BremSter masterfully deconstructs the "Parity Islands" mechanic, turning abstract topological constraints into a brilliant display of pure logical deduction. It is a sophisticated evolution of Sudoku that elegantly challenges the boundaries of spatial reasoning.
Deep Dive
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Deep Dive
SLIP on a shirt, SLOP on sunscreen, SLAP on a hat, and SOLVE a Sudoku.Added:
Hi [music] and welcome to Brains to Puzzles and a channel where I try and showcase the fun that can be had in the world of variant Sudoku and there's a couple of things happening.
Um first of all, I'm going to be solving, I hope, a puzzle called the Big Beach Parody by GDC. I love parody puzzles and I'm really looking forward to giving this one a try. I've never seen a parody puzzle like this one before and I'm a little bit daunted by it. So, we'll see how I go. But, the other thing is tomorrow a new Sudoku Chutes pack is coming out, Sudoku Chutes set 11.
Um and those of you who are um subscribed to my Patreon, even as free members, will get a notification about it and even if you're not, it will be on my Patreon page, even if you're not even signed up to Patreon. It'll appear on my Patreon page in about, oh, 21 hours, um about 20 hours actually. Um and it will be available free for download for everyone. But, here's the important thing. While I normally release these packs as pay what you want and this one is as well. Um what I really want people to do so to pay for the pack is to go over to the channels that are actually releasing the have recorded and are releasing the videos for these puzzles, which is Timur Tab and Puzzle Patzer um and actually subscribe to those channels if you're not already because they are amazing content creators and YouTube makes a big deal about getting 1,000 subscribers and they are getting close.
So, if you could do me a huge favor, rather than send me money, I would much prefer, I mean, feel free to do both, but I would much prefer if you went over to Timur Tab and Puzzle Patzer and subscribed to their channels. Also, check out their content because it's absolutely amazing. That's why I've got them to solve the puzzles. So, um really, really good stuff. Um I'm really proud of these puzzles. I think they're the some of the best coffee break puzzles I've done in ages. So, um, I think that you will really enjoy them.
Now, they will be released as collabs.
So, that you will see those the videos appear on my feed. And when they do, you'll see there'll be a subscribe button and all of the channels will appear. So, I hope you enjoy for the next couple of weeks there'll be new Sudoku videos coming out. But, let's have a look at the Big Beach Parity by GDC. Um, so there'll be a link below to where you can try this puzzle. This puzzle also came from Logic Masters Germany. So, you will also find a Logic Masters Germany link below for this one.
Let's have a look at the rules. We've got normal Sudoku rules apply, which means in every box, in every row, and in every column, the digits 1 to 9 must be placed without repetition.
We then have parity islands.
Orthogonally connected groups of cells with the same odd-even parity are called islands. So, for example, if that was a group of odd cells and that was a group of even cells, and um, I'm not even sure if uh, and that was even and these were odd and these were even. Um, trying to make this work.
And these were even and these were odd.
I don't know, that might work. This is an island. This is probably bad. Um, this is [snorts] an island of odd cells.
This is an island I'd have to make all of those odd or something. I probably got the counters wrong, but this would be an island of even. This would be an island of odd. And the whole point is these are islands of um, cells. So, anything that is connected um, are called islands.
Uh, a digit uh, circles a digit in a circle count um, is odd. Okay, so a digit in a circle has to be odd and counts the number of cells in its island. Okay. So, for example, if I had this island like that, um, let's do this a bit differently, like that. If that was an island, this would have to be a five because that's five cells in its island, okay? Um, squares, a digit in square is even and counts the number of cells in its island. So, if that was an island, for example, that would be a four. That's the way it works.
Um, I'm going to restart the puzzle to restart my timer. Let's give this a shot. So, we're going to start by making the squares as even and all of the circles as odd.
Can these connect up?
If they did, these would all have to be higher than Well, they'd be at least four. So, these would be five from five, seven, and nine.
Okay, box one is interesting because this can't be a single cell. Those both can't be odd because then this would have to be a one, but if this was a one, then that wouldn't be even. These are from two, four, six, and eight. So, this one has to grow. And if it grows to here, that's all four even digits in the box. And if it grows to here, that's all four even digits in the box. So, those must all be odd.
Can I tell which way that grows?
Well, if it was to grow to here, these would be connected. And therefore, oh, if these were connected, then they would both be giving the size of the same island and would need to be the same digit, and they can't be cuz they're in the same box. That is odd That is even. That's a two. These are four, six, eight, which means this has to grow, and it has to grow again.
But it can't connect up here. If this went down again, then this would be connect up, and you'd be able to say, "Well, this could be six and eight, but this would now be part of the same island and those would have to both be the same digit. That is odd, but this must still grow. That grows to there.
That doesn't have to grow. That could be a one.
But this can't connect up. If this connected up, then those two digits would be reflecting the same the size of the same island and therefore they'd have to be the same digit. That is even.
Now, that doesn't have to grow. You can have an [clears throat] island of size an even island of size one as long as it's not a square.
But this has to grow and then grow again because this is at least size four.
And I've now got Well, that's all four evens in the column. These are all odd.
I like this.
Okay.
This doesn't Well, then actually this can't be a one because it's already size two and it can't stop at two because this is the size of the island which has to be an odd digit. This has to grow again.
This has to grow because this is at least two.
But that could be a three.
Oh, that's all four odds in the row. So, those Sorry, all four evens in the row.
So, those are all odds. This still needs to grow at least one more.
And it can only grow one Oh, no, but I could get up to six or eight if it was 1 2 3 4 and then I would came down here.
This could grow.
But then it would stop there. But that could still grow.
That doesn't have to grow. That could be a four. One of these has to grow.
So, either this one grows to there cuz it can't just take 1 2 3 4 5. This one has to grow to there or this one has to grow to there.
That can't connect to there.
This must stop because if that's connected today, those would be part of the same island and would need to be the same digit, but they're in the same row.
That is even. So, that's all four evens in the box. That is a one.
This is now at least five. 1 2 3 4 5.
1 2 3 4 5 6 7 8. If this is odd, this would need to be a nine and pick up another cell, which couldn't be that one. It would have to be that one. All of those would be odd. Both of those would be even.
This is 4 6 or 8, but I don't know what that's doing for me. Two is in one of those two, but again, I don't know what that's doing for me.
If that's even, that's odd, and that doesn't work. If that was even, that would be all four evens in the box.
That would have to be odd, and this would be 1 2 3 4 5 in size, and that can't be valid. That can't be even. That is odd.
Which is 1 2 3 4 5 6 7 8. This can only be nine because it has to be higher than eight, and 1 2 3 4 5 6 7 8. This needs to grow by one, but if it grew to that if it hit that, it would be 9 10 11 12.
So, it can't grow to there, it must grow to there. That's all five, those are both even.
And this can't grow any further. 1 2 3 4 5 6 7 8 9. Those are both even.
1 2 3 4 5 6. Those are both odd. That is a six, and there's no six in those. Oh, this is now a four. That's locked out.
That is a four. That is an eight.
These are six and eight. These are two and four. This puzzle is beautiful.
These are all odd.
There's a six in one of those.
Not sure what to do with that. Two and four are down here.
Oh, this is 2 4 8.
I've got five odds. These are all even.
Those are 2 4 and 8.
And there's a six in there.
Okay.
So, six is in one of those. So, six is in one of Oh, this is four and six. So, these are two and eight.
And that digit has to be there. That's a two or an eight.
Four is in one of those.
Okay.
This can't be odd. Because if this was odd, those would be part of the same island, would need to be the same digit, and they're in the same column. That is even. That is all four evens in the box.
Those are all odd.
One of those is even, but I'm not sure which.
>> [snorts] >> That can't be odd because again, those would be part of the same island. That is even.
That one can be because those can be the same digit.
This is 5 7 or 9.
If it's five, that stops and that becomes a five.
Actually, that's always a five, isn't it?
No.
Because 1 2 3 4 5 6 7 8 9 In fact, if that is even, that's a five.
If that is even, 1 2 3 4 5 6 7 8 9, that's a nine. If that is even, 1 2 3 4 5 6 7 8 9 10, that doesn't work. That one must be odd.
Now, this is 5 7 or 9. Can it be seven?
No, can't be seven.
Cuz for this to be seven, I'd need to pick up 1 2 3 4 5 6 7, but then it keeps going.
1 2 3 4 5 or 1 2 3 4 5 6 7 8 9 10 Hang on.
That can't be even. 1 2 3 Hang on. Could that one Let me [snorts] check this again. I think I've worried myself. If this is even, 1 2 3 4 5 and 5, that doesn't work. If this is even, it's 1 2 3 4 5 and 1 2 3 4 5, that's 10.
It doesn't work. This is the even digit.
Those are both odd.
That is the six.
This is now the five.
And this is now a five.
This is incredible.
This is a two.
Which means that's a four and that's a two because that's isolated.
So, you can have one-size even islands as long as they're not squares.
Which means that's the eight.
These are 2, 4, 6. That's not a two.
But that's now an eight. That's a two.
So, it must grow. Actually, I knew that, but now it must stop.
1, 2, 3, 4, 5. That is even.
That is a four or a six.
Eight is in one of those two.
>> [snorts] >> 1, 2, 3, 4, 5, 6, 7. These are seven or nine. That is a seven by Sudoku. 1, 2, 3, 4, 5, 6, 7. That has to stop. That is also a seven.
That's all four evens in the box. This is This puzzle is bril How is this so brilliantly unique with so few clues?
Four evens in the row. Those are all odd.
So, this is at least five now because it sees four and I can't make it four.
That's all five odds in the row. Those are both even.
Eight is in one of those two for the row.
So, this can't be two, four, or eight.
That's a six, making that the four, that the six. This is a four-eight pair, meaning that's the two.
That is now the eight by Sudoku in the column, and this is a four or a six.
I've almost done or This is the only one These are the only ones I haven't done, and that one.
This is crazy.
Eight is in one of these, but this can't be an eight, surely.
Cuz if this was an eight, I'd need to see four cells in this box and four cells Oh, maybe. 1 2 3 4 5 6 7 8, that could work.
Mhm.
This is two and eight.
Like, is there any reason I couldn't do that, that, and those?
Yes, there is.
I've only got one more even in this column.
So, if this was an eight, could I do that?
I'd need that one to connect up.
Then everything would have to be over here, so it'd be like that. 1 2 3 4 5 6 7 8. That's four in that row, four in that column, four in that column, four in that column, four in that box. That works. So, that could just be an eight.
These are three, five, and nine.
One is in one of those two, so one is in one of those two.
Am I working with evens or with odds here?
That's not a five.
If this is a three, both of the If this was a three, both of those would have to be even because I'd have to stop the growth of the region.
But if both of those are even, I'd have five evens in the column. That's a nine.
So there's no nine in either of those.
Nine is actually up here.
One, two and One, two, three. I can get five in this box. So I need to pick This needs to pick up one from somewhere else. It can't come into box three, and it can't pick up in box seven. So it's got to pick one, two, three, four, five, six, seven, eight. It's got to pick up one down here. But how does it do that?
This has got to be No, it can do that.
It can't touch these.
Because there's no way I can pick up one in this box without picking up all the others.
So what happens if I don't pick up an an odd in here with this? The maximum would be one, two, three, four, five, six, seven, eight. So I must pick up an odd down here. But whatever the odd is in here that I touch, I'm going to pick up all five. So one, two, three, four, five, six, seven.
One, two, three, four, five, six, seven, eight. I can only pick up one odd in this box.
But it has to connect that to that. So it has to be there.
Cuz if it's anywhere else, I've to get to it, I need other odds. So that has to be the odd, and it has to connect there.
1 2 3 4 5 6 7 8 9 and all of those become even.
That's incredible.
That's now a nine.
1 2 3 4 5 This is a six because it's going to be 1 2 3 4 5 and whichever even is in there, which means that's the four, that's the six, that's the eight, that's the six, that's the four, that's the eight.
That's now six because six can't be in any of those. So that's the six, that's the four.
Six isn't there, neither is four. That's the two. This is 4 6.
Oh, I've got all five odds in this row now. So this is even, this is odd, which means that's not the eight, that's the eight and there's the parity coloring done.
There is a Oh, this is 2 4 for the box, which means that's six, that's four.
The eight makes that the two and that the eight, meaning that's the four.
The four means that's the two, that's the four and these which are two and eight are resolved. That's the eight, that's the two. There's the even part of the puzzle done. That's [snorts] brilliant.
And I've done all the circles. So now I just need to do this by only playing with Sudoku in odd.
Okay, that digit in this box has to be there. That's a three or a five and the five looks down making that the three.
So that has to be the three.
Because that digit has to exist in this box somewhere and it can only exist there. That's the three.
Putting three in one of those two.
These are 1 5 and 7. So that's the nine in the row.
Meaning that's the nine in this box and these are one and five. So these are three and seven.
With the seven looking down making that the three, that the seven. These are one and five.
Three in this box can't be there, so it's in one of those two. But these are 1 3 5. So this is 1 5 cuz it can't be three.
So one Yeah, where is nine? Nine has to be there by column logic. Well, we know what these are. These are 1 3 5 by um by column. But I don't have Oh, but the one over here means that's not the one and the one here means that's not the one. Those aren't the one. That's the one. That's the seven.
These are 1 3 5 without that one being a five.
These [snorts] are 3 5 9 because to complete the row, so that's a seven.
>> [clears throat] >> Which means seven is in one of those two. The five looks down saying that's not the five.
These are 1 3 7. Ah, where's seven in this box? Can't be there. That's the seven. So these are one and three.
Meaning that's the five, that's the one.
The 1 3 5 look up making that the nine taking nine out of there. The three looks up making that the five and that the three.
This is so good. This is 1 3 or 5 and it can't be three or five. That's the one.
That's the three. That's the one. That's the five because of the one taking five out of there. That's a 1 3. Looking down making that the five and that the one.
The one makes this the three and this the one. So there's no five in that row yet and these are 3 7 and 9.
Three comes out of there.
One looks down making that the seven taking seven out of those. Seven looks up making that the nine taking nine out of those.
The five looks across making that the three and that the five. These are down to pairs. That's seven nine and this is one three.
That's a deadly pattern.
Now, it's not the nine is looking up making that the seven, that the nine.
The seven is looking down making that the three and that the seven. The three is looking up making that the one and that the three and the one is looking down making that the five and that the one. That puzzle is stunning. 531 solves. It deserves them. That is one of the most fascinating um parity puzzles I've seen in ages. I'm just going to duplicate the tab so I can reset the puzzle.
Look how little information there is in this grid to start it off.
And yet you end up with that. Absolutely beautiful.
What an amazing puzzle and the logic isn't hard.
It is an absolute gimme.
To have a novel rule set using simple concepts with very little information in the grid and yet for it to have such an elegantly well-designed flow.
There are very few creators in the world who can pull that off.
Absolutely stunning. It's It's so much easier to make a harder puzzle.
Like you put a lot more time into it, but getting something this refined is not easy. Like making these easier puzzles takes a lot more skill. Like when it's really, really easy and it's just put a lot of grids in like what I do with Sudoku Juts half the time. That sort of drops it down and I'm not going to call those particularly hard.
>> [snorts] >> But an easy puzzle with a novel rule set that actually has interesting flow and interesting deductions like you would find in a very hard puzzle, but doesn't [snorts] actually cause you to have to melt your brain to find anything. That is ridiculously hard to pull off.
This is masterful. Absolutely masterful.
Mwah! Stunning puzzle.
Better than anything I've seen on in ages.
Wow.
If you're interested in something not quite this good, go check out Sudoku Juts set 11. I'm really happy with those puzzles, but I don't think there's anything quite of this quality. There's a couple I'm really happy with, like really happy with. But yeah, this puzzle is stunning. This is 10 out of 10.
Beautiful.
Thank you everyone for watching. I hope you enjoyed this one as much as I did. I don't think that's possible. And as always, good luck with your solving.
>> [music] [music]
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