Gene masterfully utilizes the fog mechanic to transform a simple grid into a sophisticated exercise in pure deductive logic. It is a compelling demonstration of how rigid constraints can produce a surprisingly elegant intellectual flow.
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Deep Dive
Sudoku Adventure #1175 - "Give Digits, Rav Anshel!" by GeneAdded:
Hello, let's continue our Sudoku adventure with Give Digits Rav on Shelf by Jean.
So, this continues our dynamic fog theme week. Um hope you're enjoying it. Let's go over the rules. So, we have normal 6 by 6 Sudoku rules, meaning in each row, each column, and each 2 by 3 box, we are placing the digits 1 to 6 exactly once each.
We also have dynamic fog. So, the cells that are gray right now are fogged over, meaning we don't actually get to see what is occupying that cell.
It could be blank, could be a given digit, could be a green line in this puzzle.
Um now, what the way we reveal the fog is getting correct digits. If you get a correct digit anywhere, it may or may not reveal fog. That is up to the setter. That's what makes it dynamic.
All right. Um in addition to that, given digits. So, in each box, the box number is given. So, we count box numbers in reading order. So, 1 2 3 4 5 6.
And in every box, the box number is given. Now, that means that since we don't see any of them right now, that means they're hidden by the fog, but they will get revealed as we reveal the puzzle.
All right. In addition to that, we do have a German Whisper Line here.
At least more than at least one German Whisper Line. So, adjacent digits on the line have to have a difference of at least three. So, if this was a two, then this could be a five cuz 5 - 2 is 3, or it could be a six. 6 - 2 is 4, that's still at least three. But, we can't be a four because 4 - 2 is 2. That's not good, right? Can't be a three, can't be a two, can't be a one. Too close. So, you need to be jumping a certain distance away, at least three away, as you move along this line, as you kind of traverse it.
All right. And that's it. Those are the rules. There's a link in the description if you'd like to try the puzzle yourself, and I'm going to get started right now.
I mean, the first thing I'm noticing is, you know, box one needs to have the one given, meaning that it's going to be in one of the fog cells cuz we can't see it yet.
Um, I'm going to do some coloring here and I'll explain the coloring in just a moment. So, I'm just going to color every other. What these represent is the fact that German whisper lines, by design, have to jump between low and high. They always alternate low high low high or high low high low, right? We don't know what it starts with. But, let's say this was a one, two, or three.
Then, this cell here needs to be at least three away, which puts it into the four, five, six range. And then now this needs to be three away from four, five, six, puts it back in the one, two, three range. So, we always alternate. Um, and that's what these colors are trying to tell us. Now, we already know that our lows are going to be the two and the three cuz the one is one of these two.
Now, I know that this one and this one cannot be the three.
Um, I also know this one can't be the three. So, what am I talking about?
Well, if this was a three, there's actually only one digit that is at least three away from the three, which is the six. So, in this pair here, we'd have to make this six, but in this pair here, we'd have to make this six. Now, we have two sixes in the row. That's no good.
That's going to happen here as well with threes.
And that's going to happen here as well because we can see the line continues here. Like, um, it it uh, stopped line stops in the middle. So, this line's going to continue through and we see that it goes into this cell.
So, we can't put a three there either.
And there's got to be a three, uh, we we know that both lows, sorry, we know where all three lows are. The one is up here and then two of them are either in the two greens or the two purples. Well, we already said that the purples can't have the three at all. So, these better have the three and so this is three and this is two.
Now, three needs to be next to six and then now two has to be next to five cuz six is gone.
That makes this a one, four pair and I am extremely surprised that we didn't reveal anything. Maybe we need to figure this one out.
Right. So, this this has to be one or two to be close to uh, to be far enough away from the five. Two is used, so this is our one.
Right, that revealed something.
So, um I'm going to get rid of the colors.
That was useful for this line, but So, this term whisper line kind of turns this corner. Let's look at what these need. This needs 3 4. This needs 2 5 6.
So, 3 4 Both three and four are special.
We know this is on a German whisper line. So, we know the line does that at least.
Um because the it again You can see it continuing into the cell.
So, three is special that it can go only go with six. Four is special in that it can only go with one. So, my only option here is to do 3 6 cuz this can't be one.
So, this will be three, this will be six.
That makes this the four.
Next to the six, we can't put the five.
So, this is the two and this is the five. The two is given.
True.
Uh three has to be next to six again.
All right.
Um Suppose I could fill this out. This is 1 3 5.
Now, we should think about the four being given here. So, one of these is four.
One of these is a three.
These two sixes look down and the six we know the six is given in this box, so it's not here. So, this is a six.
Um So, six is one of these two and one of these two.
This has the five given, but we don't know much about that.
Three given, the four given. Okay.
So, maybe we should think about this.
This is a This is a line.
So, these So, these are the same um low highness, right? They're either both low or both high because they share this digit in common in a pairing.
And so, we can't make them high cuz five and six are already gone. So, this is a 2 3 pair, which does make that six and that six.
Cuz the six will be next to the three in the 2 3 pair. The three forces the six to be next to it. That does make this the 4.
Okay.
4 was given indeed. 4 is down here.
Um, 3 is in one of these two.
So, 3 is in one of these two.
See, one low on high here.
I'm not [snorts] sure that there's anything else special there.
So, what's our next step? Probably just Sudoku here.
Or this line. Oh, you know, I see a little hint of a line right there.
There's a line between these two.
I wonder if that's intentional.
Not that there's a line Obviously, the line's intentional. I wonder if it's intentional. You can little You can see that little little corner there.
Um, let's ignore it for now.
But, we may have to use that little tiny corner.
Um, so, this is a 2-3 pair.
Here, we need Okay, yeah. We have the 4's looking down. So, 4 is in one of these two.
Maybe it has to do with 5 being given in this box. Yes, it is. This 5 looks down.
These aren't 5. So, the 5's placed here.
There's our line. So, the 5 is next to one or two only. That's not a 5.
Now, the 4 in this box is supposed to be given.
Sorry, no. The 3 in this box is given in here.
Still haven't found the one.
All right. Does it have to do with this?
Yeah, this has 4 on it cuz 5 and 6 are gone. So, if it has 4 on it, it also has 1 on it. So, that's 1-4 pair. That does place 4 here.
And that makes this a 2. That's 3 and 2.
We get the 1, 5, and 3.
That's 1 and 4.
That's 4 and 1. That's 4.
Right. This digit is a 2. This digit's a 3. We get the 3 here. It is given. Okay.
This is our 1.
All right. That puts a 1 down here and a 2 up here. and these are fives. All right.
Cool. That was an interesting idea to to hide the givens behind the fog but tell us that the givens exist to somewhere.
That was uh that was interesting.
Um a nice use of German whispers as well. As always, a very nice puzzle Jean.
Uh and if you enjoyed this one, leave a like, subscribe, and a kind comment below.
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