what it did to you.
Cuz those that could still with the eight nine force the seven five.
But no, it won't. Actually, good thing I thought about it. What happens if this is a three? You have to be eight nine.
Therefore, you have to be seven five.
Well, what does that make you? A six.
Six and three do not add to eight the last time I checked. So, you're a two.
And you are the six. I was like, what does that tell me? Nothing. It actually doesn't tell me a whole lot here, but that is a two six now. So, we have a six on board here.
Is it ever possible for you to be a low low digit now? That's kind of where I wanted to get to earlier with the region sums.
Cuz if that's a six, the min here is three. That could be No, that'll still work. That'll get us to 13.
Now, is there a max here I should have looked at? Four five, that'll be 17.
Mm, all right, we can still get to 17 here cuz it could be seven six with the four.
So, that's not really hitting it too hard.
Okay, the two does not tell us anything about what these are yet. You can't be a four anymore though because of the six.
Two three fours, not quite there.
Okay.
I feel as I need to be putting some digits in so I can see stuff, but I'm kind of holding off on that for the moment.
Now, is there Maybe there's another one of these types of situations where we can work something out?
Cuz if that's a three, that's an eight nine, that would be a seven. I think that could work.
Cuz I can't really reduce this nine too much.
Unless it's just the the coordination of all of them.
If that was a three, that would be an eight nine, you would be a seven.
You would be a one four.
One four three seven eight and nine, huh?
I think that breaks the nine, doesn't it?
Three, seven, one and four.
Four, we can't do eight one.
We can't do seven two.
We can't do six three and we can't do five four. That is okay. Yeah, it took a little bit of thought process there. You again can't be a three, which means you can't be a seven.
Eh, do we have something similar up here as well? Cuz if we can get me I don't even know if a one two pair tells me anything to be honest with you.
But you are a one or a two. So, we know we have both of our ones and twos taken over. So, if this is a one, there has to be a two here. If there's a two here, it has to be one here. So, this can't be one eight or a seven two. So, it's either six three or five four.
Now, what else does that say?
I guess it means that we have a three four pair as well.
So, this is going to have to be something high-ish, right? Five six sevens, eights, and nines, I guess.
Eh, [snorts] let's try you. Three sevens and eights or sorry, three eights and nines.
You will of course be the seven.
You will be the four, so we'd have the three and the four taken. Now, you could still be a six two.
And that would leave you to be the one five. Yeah, this one I looked at it previously. I think this one doesn't have the same restriction.
Okay.
Um, [snorts] starting to flounder here a little bit.
We got to find a good place to get moving. Where is it?
Let's put these digits in. One can't be one seven, two [clears throat] six, or five three.
>> [snorts] >> The max you can get up to and that's four five six. I mean, that's at least 15.
It's not going to be minned.
Can you be a one? I guess you can't be a one then.
Cuz these would be six five maxed.
That's 11 12. We can't get that low. So, you're not one at least, which means you're not five.
Let me think more about what these can do.
Cuz if that would be a Again, that's two four. I think I'm just spinning my wheels on these guys. Why am I doing this?
I'm not sure.
Uh, again, 13 to 17 is our range.
And this guy here is going to start pushing these, I think.
Well, not really, is he?
Cuz you could still be a nine and a six.
You could pop a two over here.
Huh.
Well, that's interesting. There's it's not quite as dished out as we think it is. What are the maxes here though?
Three nine. Yeah, we said this could still be a three four.
That would be fine.
Think all that works.
Okay.
>> [clears throat] >> Um, what else? What else? What else? I feel like it's math problem, but I can't quite work it out.
25. Again, these have to add to 20 in some way.
Nine eight seven six and Well, can't be a six. Can't have an eight here.
Can't be a nine here cuz that would force these to be eight and seven get us up to 24, which is too much.
Oh, and you can't be a seven either. I It was a math thing and I just was wasn't getting hard enough into it. You can't be a four, could you?
25. We need to get to 20 exactly.
Could you have gotten down to a a No, you could have gotten down to a three. You can't be a seven though.
So, you're either a three or a five.
Does the Either one of those force the same thing?
Cuz what if this is a three? You had to be a nine eight and you were the seven five. We went through that process before. What happens if you were a five?
You are an eight seven and you are a nine three. No, so those all those work in both directions. Again, okay.
[clears throat] Okay, I thought I had something I didn't. We're moving on. We're going to try to move on at least.
I might just have to start putting in digits and then thinking more about what some of these could be as well.
Don't know if I really want to do that, but I can.
Mm.
And I've got to make sure I'm not missing some obviousness in some of this.
Think all of these are still valid options on the German whisper.
Cuz we said that could be a 7, 8, or a 9.
Was there always an Yeah, there's always an eight on this, but again, that doesn't tell me anything.
One of them will be an eight, huh?
If it's you, that's obviously a two. If it's you, it's a two or a three.
I don't think there's a problem there, either.
Cool.
Okay, I can't figure anything out. I'm going to have to start digging into some of these.
There's two up here, we know.
Six, sevens, eights, and nines.
Ones, twos, threes, fours, fives, sevens, and nines.
I'm not a huge fan of this, but sometimes you just got to be able to look around a line and see what can and can't go.
One, three, five, sevens, eights, and nines.
I don't think any of that's going to tell me anything, but it may.
Close, we almost pushed a six up here, but this could still be a six.
A five was similar. We could put fives.
Don't think we can.
Well, can you really be a one?
Again, I don't know if this is going to tell me anything, really.
I'm trying to think about these two in combination.
Cuz if this is a 5 3, you are a 1 4. If this is a 6, you're always a 1 4. That's what I didn't see.
Yeah, it actually helped me that I put these in cuz it got me thinking about these. Yeah, what is this?
If you are 6 2, you have to be 1 4. If you are 3 5, you have to be 1 4. You are 1 4.
Which forces the two, which forces the eight, which gets rid of the eights. You can't have a four, so you are the 6 3.
You're not a six anymore. You are a given five. Look how that all works together once we figure out what the heck it is we're doing. You two are not twos.
You all are not fives. You all are not eights.
That's still clicking. Let's go with this way cuz I know I saw this can't be a five. So, this is a 3 4 pair. We've got all of those digits. Let's pop these in for a second, and I'll come back to my Sudoku or my German Whispers, maybe.
Two, >> [snorts] >> six, and eight. And you're not six, and you're not eight.
Okay.
That's the 7 9. You're the six in the ones. Okay.
Good. I think we're all still good in here.
Now, are you being pushed in either way? I don't think you are.
You You can't have threes on you, and you can't be a six anymore.
Okay.
Got a little bit of a a restriction going here.
Got to find the right place to move now.
I'm going to go back to thinking about the restrictions on some of these, but I'm not sure I can.
Mouse, please stop jumping around.
You're annoying me.
My threes, fours, sevens, fives, nines.
No, nothing necessarily catching my eye.
And I don't think we can do more math yet here because we're still have a bunch of options that we could go on with.
Okay, you can't be one. You can't be four.
There's either two on there or you are a two.
There's either a six on here or you are a six.
But you could just be the three Well, then that tells me you cannot be the 3 5.
Cuz this can't be both a two and a six.
But we know there's twos and sixes up here, right? We know you're not a two.
You're not a six. So, let's just go back to that thought. Can you ever be a 2 6?
No, because then we can't put both the two and a six here. You are the 3 5.
Okay, thank you. You are the one. You are the six. You are not a 1 5. You are the 2 4.
You can't be the six, so now you are that six.
Wait.
Did I do that backwards?
I did it completely backwards.
>> [laughter] >> You cannot be the 3 5 because you break this.
Goodness gracious, you are the I I said it perfectly fine out loud and then just screwed it up.
Uh this is a 7 8 9. You're not sevens, eights, and nines, so you are a 3 5 pair.
The 2 6 says you can't be the 2 4. You are the 1 5. You are the 3 4.
>> [sighs] >> You're not three or four. You are not three. That's a 7 9 pair, so we can put the six and the one in here. Now we can start to kind of bust this open a little bit.
Uh let's keep rolling, though. We said one of those was the eight. 3 5 that way, you're not five. You're not five.
That's a 7 8 9. You're a two.
You are a four.
Good.
Sevens, eights, and nines.
The three says says says you are the 8 9. You are the seven.
Good. You are the nine and the seven and the nine. That means you are not a nine, which means you can't be a one.
Keep going. Keep going. You're not a nine.
3 5s, 3 5s. You're not a nine.
Sevens, eights, and nines. I don't know if we can do enough just there.
The three we have, the two we have, the one, the two. Okay.
Now, I think you can still be two, three, or three, five. We're starting to get this limited a little bit now cuz these are nine. That's good cuz this now can't be the two cuz we said we had to at least get up to the 13. You are the six. You are the two. Now we finally have a value we can work with, 15, which means these have to get up to 15.
Um Um where 2 5? I think that's the only way that works, right?
No, you could do a 3 4 still.
Okay.
You have to be 15. You can't be a nine anymore, so you can't be a three.
Six with a one.
Can't make that work cuz then [clears throat] we'd have to put an eight here to get to our 15. So, you are the four.
You are the one. That's 10, so this has to be our five, which means you are our seven. You are the three. You are the eight and the nine. Okay.
We're moving again.
Yeah, you have to be the eight. You have to be the seven. That's going to give us the nine and the eight and the seven and the nine.
Okay.
Let's keep rolling. You have to be that two, which means you are now the 3 4.
And we can probably start dumping some of this stuff, or we can go over to here first and say the four and the three.
What are these three, though? We need a one. Yeah, it could be a couple of places.
We need the six.
Uh you can't be one or six, so it's going to be a given. This is a five.
Then these will be ones and sixes.
Okay.
Do we have Sudoku starting to poke its head in? Yeah, yeah, we do. Here's a three and a five to finish that off.
And I guess we can start thinking about how we're going to make these to be 15s.
Unless there's something else even more obvious staring at us, or we need to start putting digits in and see what happens. Let's do a little Sudoku run here.
There's going to be a one on this, and we have to get up to 15.
So, it's going to be a one plus something to add to 14. We can't use a 9 5, so it's going to have to be an eight.
Well, it could be an Yeah, it just has to be an 8 6. You are a 1 8 6, which means you are the six.
You are the 1 8, and you will be the one and the eight. Okay.
You will be our one.
Good.
What are you? Cuz now we can probably get over to here.
5 6 and 7.
You can't be five or six. You are the seven, so you're not.
>> [snorts] >> We have to get to 15. These two have to add to 12. We can't put a six on it. 5 6 7. That six will say 3 6.
You're still two or eight. I think those are fine.
>> [snorts] >> There's needs to be a one down here.
It's going to go there, which gives us the four and the one. The one.
What are you? 2 8 and 9.
You can't be 2, you can't be 8.
What are these two? This is just a given actually. Let's put it first. 9? Looks like.
And then what are you two? 3 and 4. We can do that one. Okay. 4 3.
Let's come back over here cuz we can probably start putting all this in to get our values again.
2 7 and 9, you will be our 2.
So that's going to start to tell us more with these two have to add to 13. So you have to be the 4 and the 9 and 7 and 3.
2 and 4, not 2.
Those are still open. What are these three digits? Cuz we're going to have We're going to be able to probably get these. Let's just put these first. Uh 5 6 and 8, you can't be 6, you can't be 8.
These are 5 8 and 4.
You can't be 4, so you are the 4.
Now we have to make these add to 11.
If you put a 6 here, we'd have to put a 5 here. We can't. So this is the 8, you are the 3.
5 and 3.
You are no longer a 5 or an 8, so you are the 6 5 8.
5 there.
2 or 6. Uh the 8 going this way will give it to us though. That's the 2 the 9 and the 8. This is the 6.
And after a lot of fumbling around, we're finally going to be done with this thing.
Took a little longer than it probably should have. Just couldn't quite get myself into this thing. But anyway, you are a 7, you are a 9, and you have to be a 2. There we go. So all the puzzle solution is correct. So 263 solves in a day and a half. Not bad. Took me a half hour like I said, probably a little longer cuz I was really struggling to trying to find the right position. It turned out this 8 was sitting here staring at this 5.
And we If we had thought about that properly, I kind of had to go into putting digits here just to think about all that and get it to work so then we can start getting these to be moving in the right direction.
And then my brain knew what I was doing or my mouth knew what I was doing here when I was going down to this one and then I just kind of did the exact opposite.
That's always fun. Minor dyslexia there.
Uh but anyhow, fun puzzle. Really enjoyed that one. Hope you all did as well. And uh we'll see you in the next one. Thanks a lot.
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