How to Start a Hard Sudoku Puzzle

This video was posted on Oct 7th during Sudoku Week 2020. Transcript below.

So this is Fred Hall’s third question that he asks, and he’s asking it regarding the Senior 405 lesson number one puzzle here. This is on the Club-exclusive 3-box 3-corners method. And it’s not specifically about the technique. It’s about how do we get to the point where we can apply the technique.

So let me give you a little bit of a background first before I actually get into the question so that you understand the context where he’s coming from. It’s really critical on these three corners methods and actually on most of the graduate level lessons.

You know, many, I would say generally speaking, many of the Junior, Senior, and all of the graduate level lessons, it’s really important that we find these spaces where only two numbers can go. So like this space here that six and nine, only two numbers, you know, all of these spaces were only two numbers can go down here. This space here, only two numbers can go in this space. Only two numbers can go in this space and this space here, only two numbers can go in this.

And there’s many other examples on this puzzle, but it’s really, really critical that we find those spaces. Because if we don’t, we can’t find the pattern that we’re looking for. It’s kind of like, you want to bake a cake, but you don’t have all the ingredients. You’ve got to go collect all the ingredients before you bake the cake or else you won’t be able to bake the cake.

So the ingredients in this situation are all of our spaces that can only be two numbers. And the cake that we’re trying to bake is the technique that we’re trying to apply in this case, a 3-corners method.

So his question is “what is the first thing I do when I start this puzzle?” And he’s asking, “do I begin filling in as many spaces as I can, or do I begin searching for the spaces that only two numbers can go into?” So if you watch the videos, this is my stuck point that he sent back here to me to, to consider. So this is for this lesson, this is where I got stuck, if you will. And this is the point at which we’re going to apply the technique.

What I didn’t show and in those videos is how I got to this stuck point. So Fred doesn’t really know what to do first, or what I would do first, let’s put it that way. So to answer your question, Fred, in all of these puzzles, the first thing that I’m doing generally speaking is one through nines.

It may look different. It may be a little variation, maybe nine through ones, or, you know, I might throw in a little bit of pattern solving or something like that along the way. But generally speaking, what I’m doing is one through nines. And I’m trying to get as much of this information on the board, fill in these numbers.

I mean you know, to fill in all this information and to reduce these spaces down to these double doubles and triple doubles that I’ve gone on here, I had to do a lot of just the one through nines. That’s what gave me all of that information. And generally speaking, obviously most of these pencil marks that I have on here, especially where I showed that the number can only go in two places within the box.

Like, you know, the five here and here, the six here and here. And so on, those things are discovered during the one through nines. And it’s probably actually multiple trips through the one through nines, given the difficulty level of the puzzle, but the key to finding these spaces, which is what your question is, is really how do you find these spaces? How do you find these spaces where only two numbers can go into?

And the key technique that I use to do that is “think outside the box” and that’s really what you have to do. I mean, there’s really no other choice in my way, in one way or another, you’re going to do think outside the box. So for example, let’s take a look at this column right here, column seven. And if I do a think outside the box what’s missing is five, six, seven, and nine.

Okay. So we got one, two, three, four, we need five, six seven and we have an eight and there’s nine. It’s a five, six, seven, and nine. Now let’s look at each of these spaces and I’m going to talk about what I would have known and what I was able to discover. So this space here, I probably already knew that this could only be five and six because it’s the one of two places along the row. Then the last two numbers are five and six. Generally speaking are probably, you know, conceptually without actually doing it. It’s like, I did a think outside the box, but because there’s only two numbers missing, it was too easy. So I probably already knew that one, but I got here. And the only thing I knew more than likely after the one through nines and such, that this was one of two places for a six.

That’s probably the only thing I knew, but I do my think outside the box. And I think about what, then I can eliminate from this space. And I realized I got seven in the box and five is row eliminating over here. So I realized that the only other thing that can go here is a nine. And that allows me to write the nine in the upper left-hand corner.

I come down here and I look at this space. Now, again, going through one through nines, I probably figured out that set. This was one of two places for a seven and one of two places for a nine within the box. Okay. You can see the pencil marks. But what I didn’t know was that was the only things that can go there, but I did discover it through the think outside the box, seeing that six is in the box and that five again is row eliminating.

Therefore the only two things that can go in this space are seven and nine. And that’s why I underlined it down here. Same thing, five. I knew that five could go in two places. Seven can go into places, but the only way I discovered that those were the only two things that could go in that space was because six is in the box or the row and nine is also in the row. And that leaves us with only five and seven. Let’s do another example like this column right here. This is three, five. Okay. So I would have done it to think outside the box, this space here. And I see that five can, is one of this, one of few places at five and go in the box, but three and eight can also go there. There’s nothing eliminating that.

So I don’t do anything else. I move on. I come down here, Oh, look, there’s a five in the row. And that enables me to draw the conclusion that this can only be three and eight, which then I write in the upper left-hand corner. That the only two things that can go there are three and eight.

And then I look at this space right here, again, it’s one of two places for a five, but three and eight can also go there. So I don’t do anything else, but I’m able to discover that only two things can go in there. Because of this think outside the box that I’m doing right up here. Something similar over here, so we got we got what’s missing from this column is five, six, and nine. I would have known probably that this can only be five and six because it’s part of this triple double that would have been easy to see.

What’s even easier, more than likely it was this six, nine. This can only be 6-9 because it’s part of this double double, but getting down here I am able to reduce this to only two because, again I’m doing my think outside the box. And I see that six is in this box here. And that means that the only other thing besides five, which are already would have discovered, is nine that can go in this space.

And that helps me again, these things help me figure things out. If I were to look down here, do a think outside the box on box seven here. You know, again, I would’ve known that seven and eight are the only two things that can go here, but I might not have known everything about the remaining numbers, three, four, and six.

I would have known that six could have gone here and here and four here and here, but the other number three, what can I do with that? And this space, the only other thing that could go in this space is three. The only other space that could go in this space is four, and therefore you know, I can, again, I’m using the think outside the box in a variety of ways to find these spaces that only two numbers can go into. And that again, gives us the key ingredients that we need to, for the pattern to find the 3-corners pattern.

Now your next question, Fred, is that when I find a space where more than two numbers can go in it, do I erase the numbers or do I keep them there. To me, I may not have ever written the numbers. So let’s take a look at this space right here. I mean, again, I found that more than three numbers can go in that, or more than two numbers can go in that space. And so I never actually wrote in the upper left-hand corner to that three and eight could also go in this space as in the same thing with this one, let’s take a look at this column here, column eight. What’s missing is three, four, eight, and nine from this column. And I would’ve done a think outside the box on this column, and I would’ve looked at this space and I realize that four’s in the box. So three numbers can go there: three, eight, and nine. I wouldn’t have written anything. Same thing here, three, eight and nine.

As a matter of fact, three can go in three places in the box, nine and eight can also go in three places in the box. Nine can go in three places in the box. So again, because each of those numbers can go in multiple places within, more than two places within the box, and for those spaces, both of those spaces here and here, there are more than two numbers that can go, I would never have written anything to begin with.

And you know, down here, same thing, this is three, four, eight, and nine. I’m writing the four and nine in there because it’s really meaningful information where the four can go in two places and the nine can go in two places, but I’m not going to add the three and eight to that same thing here. I’m not going to add three and eight to this, but I’m going to leave the four. I’m gonna leave the four and nine, because that’s important information.

Now maybe you’re thinking through things and maybe you’re sort of trying to find patterns. I do this sometimes I’m just trying to see, am I missing something? So I might take some notes. I mean, I might write three, eight, nine here in little numbers, three, eight, nine. I might write down, you know, this, this can be three eight in addition to four and nine, or I might write the whole thing, you know, three, four, eight. I might write everything. It just depends. I might be taking some, writing some things down like that kind of temporary notes, trying to see, is there a pattern here? And if I were doing that, I probably, yes. Would then I would come back and I would erase this stuff if I didn’t find the pattern that I was looking for.

So maybe that’s kind of what you’re getting at. Maybe you’re doing some of that while you’re trying to solve. You’re looking for you’re writing more down than you should, because you’re kind of thinking through the different possibilities and different patterns. But yes, if I did sort of take notes like that along the way, trying to look for stuff, I would erase those as soon as I discovered that they weren’t helpful.

And to me, that’s important because you know, when you’re solving this puzzle and many puzzles like this, the extra information, it doesn’t help. It never actually helps you discover more. It only clutters and potentially obscures what’s really there. And again, you watch the lesson for this 405 lesson number 1, you watch the video and you find the 3-box 3-corners, and you realize, wow, that’s easy and I didn’t need anything else. I didn’t need to write all that extra stuff.

So, Fred, I hope that helps you. I hope that helps you get a handle on how to approach these puzzles and you know what to pencil mark and what not to pencil mark and how to find, more importantly, how to find the ingredients for your cake, how to find the spaces where only two numbers can go so that you can apply all these techniques. Again, most of the senior level techniques and the almost all the graduate level techniques require that you find as many of these spaces that you can, where only two numbers can go.

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.

 

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Robert Barker