This video elegantly transforms complex arithmetic constraints into a masterclass of pure deductive reasoning. It is a highly effective guide for anyone seeking to master the disciplined logic required for advanced puzzle-solving.
Deep Dive
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Deep Dive
Working with just ArrowsAdded:
Hey, how's it going? Welcome back to the channel on today's puzzle, which called just some arrows and we have just some arrows. Imagine that. Uh it's by Realman.
I'm kind of liking uh getting into some of these just individual rule set puzzle. We've done quite a few of them recently, I think, over the last couple of months. It's It's they seem to be popping up more and more and more and I keep seeing them. They They intrigue me more and more and more cuz there's There's not as much Well, I mean, there's still a lot of going on, but there's not as much to try to have to remember and how to work through. You can just kind of use the the uh the cleanliness of a singular rule. So, that's why we're going to do this one again today. So, it's again just some arrows by Realman.
We have very short rules cuz it's just arrows. Normal Sudoku, every row, column, and 3 by 3 box will contain the digits 1 through 9 once each.
And we have arrows. So, digits along an arrow must sum to the value in the connected circle. So, these two digits, whatever they are, add to that value.
Uh these are some interesting looking arrows, but these I'm assuming it's these three digits add to this and then these digits or these uh five here add to this.
Cuz you'd have to break these off.
Uh there's no other way to actually work this right cuz what's What would happen if you tried to make all of these add to it? You couldn't do it. So, this is like a bifurcated arrow, I guess, is the best way to put it. So, hopefully everybody understands that and sees that. Uh but if you didn't, hopefully I just explained it and then that will work for you. So, anyway, with that said, let's dive this one, have a little bit of fun. Links in the description below. Let's get at it.
So, let's start with these kind of funky double arrows, if you will, cuz again, we have one, two, three, four, five values that are going into what this must be.
Now, they of course could repeat. So, it could be a one two and a one two. It's six minimum.
Plus a one >> [snorts] >> would get us to seven.
So we're looking at seven, eight, or nine.
This thing I think is the exact same thing. Yeah, it is. Seven, eight, or nine.
Now there's probably more restriction that can be done there.
We can probably have quite strongly restrict what this digit can be.
So let's think about the minimum of these. We're getting one plus one and two.
We're at four.
Plus a one. So we're at five. So the most this can ever be would be a four.
Let's put it in.
Now we're probably [snorts] going to be able to restrict most of these in a very similar way, right?
>> [snorts] [clears throat] >> Cuz again we have four there. The most these one plus one two. Well, I guess this is even less than this, right? Cuz that's a three. That's four. No, these could add to five. So that's that's fine.
So I think this could be again one, two, three, four. These could be from one, two, three, and four. Cuz again, we can go to a a max of five, let's say, plus six, seven, eight, plus the one.
And then this one is the six. So this is a three.
One, two, three max. And then again, all of these will be the same concept. One, two, threes, and fours.
One, two, three.
And actually this guy's even I didn't notice this. This guy's even longer. So these are restricted even more. I'm kind of >> [clears throat] >> took it from the wrong side.
These will be reduced even further.
This is a one two pair.
Excuse me. Three one two pair. Three one two pair. Okay. This is nine. And these are all one two pairs.
Just didn't see that for reason.
So, let's put all those in. That means you cannot be a one or two anymore. You can't be a one or two anymore.
Now, that's a minimum six. So, you can't be a three. You can't be a four or a three.
>> [snorts] >> All right.
So, what more does that tell us now? We know there's no one ones and twos in here. So, one of these will be a one or a two.
>> [snorts] >> The We could probably still get to a seven.
No, we probably can't, can we?
Cuz that's the minimum. One four one plus three to make four. Excuse me.
Yeah, I think we're going to get us a a nine here. These are all minimums as well. But, one plus the three is four plus the three is seven plus two ones is nine. Yeah, that's what this is. Okay.
Again, being a little slow.
These will be threes.
So, we now have six seven eight. You will be that one two two one one and two.
All right. A lot of information there that we we did. We just had to again look from the right side of things.
Just didn't notice the extension there.
All right.
>> [snorts] [clears throat] >> Now, we know these are a one two pair.
That's three.
So, these two have to add to six in some way.
One two three four five. You obviously can't be two. You can't be one.
That means you can't be a five.
>> [snorts] >> And or do we start looking here maybe and here?
Cuz you're a minimum three four so seven. Seven or eight can't be nine.
You are a minimum four two which is six.
Can't be nine.
This is a one. These two have to add to eight. That's not the greatest restriction as far as I can tell.
>> [snorts] >> And what then?
Do we have Sudoku maybe? Cuz we do have a ton of ones and twos.
I guess one of these is one.
>> [clears throat] >> Which means one of those is one.
One of those will be a one.
One of those will be a one. Okay.
There is Sudoku there, but it's not really too helpful.
One of those will be a two.
You can't be a two, but any of those could be one of these will be a two.
I don't think we're getting much more there. What about the threes? One of you Yeah, not a lot there.
Okay.
Let's try to dive into what we can and can't do. Can this Okay.
You have to be a three. Cuz what happens if we put the three here?
Well, this is a min four five. Can't be.
So, you're a three.
That [snorts] would give us another three at least.
Now, this has to be a four or a five to make seven or eight.
And >> [clears throat] >> I was wondering if we had any other restrictions like that we could do with where our twos and ones were placed.
>> [snorts] >> Like what would happen if this was the one?
No, that still works.
Cuz this could be a four two to make the six we need.
Yeah, that seems logical.
Um What else can we say?
Now, I I mentioned this before. I guess we can go look at it.
>> [snorts] >> We know we're at fours and fives as minimums here. 4 5 6 7 We're never going to go any higher than a seven cuz we already have a one.
In fact, neither of them can be sevens cuz we'd have to put a one here. So, seven goes away.
In fact, this one's going to be the most restricted cuz you can't be a six either. That's a six. That's a one.
We're at seven. This is a minimum three.
No go.
You can be a six cuz this could be a two.
>> [snorts] >> 6 7 Oh, it can't be cuz you can't be a nine. My bad.
So, this is a 4 5 pair. Okay.
Didn't see that interaction. Okay, so you are either six or eight four and you can't be six cuz if I put a The only way to make a six is a four with a one and a one.
Obviously, you can't do it. You are eight.
You're not eight.
Good.
So, the four either goes with the Oh, okay, it's going to be a 4 4 cuz I'm going to say you could do either a four with four or a five with Oh, no, no, no.
I'm forgetting that we have a one here.
So, dumma.
I didn't say a- a- ass. I said dumma.
>> [laughter] >> Cuz YouTube sensors ain't going to get me even though I can say such things, but uh um There's a one here. These two have to add to seven.
So, [clears throat and snorts] it's either a four with a three, which it can't be.
So, it's going to be a four with a two cuz the five would have to go with a one or a two and a or a The five has to go with the two.
Brain, please function. We're trying to make seven cuz the four can't go with the three. 5 2 Don't worry. I'm okay.
You're not a two.
>> [snorts] >> Which means you can't be a four anymore.
Let's go over to you cuz again you can't be 9.
>> [snorts] >> We currently have five.
The minimum here is three so it's going to be three. Eight, okay.
Now we can probably start digging further into some of our Sudoku.
>> [snorts] >> And or we can say can you not be a two?
Yeah, you absolutely are the two cuz the same thing is up here. If I don't put a two here, I put it here and these are meant for five. So you are the two.
>> [snorts] >> And you have to either be four or five.
Okay, [snorts] let's go back to our Sudoku now.
I don't know that we do anything with our ones but we have more [snorts] twos and threes we can work with. One of these will be a two.
One of those still.
Okay, now we can do the two over here cuz we know this one obviously can't be a two.
So this is our two.
>> [snorts] >> This means one of those, not the greatest. Let's go to the threes then.
>> [snorts] >> Threes, threes, threes, where do the threes go? One of those.
Not sure on that one just yet. We know of course these are from six, sevens, eights, and nines. I don't want to put all that in yet just yet I don't think.
>> [snorts] >> So I don't think the five tells us much does it?
>> [snorts] >> Or do we need to go back to you now cuz again yeah.
Why did I ever put a three in here?
I'm not quite sure I knew.
These were three. These had to add to six. Can't ever use a three. You're a one. You're a five.
>> [snorts] >> Okay.
Brain is not 100% yet as you can tell by my voice.
>> [laughter and snorts] >> We're getting there.
We are slowly slowly getting there.
Let's go through the Sudoku one more time now.
I think the twos are all set, the ones are sets, the threes are set as far as we can go at the moment. Now, what is the min here?
It's [snorts] going to be three, four, and that's it.
Cuz if I try to go higher, it's three, six. This is a nine, it can't be. So, you are three, four. You are seven. We just know that this is the three. This is the four.
Good.
None of those are sevens. Didn't we say these were two of something? Maybe I was looking at the wrong way.
I thought this was a pair of something.
I guess I'm wrong. Anyway, uh these will be six, eight, nine. Let's put them in. You're not eight, obviously.
So, we have an eight looking here, so we can put an eight here.
At least one of those two will be an eight.
>> [snorts] >> What about these three?
Need a four somewhere. It can go anywhere, and that's five and six.
So, [snorts] I think those can go anywhere they want.
I'm going to start putting some of these in, cuz we're going to get to the point where we're going to probably have a trip or something going on.
And let's see what else we can do.
Don't think we could do much more with those. Let's start thinking about the minimums over here, maybe.
Or maybe [snorts] we start thinking about this guy, cuz again, we had to make these add to eight.
>> [snorts] >> What are the possibilities when you're a minimum six?
Can't be one, two, three, four, or five.
So, [snorts] it's six or seven with a one or a two.
I guess either could still work.
>> [clears throat] [snorts] >> Does that push anything here? Cuz again, you Yeah, we [snorts] probably can't put Well, let's think about it. Cuz again, we don't have the three restriction, but we do have one, two, and four. So, you could be three, six, seven. I guess you could also be Oh, you can't be eight, but three, six, or seven. So, what does that tell us about this digit?
>> [snorts] >> It could be one or two. Can't be three.
It could still be a four. Can't be five.
Can't get into the sixes.
Actually, no, it could be a six.
Cuz it [snorts] could be a six three with a nine. That is possible.
Okay.
All right. So, that was not as helpful as I thought it might be, but that's okay. Let's move on to something else, if we can.
Do we want to dig back into Cuz I think we've used all the arrows for the most part.
Except for what's going on here.
Now, of course, they can't be one, two, three, or four. So, we're looking at five, six, seven, eight, or nine.
I think all of those are still possibilities.
Two, [snorts] three to make five.
I guess we can't make a six.
Four [snorts] three to make a seven.
Six two to make an eight. Six three to make a nine. Okay.
>> [snorts] >> Uh one of these will be a five, though, I just realized. Cuz this five blocks this one.
Sadly, that doesn't really say anything about these. I thought there might be a restriction there.
>> [snorts] >> But a no-go.
All right, phone.
Quiet. Trying to work here.
Uh All right, let's go back. Let's do another quick look on Sudoku. So, I feel like I should be at a stage where I can do something.
>> [clears throat] >> But I'm not quite seeing where it is.
One of those two will be a four.
Mm, maybe not.
Can be No, it's one of those a seven.
Okay.
It was worth the look. Again, we know one of those is an eight, but I don't think we really have a ton with nine. Oh, we do have a nine. That's what it was. I didn't look at the nines. One of these is our nine.
Which means you have to be our six.
That's going to start impacting these other guys, by the way.
>> [snorts] >> So, this is an eight-nine pair. What are these three maybe?
We need a three somewhere.
Yeah, there's two options, sadly.
So, it's three, four, and six. Three, four, six. You can't be three.
>> [snorts] >> That's the only restriction. Okay, let's go back across here, cuz again, you can't be a six anymore.
10. Is there any more restriction now here?
Six, two, three, four.
Seven, two.
One, six. No, it looks like we still have all options available there. Okay.
It's worth the look, though.
Uh let's see what else we have, though.
Three, four, five, six.
We know fours and sixes get pushed over to here.
Mhm.
Three, four, five, six, as well.
We know there's a seven up here.
We know there's the nine down here.
>> [snorts] >> One of those will be a nine.
One of those will be Huh.
>> [clears throat] >> Okay.
Let's uh let's start putting some of this digit in then, I guess, cuz I I'm not quite seeing enough of this.
Six, seven, eight, nine. You're not six or seven.
So, we do get an eight-nine pair, which means this is a one, two, four. That's useful.
Can't be a one.
6 7 8 One of [snorts] these two will be a three.
Eh, not a huge fan of that.
2 6 7 5 5 6 7 8 9 uh You're either 5 6 or 7. It's not helping.
4 and 5 pair. These are from 6 7s 8s and 9s.
>> [snorts] >> Let's put them in cuz again there's there're little restrictions here.
And they may be enough to start pushing something else.
6 7s 8s and 9s. I just struggling to see what it is here for a second.
One of those two is a five.
>> [snorts] >> Does that matter? Doesn't really feel like it, does it?
All right, what am I missing?
I'm [snorts] missing something obvious.
Where oh where can you be?
Like where does the three go in this row?
Only there.
So you're not three. So this is the 3 9 pair.
And you will be the nine. You will be the three.
All right, let's keep rolling with the threes cuz now we can put the three here and the two here. It's going to tell us the four.
It's going to tell us you're not a four.
It's going to tell us you are the three.
So let's roll with this Sudoku for a second cuz I think we're done with a lot of this.
We have a 1 2 pair.
1 2 1 2 2s are done. 3s are done.
I know we have some things I can work on there. I just want to check out these uh couple little things first.
This is just a what? A 5 7 pair.
Which means you are a 4 6 pair.
4 6 5 7, okay.
All right, what about those nines? Cuz we had a couple of things there.
Yeah, maybe not as useful. Okay, anyway, let's go back to this cuz you can't be nine or eight anymore. In fact, you just are five. So, this will be the two and the one. Yeah, that's all I had to do. I was holding on it cuz I thought we might get more Sudoku, but we didn't.
You are not fives.
Go away.
That's a 6 7, so these have to be from eight and nine.
That's an 8 9 pair. You're not 8 9.
One of these two will be the other 8 9.
All right. [snorts] We're making some progress here.
This is the only place for a seven in the row, so that's going to force the five.
This is a 4 6, so you're the five.
Okay.
Anything Oh, the five here says four, which says seven, which says five and seven, which says not seven.
Which means you are the seven.
Which means you are the six. You are the seven.
You guys are not the sevens as I was already about to do if I can get my hands to work properly.
One of those two will be the six. 6 8 9, okay.
The four here says 6 4.
Which says 4 6.
This is a 6 8 pair. Obviously, this one has to be the six and the eight and the nine and the six.
You are not nines, so you are, which means you're 8 9 8.
Good, we're almost done with this thing.
We just have to do the last little bits.
Um We need a six, we need five, and we need a nine.
None of those are necessarily givens there. What about you?
We need a four, one of those two. We need an eight.
Any of them. And we need a nine. Okay, there we go. You're the nine.
Which means you're the four, which means you're the eight. That's going to do it.
Six, eight.
>> [snorts] >> You're a given of six. Does look like it.
Now, these are the five, nine.
And they're not quite resolved. We'll have to go down here.
Five and nine. We can do that one, though. You are five. You are nine.
Five, nine.
Five, not eight, or four, or six. Hello, fat fingers. You are seven.
What are you two? Four and five. So, four, five.
Let's just finish this off.
Need a four, it goes here. We need a seven, it goes there. We need a six, and we need an eight. There we go. Okay.
Solved the puzzle, the solution is correct.
Uh, we got there eventually. Yeah, got a little stuck up there for a second, I think, because I was First off, at the very beginning, where I started looking at this, when I should have very clearly started here, but I just did not uh see the extension of this one.
>> [snorts] >> And then there were some other little bits and bobs here that we could have worked through. We just had to find a little bit of a starting point, and then once we did that, we were moving along.
So, good puzzle. Love a good singular rule set puzzle, where you can just focus on that rule and not have to jump all over the place. So, love the puzzle. Hope you all did as well. And we'll see you next one. Thanks a lot.
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