The Onagon technique is essentially a sophisticated rebranding of systematic trial-and-error that prioritizes brute-force efficiency over the elegance of traditional deductive logic. While it undeniably speeds up the process, it risks turning a nuanced mental exercise into a mechanical task of elimination.
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Deep Dive
How To Solve Extreme Sudoku So Fast It Feels ILLEGALAdded:
Want to hear something insane?
A computer solver has to use 23 advanced strategies to solve this extreme Sudoku. But I'll show you one simple trick that will solve this puzzle so fast you'll feel like it's illegal.
And with that, it's solving time.
Look here with the fives. You notice with those two fives and these two fives, you can actually solve for five right here in block four. And then if you look across row four here into this cell, you might notice because of the 1 2 3 4 5 7 8 and 9 that all see this cell, you can solve this cell for a six. Greetings, friend.
This classic by Talking Freedish has over a 90% approval rating on Logic Masters Germany. I'll show you the amazing trick that takes the place of 23 advanced strategies. First, you need to test this puzzle for restrictions. If you look at the ones, the twos and the threes, you're not going to be able to make any solves or relevant marks. But if you look at the fours, you might see here with these two fours, you have two places for four in block six. So, if you can have one place for a digit in a block, solve it. If you got two, mark it. Other than that, just move on to the next digit. Go up to the fives and you'll see that you can mark fives here in block two and you can mark fives here in block eight and fives here in block nine because of these fives.
Okay, move on to the sixes. You made one solve for six.
You can actually mark sixes here in two spots in block nine. That's it with the sixes, move on to the sevens.
And you'll see that two places for a seven in block eight and then in block one only two places for a seven right there. That's it with the sevens.
Not a lot more solves going on here with the eights.
You have two places for an eight in block eight and then in block six with these eights two places right there, so mark those.
And then with the nines two places for a nine in block two with these nines and this nine, two places here in block three and then in block four with these nines.
And this nine two places right there. And then in block seven with these nines and this nine, you can mark nines right there. But that is it.
There are no other relevant solves, marks. You can do the pairs and triples, you're not going to get anywhere. This puzzle is extreme rated.
And now the question of the day, when you get stuck like in this position, what's the first thing you usually do?
Do you scan the grid again or try something new?
Normally, I look and make sure I got all the marks done and then I'm going to start looking for something new. But what about you? Please, please, please, please share in the comments. I want to hear from you. I answer every comment.
You're helping me grow the internet's best Sudoku community.
And so a very hard extreme puzzle like this it's a time to look for advanced strategies and you probably don't want to do 23 advanced strategies, so I'm going to show you that simple trick.
You can look at individual single candidate strategies and mark up where all the ones, twos through nines are and look for things like X-Wings and skyscrapers. You can look for bi-value cells, start marking up bi-value cells and look for those strategies like the XY-Wings, you're not going to get very far.
Think of the third option.
Third option with a handmade classic in particular is look at setters intent.
Talking Friedrich gave you some hints.
And some of the hints include the name of the puzzle and the picture. So, I'm going to show you the picture that Talking Friedrich put on Logic Masters Germany.
Okay. So, you notice this is the picture. It's called mini golf. So, this is a golf ball. These are like the little barriers and you can see this is the hole and it's on this cell right here. That's where the hole is. This is a huge clue. What is Friedrich trying to tell you about this cell? So, you need to study that cell.
So, what can it be? It can be a 1 2 3 or a 4, right? Cuz you got a 5 6 7 8 9 right there.
And what we have to look at is go, well, what are the possibilities for these? There's four different possibilities, 1 2 3 or 4. What is there any of these possibilities that you can eliminate? And there there is if you use advanced coloring. So, I'm going to use some red here and I'm going to show you what I'm talking about. So, if this was a 4, if we don't know, but if it was a 4, what would happen to the puzzle?
Well, this cell, and I'll just put everything in red using advanced coloring, this cell would have to be a 4, right? Cuz that can't be a 4 anymore.
And the 4 covers this cell.
Then these two would make a 4 go right here and I'll put that in red. And then you'll notice because that 4 be across here, where could the 4 be in block one? It has to be one of these two cells. And this is where advanced coloring comes in. If you are coloring using lock candidates like this, it's advanced coloring and I'm just using one color at a time here.
So, a 4 be one of these spots to go with this 4, it would force a 4 in block 7 to be right there.
But, you have a 4 right here.
That can't happen, right? So, if this is a 4, the only place to put a four in block seven would be right there. So, you know you can eliminate a four as a possibility to this puzzle.
Okay, what about the three?
Let's see if we put a three there, what would happen?
Again, use that advanced coloring and you can just go straight up to here and notice you still have now this locked pair, it'd be one of these cells here in row one.
Can't be any of those spots, so it would be the three would have to be one of these spots. Well, because of this three here, it would have to be right there.
And then you notice, cuz the three can't be in those spots anymore, you'd have to put it in one of these two cells right here.
But, you already have a three in the row.
So, that can't happen. If you put a three here in block seven, the only place to put a three would be one of those two cells. So, you know you can eliminate a three. So, this is like, if you've ever taken one of those hard standardized tests or certification exams and have multiple choice and there's four possibilities and you're like, I don't know which one of these is actually the right answer.
So, you end up eliminating three of the possibilities. If you can eliminate three of the possibilities, whatever's remaining has to be true.
It has to be. So, let's see here at the twos. What happens you put a two here?
All right, if you put a two there with this two, the two would be in this cell right there.
Couldn't be in those cells. Two would have to be in one of these cells right here.
And guess what? Can't be there, it's got to be one of these two cells. And you see how previous did this? You got these blocks of cells here and here and here, puts a bunch of restriction along the column and the rows.
And so, you notice the two can't be here cuz you put a two there.
And so, this strategy I use advanced coloring to show it, but it's actually called an onagon. And what that means is you can eliminate any possibility that breaks the puzzle. It you know, so you show that the other other can't be there, two, three, and four.
So, you cannot positively prove, like you may not see that this has to be one, but you know it cannot be a two, cannot be a three, cannot be a four. This is amazing trick, very clever. And so, what you end up with is a one in the hole, or like a hole-in-one, like in mini golf. So, that's what the meaning of the puzzle name meant. Okay, so now you guys see, how much reward are you getting for figuring out that this has to be a one.
You'll notice with these ones, you can solve for a one right here in block six.
And then, with this one cut across, you can actually mark ones right there to go with these ones.
So, you can solve for a one right here, solve for a one here in block five.
And you end up with ones here in the same spots as the eight, so you have a nice one-eight hidden pair. One and eight can only be in these two cells, nothing else can be there. They act as a pointing pair.
And so, you can eliminate one right there, since the one has to be in these cells, and you can solve this for a one. And so, everything I've showed you so far, including the advanced coloring, I cover it in my 30-day Sudoku Challenge. If you need help with any of this, you want to build a dementia-proof brain, sharpen your mind, help prevent dementia for up to 20 years, click on the pinned comment. Learn more.
Okay, after doing all that with the ones, you can look at these ones and just finish up marking the ones up here in block two.
So, you made some restriction here in row eight. Go back to the scene of the crime, what can you do? You just need a two and a four with this two.
Means that's your four, and that is your two.
Okay, and then across here, you just have a three, four, and a nine left.
That's a locked triple. I'll color that.
This can't be a nine, and this can't be a four. But now, a three, four, nine cannot be anywhere else along this row.
So, you what you end up with is a two, five, and a seven. Well, with the two, seven right here, this now has to be your five, which displaces that five, and you can solve this cell for five, giving you a two, seven naked pair there.
And all these marks you've made, they're going to clue you in on where to look for your next solve. So, don't feel like you wasted time putting marks in the puzzle. Now, remove those colors, and after making those solves with the fives, now you can look up here in row four.
You just need a seven and an eight.
Well, with the seven, that's your eight right there.
That has to be your seven. Now, you can displace that seven, solve this cell for seven.
Okay.
And then, continue looking up here in block one. You just need a two, three, and a four. Well, with this two here, that's got to be your two. With the three there, that's your three, and that's going to be your four. Okay. And notice with the three and the four here, that can only be a nine, which means that's your three, that's going to be your four right there. This nine displaces the nine, solve that for a nine. Leaves you with a nice six, eight pair right here, and then remaining block four is a two and a three, but you can do better than that because you can now look at these two cells, and notice that's a three, four. To finish up block six, since one of these has to be a three, that's going to be your two, that's going to be your three right there.
And now, the next part's a little bit tricky.
You actually got here in row six, where can the twos be?
Because of these twos, you can only be in these two cells here in row six in block five. Well, the twos can only be here in block eight. And so, I'll color that. You'll notice that the twos are restricted to columns four and five in blocks five and eight.
So, you've eliminated twos as possibilities in these cells. So, where can the two be in column six here? Well, because of that two can't be there. It's got to be one of these cells. This is a claiming pair.
You actually have to find this claiming pair uh to put more restriction on these cells.
Now, these cells cannot be twos, right?
You put a two here, you run out of places to put twos in blocks five and eight. And so, you'll notice here in row three, you have a 1 3 6 8 9, you have 2 4 5 7 to finish the row. Well, you got the four five and the four there.
You just eliminated two, so this is a naked single seven. And then with this five, you can actually displace that five. Solve this for a five now.
And now you can use the seven to disambiguate the two and the seven right there. This is beautiful stuff. And so, what you end up with now is you can take that two, displace the two right here. Solve this cell for a two.
All right. And where do you go from there? Well, let's look at row three.
You just need looks like a two and a four. You got the four right there. So, there's your two and there is your four.
Remove the two from right there.
And now look at row two. You just need a two six and a nine. Well, you got the two and nine right there. So, that's got to be your six. And the two right here means this is going to be your nine. That's your two. Displacing that nine, so you can solve this cell for a nine. Remove the nine from right there.
And you just want to attack the places where you have the most restriction. So, you have a three and a six here.
Pull that six up. There's your six, there's your three. Now, you can disambiguate the three and the four right there. And you'll notice with these two threes, you can actually solve this for a three in the corner. Bump, bump, ba.
All right, displacing that six, solving this for a two, and you just want to continue on and finish the rest of the solve.
You got a two, three, five, six, seven, nine in block two. You need a one, four, and an eight. With the one four here, and the four repeats, you can use my neat naked triple trick. Solve that for an eight. Only place the four goes right there, displacing that one. And now you can disambiguate the eight and the one right here. Get those quick solves when you use those marks.
You'll notice that you don't have a six in column four, so that's got to be your six. Disambiguate the six and the eight right here. And then solve these together. You just need a seven and an eight. Well, pull the eight down. So, there's your eight, and the last cell is a seven.
Now, check out this next video to see how to apply advanced coloring on another extreme rated puzzle.
Thank you so much for watching.
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