Algie Seat’s Hard Grad-Level Sudoku Puzzle

This video was posted on Oct 6th during Sudoku Week 2020. Transcript below.

Hi, Chad Barker, your Sudoku professor. And today I’m bringing you a puzzle that Algie Seat is stuck on. This is it right here. This is from I think it’s a book of puzzles called Grab and Go. I’m familiar with, I’ve seen those before, so it’s probably a series of them. I don’t know which exact book this comes from, but the interesting thing is that this is rated hard. That’s all it says, it’s just hard. Actually, I think it’s much harder. It’s probably like in the “very hard” category. It’s not just hard.

So let me show you what Algie has done. Algie’s at this point right here. A lot of progress has been made down in this box is a eight and nine, and there’s a few other numbers filled in. Other than that, Algie’s done a lot of think outside the box to no avail, I mean, made some progress. There’s, you know, you figure out a few things, narrow some spaces down, but Algie’s tried I could see tried some three corners and things like that and not been able to solve it. And I completely understand why, again, this is this is not just hard. Okay. This is very hard. And actually Algie, this is a graduate level puzzle, in my opinion.

Now there may be another solution. I certainly didn’t find it, but there are at least two different graduate level techniques that you can use. And just to relieve you of any concern, I got to the exact same stuck point that you did. Here’s my stuck point with my pencil marking. Same numbers are filled in my pencil marking looks a little bit different than yours, but nonetheless there it is. Now you are not a graduate member Algie, but I’m going to show you one of those graduate level techniques that you can use.

And I’ll hint at the other one for those who are graduate level members, you can get in there and see if you can find the other one. For that matter, if you’re trying to solve this level of puzzle on a regular basis, even though it just says hard and it really should be rated a little higher, you’re probably ready for the graduate level techniques. And so you might want to pick those up.

So now again, everything goes along fine until we get to this point. And then the problem we run into is that there, there really isn’t anything else to work with. Or you have vast areas of untouched space here that you don’t know. I mean, there’s pencil marking, but that’s about it. Lots of spaces that can be multiple numbers, three or more numbers that we don’t even pencil mark them all.

And so what I noticed, first of all, I’m going to show you, the technique that I’m going to show you right now is what I call a potential deadlock technique. This is one of the first techniques that I show you. Now, unfortunately, this is not a simple version of the potential deadlock. So if you don’t understand this, I get it. So in that regard, it is actually a more complicated version of the potential deadlock. Normally we’re finding just pairs of double-doubles that deadlock, this time, we’re finding three double-doubles. I call it a triple double-double deadlock.

Anyway, let me show you what I noticed. So I noticed down here, we’ve got a six, seven double double right down here in box seven, and then up here, we have a three seven double double in these two spaces. Let’s underline that to be clear. So if, for example, we could find a three, six double double in these two spaces right here, or we could find it in one of these two spaces right here, we would actually deadlock. So if the red space, the space I’ve marked with a red dot ended up being a three, six double double or the spaces I’m marking with a green dot end up being a three, six double double. Then we have these three parallel double doubles, the three six, the three seven and the six seven.

And there’s actually no logical solution for that. That’s what we’re looking for with the potential deadlock. We’re looking for, can we create a situation that deadlocks the puzzle? And that’s what I call the “no logical solution” is a deadlock. There’s no way that you can solve the puzzle logically.

So in this regard, I’m looking at the puzzle and I’m seeing that, okay, the reason I can mark these, I can focus on these spaces that I’ve marked with the red and the green dot is that we have three and six here along this row that eliminate these two spaces are ready and three and six are eliminated from this middle space. So the only places that three and six can go are the ones that are marked with a dot. Now I look around and I say, well, how can I, how can I make one of these pairs of dots, these spaces where these dots are, how can I make them three and six? And I come over here and I realize that, Hey, you know, if this space here is a three, this space would be a six, right?

Because this space right here can only be three or six. So if this space is a three, this space becomes a six that eliminates three and six from the red dots. And then these two spaces here, let me just change my color. So these two spaces then have to be a three six double double. All right. So then we have, our six seven, three six, three seven, triple double here. Six seven, three six, three seven, triple double there. They’re all parallel. And there is no logical solution because actually there are two solutions to that pattern. So you can’t have that.

Now, the other thing that you can do is you can also note that if this space here, instead of being a three, like I’ve noted, if this space is a six, then this space becomes a three. So either way, if this space is either three or six right here, then we’re going to have three and six eliminated from the spaces with a red dot. And we’re going to end up with a three, six double double right here where I’ve indicated it and that’s our deadlock situation.

Alright. So let’s figure out what we got going on here. So let me actually move this up just a smidge right to there. And let me see what we’ve got in this column here. I had already done the think outside the box. Obviously I’d done think outside the box everywhere just like Algie had. Actually it’d be easier if I just did the think outside the box, along the row, not along the columns, let me recenter that a little bit. Okay. So if I do the thing outside the box, along the column, what I end up with is we’re missing three, four, six, and nine, right? This space right here already had nine eliminated from it.

And four is obviously one of the possibilities. So before we got started, this space could be three, four or six as a three possibilities. I could go there. Now we’ve discovered that if this space is either three or six, we have a problem, right? We’re going to create this deadlock situation. So this space cannot be three or six, and it can’t be nine. So if we look at the thing outside of the box, there’s only one thing left for it to be, and it has to be the four. All right. So let me do that real quick. Erase a little bit of stuff here so that we can, I’ll erase this, and I’ll erase this over here. And let me go ahead and erase this pencil mark here. Okay.

So this has to be a four. Now, let me then erase some of these other notes that I’ve made over here. So now we know, because that’s a four, that we are not going to be able to create this three, six double double. So we’ve taken the action that is opposite of the condition that would create the problem. In other words, we found something that would create a problem and we then went in the other direction. That’s the way a lot of the graduate level techniques work. We are finding a problem, we’re peeking into the future of the puzzle just enough to see a problem, and then we’re avoiding that problem. So that’s what we get with this right here. We get a four right here.

Now we filled in a number. This is great. So we start looking around and we think we can just go ahead and fill in the rest of our fours or something like that, but that’s just actually not the case. So we have to look a little harder. Yeah. I mean, if we already have the fours up above and down below, so filling in the four doesn’t help there. And if we look across, well, four is already eliminated that row. So the only thing that we’ve really done is we’ve eliminated four from this space right here. Four is already eliminated from here. So the only thing we did is reduce where four could go by eliminating it from this space right here, and then that, so that that’s, the based can still be three, six or nine. This one’s can still be three, six or nine. This one can only be three or six.

So that doesn’t look like much. But now we need to look at, well, what else going on in this box, we filled in a space in the box. So what can we do with that? What can we do in the box? It’s not the number that matters, it’s the fact that that space is no longer available. And actually, if we look at where can three and six now go in this box here, we see that it still goes here, obviously, but it’s also eliminated from this space, this space and this space. So now three and six can only go in two places here and here. All right. So let’s do that. Indicate the double double, that is.

Three, six double double here and here. And now if that’s the three, six double double, then these remaining three spaces have to be a one seven, eight, triple…It looks like it’s going to be a triple double. And the interesting thing is that one is going to be now row eliminating.

So eight goes here or here, and then one goes here or here again, one is now row eliminating. And that allows us to come over here. And this becomes a two, and this becomes a one. And then this space here has to be a four, which then allows us to fill in for here. And let’s I see here, there’s then there’s a lot of other things that we can do. So this becomes nine. This becomes a four here. This is a two here.

And then up here, we go to two, this becomes a one nine, which we’ll fix in just a minute anyway, or we could fix. The bottom line is at this point, we are, the rest of the puzzle is fairly easy to solve and Algie, I know that you are more than capable of solving it from this point. So I don’t really expect that you will fully understand. There’s no way that you could fully understand the potential deadlock technique, given the brief explanation, because I have multiple videos on this and we start with a lot simpler situations. And then we move into that more complex situation that we saw. As I mentioned, there is another graduate level technique that I spotted on this puzzle. And that is what we call linked double doubles. That’s a technique that I released last year. It’s actually a fairly straightforward technique.

And in this respect and this puzzle here, it would have been easier to see the linked double doubles than it would have to do the potential deadlock that I did. So just as an aside, at least in my opinion, and there may be other solutions on this puzzle. And actually, I certainly hope that there isn’t any easier solution than what I just showed you because you know, as far as a junior or senior level technique than I should have seen, should have applied.

But, you know, Algie, I’m pretty sure that you and I, between the two of us, we figured out that that’s not the case. But who knows, you know, we could always have missed something, but I do want to say with regard to the link, double doubles technique, if you’re a graduate member see if you can find it on this puzzle, it does lead to a solution just like this one did.

However it’s in a different area. The linked double doubles from from a geographic point of view on the puzzle is completely different area than the potential deadlock that I showed you. Alright. So Algie, thanks for the puzzle. I hope that helps you’re at that edge. You know, you’re solving these puzzles, you’ve plowed through those Senior techniques. You’re doing great. And now, you know, you’re at the point, you’re tipping over where you’re going to start running into more and more puzzles that are really, really hard. And so these graduate-level techniques are probably where you’re at right now. These are the things that you really need.

Hey, if you liked that lesson and you want more like it, you may want to check out the Sudoku Professor’s Insider’s Club, where you get access to lots of great resources, solving tips and strategies, our exclusive puzzle library, a fantastic community of like-minded Sudoku enthusiasts, and much, much more. There’s a link in the description down below. I’m Chad Barker, your Sudoku professor, and I’ll see you in class.