In this variant of sudoku, each cage must contain digits that are either all even (oil), all odd (water), or a mix of both, with the constraint that oil (even digits) always floats above water (odd digits) in mixed cages, and digits within each cage must sum to the given clue without repeating.
Deep Dive
Prerequisite Knowledge
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Deep Dive
Searching through the Fog to find Oil and Water
Added:Hey, how's it going? Welcome back to the channel. Today's puzzle, we've got another Bob's puzzle. Uh, it's been a little while, I think, since we did their last one from them. Again, I we had done a bunch of series of theirs from the Lord of the Rings and Hobbits one. So, um, not assuing him anyway.
Just u haven't clicked on some of them just because we've done so many of their puzzles at this point already on the ca on the channel. But this looks like a fun one. I think we did an oil and water puzzle from Blobs earlier as well if I remember correctly. But this one is using an oil and water and it's mixing in some fog. So, you hooked me. Give me some uh fog and I'll solve it. I'll try to at least. So, let's go into the the rules and see what's going on. See if we can get this thing done. What do you say? Foggy oil water by blobs. Normal sodoku. Every row column 3x3 box will contain the digits one through nine once each either. Oh, sorry. Each cage is either full of oil, even digits, full of water, odd digits, or a mix of both.
That's a normal oil and water type of thought process. In all cases, each row within a cage is a just one type of oil or water. Oil floats on water. So, even digits will always be in rows above odd digits in mixed cages. So, um well, let's ignore the three here for a second. We could this cage is going to be some either fully oil fully even which obviously it won't be or fully water odd. It could be or it's going to be some mixture of the two. Now if it's a mixture the oil could be sitting right here and all of this could be water cuz the water will always settle down to the bottom. So whatever you have, if you put a piece of water here, you have to fill the rest of this with water or your just water and the oil will settle on top of it kind of like that. So oil water keep separate water on the bottom, oil on the top cuz oil floats on water and oil will be even water will be odd. Got it? Good.
Killer cages digits and cages do not repeat. Digits and cages must sum to the small clue if given. So we know this will be a 32 and they won't repeat obviously and the grid is partially covered with fog. Placing correct D is will clear the fog from surrounding cells possibly revealing more clues. So it feels like this is standard fog. So if I were to put this digit in, this fog would clear because of the the nature of the the way it's stated. Don't know if that's exactly the case, but we'll find out when we get in here. Once we get some uh digits put in, it'll it reveal itself to us. So uh that said, why don't we just get into this thing? Link's going to be in the description below.
Let's have some foggy oil and water fun.
Sounds kinky. Let's get at it. Links in the description below. Uh so water you are. Let me put this up here so I can remember the um oil water s system going on here.
Now if we know you're a three 9 8 7 and six gets us. Okay. So we know what these are essentially because we have to get to 32 and we know we have one of them is a three. The remaining four digits the most they could be is 9 876. Well 976 is 30. We already have three. So we have to remove one digit. So it's going to be 9875.
Now if we know that all of the odd digits are water and all of the even digits are oil, we have to put that even oil digit at the top and that will clear that up. So this is go standard sudoku and you will all be water. You will be oil. Oil's orange. I don't know why it just is. Um, so there we go. Now we can start to think about what these digits are. 1 2 4 and six. It looks like you obviously can't be a six. Now, we don't know where this goes, but we can think about it, I would guess, because we can think about the orientation of the cage and our oil and water constitution.
Now, you could be a two cell cage where it be a one with a five or a two four pair. They're both of the same variety of oil and water. So, they will both work in this case. Or it could be a three cell where it would be 1 2 3 [snorts] and the oil would be the evens and the water will be the odds. But does that actually work? No, it will never work because if we think about where would the how would we make this work if it was three cell because we have if it's a one, two, and a three, we know the one and the three are both water.
They have to be low. Oh, I guess we could make that work cuz we could do the one and the three here and they can pop a two up here and the oil would be the two sitting on top of the one. Okay, so that does work. I just had to think through it fully before I got there.
Okay. So, the answer to that was I have no freaking clue.
What the heck is going on with that?
Now, I don't think we can say anything about you. Can we? Because we don't know if you're oil or water right now.
I'm [snorts] guessing you could still be either. Now, if you are oil, the oil has to fill up the entirety of this cage, wherever it may go to. We don't know how much further it goes. 1 3 5 7 and 9. It would be No, sorry. Evens. It can't be oil. There we go. Cuz we'd have to fill all of this. But we It's in a cage and they'd all have to be different even digits. Well, there's only four even digits. We can't get the oil all the way up to the top. So, you can't be oil. You have to be water and you have to be odd.
So, you will be a one. Good. That side worked.
Now, let's start thinking about the 21 cage. I guess now we again we don't know if it's three digits or what at this stage. [snorts] Um I guess we can also start putting these in as oil now. Does that tell us the the six? It does cuz now we Well, no, it actually doesn't, does it?
Yeah, it does. It does tell us what the six is, doesn't it? cuz let's go back through our thought process. What could the [snorts] um the six be if it was a three cell? It would have to turn. But if we know your oil, it would have to turn downward.
This would have to be the three because the three has to be the water that's on the low side. But then you'd have to make this oil and it have to be a one.
But it can't be a one. We can't make them level because the oil and water can't mix. We can't do this cuz the oil would have to go all the way up. So this just is a two cell six which means you are a two four and you are both oil and that will be the end of the six. Now does what does that do for me? I'm not entirely sure but I think I'm correct so we're going to stay with it. We know one of these two will be a six by the way if that helps. And the 5 79 pointing at the 21 does that help in any way? Because what's the minimum these can be or the most they can be I guess is a better way to think about 86.
Is that really helpful?
Uh not really because it would just be a 14 and you could be a seven. That won't work because that would be the opposite way of water and oil.
[snorts] Now, is it ever possible for this 21 cage to ever be fully oil or water?
I'm thinking the oil would be the best place to think about it because if we know it can't be all oil, we can probably start thinking about putting water down [snorts] or the or vice versa. Essentially, [snorts] what happens if it's all oil? I don't think we can ever get to 21 with all oil, right? 2 4 6 and 8. No, it'd be only 20. So, there's no way this is all oil. So, there is water.
So, the question is going to be, [snorts] could it be all water?
Because again, we don't know where it goes yet. We haven't worked that out.
Or is it just like water down here somewhere with a blob of oil on top? I guess we have to go through both or certain different scenarios to see if that will work cuz let's say these were water.
They would have to be a one and a three.
So obviously we couldn't just stay in the two cells. We'd have to dip down to at least get us where we can put another bit of water in.
Then I guess you could still be water.
If you were to be oil, you would have to be a six. Does that matter?
It would [snorts] leave us 15. We can make that work. We could just use three water digits, right? [snorts] Obviously, you wouldn't be able to do two of them cuz that would make it an even number in total.
Um, yeah, I think we could do that. We can make 15 with three those odd digits, right? Yeah. 3, five, and seven would Well, [snorts] that couldn't work because of the situation of this nine.
95 and one would work. But then again, we still have the same problem.
Is it just not possible to make you oil because of what it does to this? Let me just kind of [clears throat] put it in as a description.
Or these could be all oil and then we can find a way to put water down below. That's probably also a possible solution.
Um, let's think further.
What happens if we go water here?
All of this will be water. We know you will be a 13. Let's just kind of roll through it.
you will have to be from 57 or 9. This cannot continue this way. It would have to drop down to another 5, seven or 9.
So, we'd have to be we'd be at and it'd have to continue either turning this way or turning down because we can't make 21 out of these digits, right?
No. Because the most we could ever do would be 20. So, we'd have to either we'd have to continue.
That would be all of our digits of oddness.
Where are those actually add up to? 49.
No, there's no way that'll work cuz we can't make the math work [snorts] cuz all of the odd digits together are 25.
That doesn't equal 21.
Just letting you know.
So I don't think we Yeah, we can't ever make you water then. So you will have to be oil because there's no way to make the math work. We'd we couldn't put we'd have to extend beyond you at a bare minimum because of what this is doing.
Well, that's four odd digits adds to an even digit. So we'd have to continue.
But then we're overshooting. So you are actually just oil and you will be a six.
Cool.
Now we get a 23 here. You will be a 986.
It's the only way 23 can work. You will be that six.
And if we know you're six, you are oil.
So you have to also be oil and you will be that water. Just keep filling up our oil and water. Now we are seeing this guy go for a little ride, if you will.
Now, we know these all have to be oil as well because we don't have enough room to put more water in here. If we put one water, we have to put all water ain't going to happen. Your oil, you are 2, 4, and 8. What are we sitting at here now?
That is uh 20. So, we have to put a one with water to finish. And then that will be a three. And then these will be seven and five.
and I'll make you water cuz you're odd.
So all of these will be water. I'm not going to color the non-cage ones, I don't think.
[snorts] Uh so let's keep let's keep going with the 24 here. So how do we make a minimum of four? Well, but no, he said it had to be 24 was the Oh, no. 25 was the most, wasn't it, that we can do with all odds? Yeah, 25. Uh so we can't go up to another. We have to stop here and we have to make all these add up to 24. Well, if 25 is the limit, we have to remove the one. So, you will be from 9 five 7 and three. You're not a nine. You guys are not threes. You are the three. Good. That's a five seven pair there as well. Did any of this help me?
Um, we know one of those will be a nine.
We know. Yep. This can't PO9. So, where does the nine go in this region? Right there.
Okay.
And can we think about what you are? Cuz you're going to have to both be either even or odd, but we can do a 10 in either version of both even or both odds. So, I don't think that's going to do too much for me. We can also go over here and say you have to be from 1 3 and six.
And these have to be what? Five and seven.
That doesn't really tell me what you are. We know there will be what?
Whatever's left over of the two or the four and an eight and a nine, we'll put them in for now.
All right. Do we go back to you? You are water. It's 1 2 3 4 five cells. We don't have the top of this thing. So, we don't know what the value is at this stage.
Now, we've got an 11 cell.
It could just be two or it could be turned to a three or continue maybe. And I guess it can't be a four cuz it would have to be um well, maybe it could be a four cuz it be have to be 1 2 3 and five.
No, that wouldn't work. See, we they'd either all be in the same row where we can't mix the two or we could do like a T- shape, but then we'd have to put the odd down here and evens up here, but we don't have the right uh grouping to do that.
[snorts] Okay. Um, do we just have to think about what you can be? Is there something more in this maybe?
Cuz I don't think I can use this. I don't know if I can use the 11 yet.
The problem is I think you could be a lot of things now. You can't be a a nine.
Well, actually, you could be a 91 if you're the nine and you're the one, I guess. [snorts] Yeah, there's a lot of things you could be.
Now, there's only one high digit that you could be, but it still would work with 73.
Those would both be water, huh? Okay. [clears throat] Is there anything else we can do for Sedoku?
problem is, well, try to think about if this could be an eight.
If it's a two cell, obviously it can't be because we'd have to put a three there.
But even if it's Now, if it's a three cell, it could we could put an eight here because it'd be an 812.
The eight and the two would be up here and the one would dip down to here and that could work.
So, I don't think we get anything out of that. Do we have anything? Oh, duh. I'm just being slow. This was a three right here. You're 37.
[laughter] You are water. Okay. Now, we do know it's a three cell 11.
So, [snorts] and you're not a seven.
Can we just work that out?
Or is there more just obvious Sudoku that we can do?
Good question. Let me think about the three cell 11. What's what are the the versions we could do? Maybe. It's kind of hard to think about that though because it's three cells and then we have like an open canvas if you will.
Oh, I can I could could have gone up into here. I didn't realize it in terms of oil or water cuz you can't be oil because we would have too many oils. You would be water.
Okay, that does help us with the 11 then because we already used four water.
So if this 11 Yeah, this 11 has to have an odd digit.
It's only going to have one of them. So I think we're going to get the 812 that we were thinking about cuz how do you make 11? It's either two evens and one odd or three odds. We can't use three odds.
Can't obviously put three evens because that would be an even digit. So, you have to be water. You have to be oil.
These have to be oil as well. Just meaning that you will be the oil on you.
But I don't know how much that helps.
And then these have to be uh two uh two versions of even and you will be that odd.
Now, there's probably more than one way to do that. Let me think about it.
Just go kind of going through the options in my head. Like say you were like a 24, you're at six. You can make that a five. That would be fine.
2 six gets us to eight. That won't work.
28 [snorts] would put a one here. That would work.
46 would put a one here. That would work. Yeah, there's multiple ways we can make it go as there. Okay. So, you are from twos, fours, sixes, and eights.
Let's just put those in. You can't be an eight. Can't put a three in any of those, but it could be in any of those mayhaps. And we don't know where this cage goes to, if it goes up to here or not. Oh, actually, we know it does.
Well, we don't know it does, but we know you can't be a three cuz you have to be the last even digit because this is all of our e our odds. I'm not going to color that, but we know there's a three in one of those two. What are these?
three 1 3 5 and 9. You can't be one. You can't be three. You have to be from 1 5 or 9.
And then you will be 2 4 6 8 2 4 6 and 8. These will all be odd digits. 1 3 5 sevens and nines.
Two three. There's one more even down here. And I'm sorry, two more evens and one more odd.
Two more evens and one more odd. You can't be a three, I guess.
No threes on any of those. Okay, let's see. How do we continue this thought process now?
Where do we have some? Is there just again, is there some sort of sedoku we can use here?
I don't see it. If there is, we know one of those will be a three.
We know there's another even somewhere, but I don't know if it's over here or over here.
We know you're odd. We know there's something else going on over here with another even and the nine.
Okay, where the heck is this next move?
Let me see. Let me see. Let me see. Let me see.
579 five. There's got to be some way to differentiate these. Like you probably can't be nine. Yeah, there's no way you're nine. Could you ever be a five?
Yeah, I think we said we could do a five, right? Yeah, cuz we could do a two four here and you be a five. So, we can't restrict you any further. We know there's a nine in one of these though.
These will be a nine over here somewhere.
Um, now I was trying to think if there's more restriction here, but I don't know if there is cuz I think we we used multiple ways of doing 2, four, six, and eight up here and gave us multiple ways of putting the the one or the five there.
Yeah, cuz like the two four could go with the five. The two six Well, 26 won't work. So maybe we do have to just dig you out.
Let's think about it. Can we ever put a six on the answer there is yes, though, because we could put a four six with a one.
Again, that's not really getting me there. That's a pain. Um, so it looks like there's multiple ways this could work. [laughter] [snorts] And again, you could be an 82 with a one. So, we can't remove the eight or anything like that.
Okay. Um, let's recalibrate. Let's try to think about what else we can do.
We know there's a three in there.
What can you There's too many options of what you could be. I think there's only one more even down here.
I guess that means all of these have to be even then.
Yeah, that's true. Maybe I should color these all in.
just because it'll give me the visual, right?
Uh, you guys can't be sixes. I guess you have to be a six then. That's what I needed to see. It It took me this to figure it out, but those were sitting there the entire time. It was Sudoku. I just didn't go down far enough. Six here says you are four. Okay, there we go.
Get rid of you. Get rid of you.
That's a 2 eight. You have to be from five and seven.
You're not a seven. So that's a five pair.
Again, we'll put the color in just because it's going to help me visualize.
All right. What did this do for me?
One of those is going to be a Oh, okay.
One of these is a four. So, you have to be our four.
That's a 28 pair, which I don't think matters at the moment.
28157.
Again, we know there's a four over here somewhere. We know there's a two over here somewhere. Okay, so let's keep going with it. Eight and two.
The problem with coloring on fog of war puzzles is they tend to obscure what the fog is and isn't at the time. But hey, that's a personal problem that I have to deal with. [laughter] [snorts] Uh, let's keep going. What else do we know now about some of this stuff?
We know you have to be the o even digit, excuse me, because we have the 1, three, five, and seven already. And we can't put a nine there.
[snorts] You could still be odd seven.
Did we get anything else in of these out? Oh, we can't repeat the one. Duh.
That's why I was again not seeing the because I'm looking at the color and I'm not looking at the cage. You are that one. Okay. So, we do know you end here.
That means you are our five now that we've done the leg work. So, you will be the seven and the five. You will be the one. You guys can't be sevens. Okay, we're starting to go now. You will be the eight.
And we can just put you guys in two, four, and seven. You're not seven.
2 4 6 8 3 five and nine. I don't know if we know what those are. Do we get any more clues that we could work with here?
Or do we have to go back to our Sedoku?
One of those will be a one and try to use some of that information here. What about these three digits real quick?
One, two, and seven. That's not Oh, we have a little 18 here. I didn't even notice.
Is that helpful?
Probably. We can probably figure out the oil and water situation here.
The problem is I think Well, we know it has to at least be three cells, but that doesn't tell me a whole lot.
Let's try to think about oil and water here. If I put you as being water, all of this is water. That won't work cuz we have six waters. So, you can't be water. You're oil 2 468.
You very well could be water cuz again, we don't know where you go. We know you will end here.
Now, this Okay. Oh, yeah. There is some work we can do with this. I was going to say this could extend, but it really can't.
It has to be these three digits, I believe. Cuz what happens if I put two even digits here? We're at even. So, the only way we could if we extended this thing, it would have to either be two evens or two odds. But we know because of what's going on here, this is one of each.
So I can't extend at three. And if I can't extend at three and these are even, we have to stay even. So you have to be that other even. You have to be the odd.
You will be from 2, four, and six.
And does that help me? Again, I don't quite know. You can't be the eight.
Let's think about the math of them then because that should tell us what these are, right?
It's going to have to be the 84 6. The only way it works. So, get rid of those.
Put the eight here.
And now we can start to move a little bit more. Okay. One of those is a two. 2 4 6. This 18 is going to help us in some way, right?
We need to have one of these at least be even. And it's going to only be you. So you are going to be the even oil that's sitting on top and you are going to be the two that is an 18. You will be waters.
So these two have to add to 16. They will be 97.
You will not be 97. That's a 135. You will be our nine. Now we're going to start pushing further. 53.
You're not nine or five. So you're seven. Good. We're getting more information. You're not seven or five.
So, you will be the nine and the five.
You will be the seven and the nine.
And now we're moving and grooving.
You're not a two.
You're starting to move and groove. This is an 11. How do we make 11? 65.
Good. Go away. Fives. That six says you're not. It also says these aren't.
So, now we know there is a six in this 11 cage. Now, of course, this one didn't have a clue in it, but if we know it's a six, and we know we have a one, we're at seven. We need four more. So, you are a 4 six.
4 six, which means you will be a two.
You will be a four and a two. So, that six finally came in handy there. Uh, we can go back here and say you're not four, so you will be a 28.
This 4 six says you can't be a four.
Anything else?
I think we're going to have to jump into some of these other cages. Now, these are water, which means you have to continue waterifying, which means you can't be even.
You can't be even.
That cage is probably going to have to extend.
One of those two has to be our six. We know that already. What are these digits now? 8 9 and four. So you will be a nine because we know you had to be water.
So you will be the 48.
And we now know there's more water cuz water always keeps sinking. So these have to be Oh, wait. The five here. We can go to the 95. Let's do that first.
Then come back over. You have to be 1 and seven. If that's the case, you will be a two. You won't be. And you have to be four or six. Don't think I know which one that is yet. I think [snorts] I will now probably stop coloring.
Uh let's see. The one seven will say you are three and five. Remember again, you can't repeat digits. That'll be seven.
You have to be a four. So you will be oil. I'll color the cages still, but I'm not going to do the rest of it now just cuz I said so.
>> [laughter] [snorts] >> Uh, let's see what else can we now do.
Uh, good question. Good question. Good question. Four here says you're not four, so you are.
That will be a two seven pair.
Sixes. Oh, the four comes back down to the eight and the four. Good.
Now, the question is going to be where do we move to next? It's probably just some sedoku of some sort.
Yeah, we've got X-wings all over for Well, no, we do have an X-wing on ones, don't we? So, you will be the six and a one.
Okay, that's helpful. Let's go to the twos and so forths and see if we can find anything else now. One of those will be a two cuz we're probably going to use that to figure out oil and water.
And I don't think I can say anything about the twos up there. We know there's a three up here. It's not you.
[snorts] Now, do you just have to be oil?
I guess not. You could be a seven of water.
Yeah, that's still possible.
No. No, you can't be water. If I put water in here, all of this is water. I can only put one piece of water in you.
So, you can't be water either.
So, these are both oil.
That's the case. You are two or eight.
You are from 2, six or eight.
Now, we don't know what this is. So, I don't can't rule you out as being water.
Uh, those two will be uh oh, we can go back to here cuz that's now the 28. So, you will be the seven and the two. We know these will be odd. One, not one.
Three and five is the only thing that fits there for the row. You two, well, we know one of you is a nine. The other one's going to be an even digit.
I guess it could be either cuz you could be even eight or you could be even two or six. What about these two? Cuz we have all of our even. So, you have to Okay, you have to just be water. Well, not you. Just put that one in there.
Anyway, ones and sevens.
So, we do get a one seven grouping going on here. And until we figure out what the math here is, I don't know if we can work it out. You are 268 and nine. You can't be 2 or six. You can't be eight.
Let's put all that stuff in there and see if we We might have to go to the 14 now.
Let's see just one more time if we have any more sedok staring at us before we go down that road. Again, we know it's one of those two. We know one of those three is a two.
Cuz if I can get some more information down here, it'll help me to work out what's going on.
Yeah, it's a bunch of options for the threes there. Oh, the four. Yep, there we go. You are the six. Four, six.
Good.
That four will come to the six and the four as well. Good, good, and good.
Good. You're not a six either.
Let's keep going with this one because I think we just put a four down here.
Yeah, you are four. That should clear out the fog and tell us what we need to know. So, you're either 95 or 86. Guess what? You can't be 86. You are 95. 9 and five. You [snorts] will be eight. You will be the nine. Now, we know what the math is and we can go through it. Once we decide we want to the eight will say two. Actually, we don't even have to worry about the math. Maybe two six.
Well, I guess we will at the end here.
[snorts] Uh, let's see. You will be our two. Yes, I'm I know there's math there.
I'm saving it. I'm savoring it. You're one and seven. You're three and one. You are a given eight. You are a given three. You are the five and the three.
And now we can do our math. That's eight. You have to be the seven and the one and the one and the seven. There we go. Oh, wow. That was 35. That did not feel like 35 minutes. I will put that out there. [snorts] I thought that was like a 20 minute shot there. Okay, cool.
Uh, it's got a ton of solves. I think it's been it was posted somewhere else previously. A lot of blobs puzzles have been set some other time. Then at some point they get posted up to Logic Masters Toys Land. So, uh, again, very fun puzzle. Bob's puzzles are always really good. Oil and water puzzles are always pretty fun. Fog of War is always really fun. Got the trifecta today. So, [laughter] very good. Hope you all enjoyed that one and we will see you next time. Thanks a lot.
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