This video is a masterclass in cognitive synthesis, turning a multi-constraint nightmare into a clean, logical progression. It demonstrates that even the most daunting puzzles are simply a series of interconnected certainties waiting to be unraveled.
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Hey, how's it going? Welcome back to the channel. Today we've got another fun puzzle in front of us and from another new setter. Well, technically they said this is their first published Sudoku, which says right here on the very front here. Enjoy my first published Sudoku puzzle. I'm assuming they probably have made other Sudokus, but never published anything until now. Love to see it. Been interesting. We've had a few of those recently now where we've had new setters. I think there's maybe three or four of them that I've I've done puzzles of recently. Now, of course, depending on how I sequence all my videos, I don't really ever know. You may have seen one or two of those by this point. You may not have, but if you haven't, know that there are a couple more coming out that are out there. So, just interesting. Love to see new setters. So, excellent puzzle to start with then, I guess. So, we're going to jump in. This one is called Crosshairs by Fibonacci Cascade. Good name.
First puzzle, of course, published.
Let's go into the rules cuz there's nothing crazy here. We've got standard Sudoku.
So, every row, column, and 3 by 3 box will contain the digits 1 through 9 once each. We've got an anti-knight. So, remember our aunties, please. Cells that are chess knight's move apart may not contain the same digit. Whatever you are, none of these can have that same digit cuz they are a chess knight's move away, which moves in an L shape. Then we've got killer cages. So, digits inside a cage do not repeat and sum to the given value in the upper left. So, these two add 13, these two 11, these two 12, etc. etc. And then finally, we've got a white Kropki dot. So, digits on either side of a white Kropki dot are consecutive. I.e. Those two cells right there will be consecutive.
That's the only white Kropki we have.
So, again, we have to remember we have an anti-knight cuz I usually forget those until about partway through where like why the heck can't I advance?
So, keep putting the widgets on your heads. Like I said, it'll keep you there.
But, uh let's get into this one. Let's see what the Fibonacci Cascade has to show us.
I've heard good things from the comments in the Logic Masters Deutschland. So, let's get at this thing. Link is in that description below. Let's have some fun.
All right. So, I saw a couple of things.
First off, you will be a 1 2 4. You will be a 9 8 6. There's no other way to make 7 or 23 in three digits.
We're also going to know that we've got and I think I can see why we have a crosshairs here for the title of this.
We know you are 7. We know you are 16.
We don't know what the heck you are at this stage in terms of the values, I don't think.
>> [snorts] >> Yeah, there seem like there could be multiple ways we can go about this one.
So, so what do we have? We have 7 and 16. So, [snorts] we're looking at 23.
So, these digits here are going to have to add to 22 in some way.
Now, we have to use a 9 to make 22.
There's no other way. The lowest you could ever do is 21. You could do 8 7 6.
What about this? Cuz we've got some big boys here. We've got 23 and 14.
So, this is looking at 37. So, these three digits are going to have to add to eight. Clearly can't put a nine on there.
Also, we're going to have a one in that eight group.
Can't put the one there. So, we have this kind of interesting little gapper going on. Now, is this 16 or the 14 further restricted because now of what those things are pointing at?
Let's think.
>> [clears throat] >> Cuz what's the That's the max here.
Well, the minimum here, I guess is the better place, is 3 5 6, right?
So, we're looking at 14.
Now, does that mean we can't or we have to put a three in it? Cuz what happens if we don't? We're 5 6 and 7. We'd be at 18. So, that's a no-go. So, yes, there has to be a three on this thing.
We're probably going to have a similar restriction here.
Now, what are the options here though?
Is Can we get into that or is that getting too uh soon into this thing? So, if we know there is a three, we have 13 left over.
We can't do 9 4.
So, it's either going to be an 8 5 or a 7 6. Yeah, we still have those possibilities, I think. So, let's go over to the 14 for a second and think about the minimums. Well, these might not be as helpful cuz there's two three and four at this stage which is just nine.
Uh so, we probably can't do too much there.
And there's not going to be like the 16 a minimum sitting there telling me what's what.
Now, we can use our knight's move that I remembered is there and never forgot.
You can't be a one.
You [snorts] can't be a nine. Oh, we can also Well, we can't really Yeah, we can.
We can do some restriction here. I noticed the Kropki and then I got caught up in our little crosshairs. So, I kind of forgot to come back here. You can never be a nine.
Cuz this would have to be an eight.
Ain't going to happen.
Now, if you are the eight, you would be a seven and then you would be a three.
If you're a six, you will be a seven.
You will be a three. Well, I guess this is a 7 3 then.
Cuz obviously we can't go from a six to a five and put two fives in the 10 clue.
Okay.
Now, what does that start to tell us about any of these maybe? Cuz we're going to start to put some pressure on some of these things. And we're also going to have some restriction here on this 11, I just realized, because of the 1 2 4.
So, we're never going to be able to do a 9 2.
And we're never going to be able to do a 7 4.
But, we still do have the 8 3 and the 6 5 options there. So, there's a little bit there, but not a ton.
And let's think further now if any of this gives me further restriction.
Cuz nothing is sticking out at me unless the three and the seven are doing a whole lot. Like you can't be a three.
Uh although I don't know that that's going to tell us a ton of information right there.
Guess we know none of those can be threes either. So, we're going to starting to put them into those.
Now, what did we say this was? Did we say this was the eight, right? So, maybe we have to just think about what the values there can be and there might be something that's just a given.
Right. So, let's make sure we're correct on that. Yeah, cuz we're at 23 and the 14. We're at 37. So, we need eight more to get to the 45. So, it's either the 1 2 5 or the 1 3 4. Now, you can't be 1 2 4 or 3. You are 5. There it is. We got crosshairs. Imagine that.
Since this thing has a five on it, which means it has to be the 1 2 5.
Good. Now, we can get into our 14. These should just magically appear and make the values correct. 3 7 and Nope, I did that wrong.
Uh Wait. How did I do that?
This has to be 3 7 and 9, but No, not 3 7 9. 3 And how did I get the Oh, this is just a nine, but forget it.
I can't look at what I'm doing.
>> [laughter] >> We need a three, a four, and a seven.
That will work if I again can get my brain to process things correctly. And again, I didn't notice here that we did have the fact that we removed the nine here and we had the nine in the knight's move. So, this was going to be the nine always.
All right. Now, we do have the 3 4 7.
Once I figured out how to count or even just look at things and see what's left over. Now, does that tell me what's the the 10 is now? Cuz it can't be 7 3 or 6 4.
>> [snorts] >> But, it could still be 9 1 or 8 2, I believe.
Now, you can't be a two either though.
So, you're a four.
Let's pop that in there. Now, let's go back to the math here cuz we know there's a nine and a five. So, we should be able to just tell what this last digit is. And I don't remember what the heck value we're going for.
Uh 20 So, we needed a 22. Okay. So, we're at 14. So, we need an eight. This is a 9 8 pair.
And if that's the case, guess what?
That's looking at that. This has to be the six and the eight. And then this will have a given and we'll probably be able to get onto our 11.
Again, maybe depending on what the heck I'm doing with myself. 3 6 7 does add to 16.
That's a miracle.
You are not the three, of course.
And do we have anything else we can do?
Cuz we know one of these will be a three, right?
And it's not you. So, it's you.
We know this is now the seven. What do these have to be? Four and six.
I think both of those could still work.
Now, but that six does say you can't be a six cuz we'd see both of those.
And I don't think any of these other digits are staring at me. You can't be a three.
>> [clears throat] >> We might be able to come back over here in a second, but let me just try to Or maybe we just need to go into our 11.
Cuz you could be a 9 2 technically.
You can't be 8 3. You can't be 7 4 and you can't be 6 5. Yeah, that's all it was. Okay, you are the 9 2.
If that's the case, you I thought I saw something here, but I guess I didn't. But, this is the one and the two.
I was looking at it from the opposite direction.
These are two and nine.
Can put anything here? I don't think we can.
You can't be four on a You can't be four or six. So, let's see what the options here are.
We could put a one, can't put two, can't put three, can't put four, can't put five, can't put six, can't put seven, could put eight or nine. So, you are just one or eight. Okay.
Wasn't sure if that was going to get me there or not, but hey, it's worth a try.
Uh what did we say this one was again?
It was either going to be the 9 1 or the 8 2. Yeah, I think it could still be those. Okay.
Uh what about you now? Because again, we've Like over here, we started to have digits pointing over here.
Cannot be 9 2.
It could be 8 3.
Cannot be 7 4.
But it could still be uh the 6 5, couldn't I? Guess let's Oh, no, it can't be a 6 5 cuz both the 6 and the 5 look at you. So, you are the 8 3.
That's the case. You are the 8, you are the 3.
Good. So, that 8 will say this one is that one. So, I just took one step too soon to try to think about this value.
What about these two now?
Cuz we need a four somewhere.
We know it doesn't go there. Well, no, it can go here. Sorry. It was this one I was ruling that out for.
We need a five and we need an eight.
Well, guess what? This is the eight. And this will be the four five. Now we can say that this is our six and four.
You can no longer be a four, so you are the seven.
You are not sevens. That is a three four and nothing at the moment is looking at it.
What else can we do down here? Anything?
Or do we know We know what you are. So, you are the nine.
And then what are these three? Cuz maybe we just have some restrictions there. 5 6 7?
You can't be five or seven, so you are six.
You are a five seven pair. Okay.
Um moving on then. We're going to have to find another one of these groupings we can work with.
The 12 looks slightly restricted cuz we can't do the 8 4, but we're still on the 9 3 or the 7 5.
And I think both would work.
Again, this 10 hasn't shown us anything yet.
You I don't think you've shown us anything. So, we might just have to start thinking about base Sudoku and where things can and can't be placed now [snorts] that we have these kind of restrictions.
Could be.
Might not be.
We know one of those two is that three.
We know there's a four up [snorts] here somewhere and it can't be you.
Let's try to go through those things. We have a Okay, that's what it is, the six.
So, we can use our Sudoku. I just wasn't getting to the right number. There's no six in any of these.
Can't put a six in the 10 cuz we had to put a four. So, this is six.
Do we have anything else like that?
Cuz this again is still just I'm going to put this in cuz I keep saying it and it's annoying me that I I can't remember those digits right off my head.
So, what can't be a one there. I think everything else is still possible.
Now, we're starting to get close to having like a quad or a trip here.
What's going on down here? We need a five.
It can't be you.
I think that's the only given down here, isn't it?
It appears to be. Okay.
Uh let's see what else we can get through then.
Cuz that six affect this in any way? Cuz again, these can be 9 4 or uh 8 5. Now, they can no longer be the eight or the seven six. You can't be the nine, so you can't be the four. Again, I'm probably overstepping this one just a little bit to start, but we got to do what I've got to do. Nines, no and no. Oh, wait, we can do nines. I think we just need to go down our Sudoku and see how things are working cuz no by that, no by this, no by You are nine.
Which means this cannot So, again, I took one step too early. You are not a nine, so you can't be a four, so you are that 5 8. Which means we have an X-wing on fives. One of these will be a five.
The seven now has just removed the five from its option, but I don't know if that's enough.
Uh let's go down the again, keep going down Sudoku land. One of these will be the nine.
And see what else we can find cuz we know one of these will be a nine.
Let's try the eights, see if we get more information cuz I think we're going to.
One of Yeah, this is an eight.
So, that's going to tell us the five and the eight again.
One step too early. Eights.
So, now we know none of these are eights, so you are an eight.
Okay, here we go. One of those this one cuz we can't put that one is eight.
Now, where does that say an eight goes in here? Can't be any of those. It's going to be one of those two.
And I guess we can't quite say [snorts] yet cuz we don't have any of those looking at it. So, you're not eight though, by the way.
Which means you can't be two and you can't be nine because of the other restrictions we had over there.
Okay.
Let's uh move on to the next contestant.
Sevens.
Can't put a seven in a seven.
Mm Oh, the five. Let's go over here first cuz we get the seven and the five.
Again, use what we have cuz now we have another bit of info, although it didn't really tell me very much. What about the sevens going this way? Yep, there we go. Those can't be sevens by knights.
No sevens, no sevens. One of these will be. So, we're almost pushing a trip here. So, let's keep going down that line. No sevens, no sevens. One of those will be.
If this is a seven, this has to be a five and I think we can still make that work.
So, let's move on to the next again, sixes.
No sixes.
No, no. One of those two and they both look like they're still available.
None of those.
You could still be or it could just be a 1 6 to make the seven. I think that's still possible.
No six. One of those two. Can we do anything else with sixes before we move on?
I don't think we can, so let's go the five. We had the marking for the five already. Again, got to look at my markings. I tend to look at the big numbers first before I get into those.
Uh none of these can be fives. You can't be a five, so one of these two will be.
None of those Oh, this is a five can't go here, so this is a four five pair.
So, that should limit these two to some sort of useful contraption, right? You are ones and twos.
Maybe not as useful as I hoped cuz two doesn't see it, the one doesn't see it.
All right, let's go back to our Sudoku yet again.
Again, one of those two will be a five.
I guess we can I mean, we could start clicking away on some of this, but I don't know if it's good enough. Let's do the fours instead.
No and no. Yeah, that's better. One of you will be the four.
We already know it's one of those two.
Mm none of those.
This could still be a four three, I believe. Oh, wait, you can't be a four cuz you would see both of those. So, there is a four up here, which means you are not four, which means you are good. Again, this could still be a four three, so I can't push the four there yet. But I guess we can say you can't be a four cuz this three sees that one.
So, let's do it.
And let's move to the next bit. I don't think we have any more fours, so let's try those threes.
See if we can find anything there. None of those.
Not you. So, one of these two. We're starting to push those.
One of those three.
And either one of those could still be cuz we're not seeing both of those.
All right, let's put these in and let's see what that does down here.
This is a 3 9 pair. Again, we're finding some information, so that's always good.
And Oh, the nine here. Why did I not get rid of you? Let me make sure I did that.
Oh, I did that wrong.
Hold on. This was not the nine. This was. I must have misclicked that cuz you saw you and then those all saw those.
So, it was one of these was the nine.
My bad. I almost screwed that up. One of these is our three, so we don't have a 3 9 pair yet.
Let's keep looking. But we can Well, we are starting to restrict again the 11 possibilities and it's and at some point we're going to hit on these guys out here and it's going to give us some extra work we can get done.
Uh but let's again, keep on keeping on.
We know it's one of those. We know one of those. We know it's one of those.
No, no.
I think that's probably the limit of the three restrictions. Let's try the twos and the ones one more time.
See if we can get anything out of them.
There's really nothing on twos, so I mean, I guess you can say neither of those can be two, but eh.
None of you, none of you.
No, no, no, no. Eh, okay, there it was.
It is the one.
Imagine that. I start high and it ends up being the low digit that is given digit. But when I start with the low, it's always the high digit.
Let me make sure I'm correct cuz I've screwed this up before.
Not you, not you, not you. You two can't be. You are the one, which means you are the three, you are the nine, you two nine. Perfect.
All right, what did that tell me now?
Cuz I don't think that tells me just enough for this. But now that we have these nines sitting here, this has to have a nine in it. So this is a three-nine pair, which means you are the seven.
Again, no nines, no nines. That one sees that one three-nine.
That gets rid of the three here, which says you are our three.
Do we finish with our nines or do we need to go do the three cuz we just picked one of those up?
I don't think we have anything else left on the nines there cuz none of those see anything that I can that I can put a handle on. So let's try that three.
No, we already know one of those.
We already know one of those.
None of you, not you, not you. Yeah, I don't think that told us enough there.
At least not that I can see. Okay, so we've got a three-nine now.
Uh was there anything maybe let's go back to the ones cuz I think there was possibly still some work to do there. We know one of these will be a one.
That means you can't be a one.
It's going to be one of those two, but those are still both in play.
These ones don't see the the ones that we've already reduced. None of those can be ones.
You can't be a one cuz you'll see both of those.
You can't be a one because this one sees it.
One of these is our one, which means you are not, which means you are.
Good.
We keep getting closer and closer. Now that's going to give us this 10 finally.
You are the eight, you are the two.
That's going to give us the nine and the eight. And I'm pretty sure the eight and the nine there's had some other restriction, did they not?
I was waiting for one of them to drop.
One, two, three. Oh, the eights are just done.
No. One of the Okay, yeah, we can get an X-wing on nines. So I think that's might have been what it was.
So we have X-wings on nines. None of you can be nines. You are a nine.
This is a one-two pair. You have to be the one, so you're the two and the one.
Now this stuff will start all working together for us. Let's go back down our line.
Perfect. Where does the one go? It goes right here, which means you have to be the six, which means you have to be the two, you have to be the four, you have to be the three, you have to be the seven, you have to be the five, and you have to be the two.
That forces the one. This is a one. This is a nine.
See how all this stuff collapses? What are you? You are a two. The nine says three and nine. So we did a lot of legwork early on where we probably didn't necessarily have to right away, but we got it done, so it made us makes this all easier.
Where are you two? Or actually just what are you? You are a six.
And that tells us you are the three.
Do these threes and fours have anything?
Not yet. The five here though says four-five.
Let's dive over to here.
We've got twos and fives.
Uh two Oh, the two here, yep, we'll say and that one as well. It's double.
Fives and twos. That five's going to come over to here to the four and the five. That five's going to tell us this is five.
Perfect.
This is a three-four pair left over. You are the four three-four.
What are you cuz you're just a given six? You are just a given two.
Six-seven. You are a given. That's going to tell us the 11, which is four. Took me a second to find it, which means you have to be our seven six-seven.
And then you are the final six down.
Thanks for solving my first puzzle.
Thank you for making it. Really enjoyed that one. It's got us 500 solves in less than two days. So I mean, good puzzle.
Really enjoyed that. Great logic.
Uh everything flowed really beautifully.
Everything kind of worked nicely if you're just Obviously, I do it every time. I try to always think of what the the meaning of the title is. And course when you looked at this to start off, we got this crosshairs looking into here, and that was what got us moving in the right direction for all this stuff.
Wonderfully named, too. Love it when you have good names that give you maybe a little bit of an idea of what you're doing. And then once I just started looking in the right places, everything started to work together. And we We remembered our anti-knight. We did not forget it. That's amazing.
Well, we forgot it for like 37 seconds, but nobody Nobody knows that except for all of you.
Anyway, really fun puzzle. Really enjoyed this.
Uh Fid Ma Chi Cascade, I hope you maybe see this and and uh uh keep making more puzzles and get the you know that the uh the bug to keep doing it because of any kind of, you know, attention you get from all this stuff. But uh really enjoyable puzzle, so really really really liked it. Hope you all did as well, and we will see you next time. Thanks a lot.
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