Linked Double-Doubles Webinar
Hey everybody. This is Chad Barker, your Sudoku professor. This video that you’re about to watch is an excerpt from an Insider’s Club Webinar that we did after we released the linked double-doubles technique, which is part of our master’s level course.
On this webinar with me is Brian Garman, who is a top contributor to the Club and the impetus behind the linked double doubles technique. So, first you’re going to see me in the studio where I show you the technique in action on a puzzle, which you can download with the links just below this paragraph, if you’d like to download that and work it yourself. Then I’m going to be back in front of the computer, answering questions from webinar participants.
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As we look at the puzzle, we’ve made a good bit of progress here, but the key is how do we find these things? And what I have found to be the most helpful when I’m looking for this pattern is to first look for and find the cross box double doubles. Let’s not look at the in-box double-doubles first. Let’s look at the cross-box double-doubles and then see if we can find the in-box. Now for you, you can try it different ways. You can look for the in-box and see if you can find the cross-box. Again, I find it to be a more sure method to find the cross-box first, and that’s what we’re going to do.
So we look, there’s actually no cross-box double doubles on rows. In columns, we have one here, in column six, we got the four, five. And then in the column over here in column eight, we have the five, nine.
We look at the five, nine though. We can see that this end point of the double-double ends in this row eliminating five, six, nine triple combo, as I’ve explained in the prior lessons that this is never a situation we’re going to be able to link with anything.
This is all row eliminating, and therefore it’s going to eliminate the possibilities of finding a common number along the row. So this cross-box double-double is out. That leaves us with only one cross-box double-double to consider: that’s our four, five.
So the way I do this is again, I take this and I want to scan across. I can scan back this way or that way, if we look back over here, I mean we’re not going to look in the box. We’re going to look outside the box and we come across these triple combos over here. That’s not helpful. We scan this way and we run into this space right here. So we have this four, five. We’re scanning across, we find this five, nine.
Ah, well, there’s a couple of things that we just found. It’s part of a double-double in the box, right? Five, nine double-double. And it shares a common number. So we have our three components, okay? We have a cross-box double-double, we have an in-box double-double that shares a number and shares a common row at one of the end points, alright?
So then what we do is we take the other end point here and here and find out where they intersect and see if we can do an elimination. We come down from the column there and across the row, and we find out that the space is already filled in.
Oh, well. We found the pattern, couldn’t do the elimination. Well, let’s keep looking. And again, we’re going to keep going across and we find this five, again, we have this five, six over here. So now, do they share a common number?
Yes. Five, the end points, because this is part of this five-six double-double in-box. And we have found that they share a common number, which is five now. So we have all the components, now we need to look to see what we can do with the other end points.
So these are our linking end points along the row. So we go to our other end points here and here, and we find out where they intersect. And that’s right here in this row, in this column. And this space right here cannot be the common number of five.
Let’s do the logic. So if this is a four, then this space has to be a five, which would cause this space to be a six, which causes this space to be a five. Or this space up here is a five. So either this is a four or five. If it’s a four, five winds up here, or it’s a five, which in any case five is going to wind up in one of these two spaces, eliminating five from that space.
Or we could stick the number in there and we could do the conflict method and we’d find out that we’d have a conflict somewhere if we put five in that space.
Okay. Anybody got any questions on that? Now, Brian, maybe you could tell me, is that how you would search for these? Would you start in the column looking at cross-box or do you have a different method that you use?
I like your method actually. It makes it more systematic. I tend to just look around and kind of globally if I see the five, six, five, six, four, five…Yeah, I don’t think I’m just as systematic as you, I liked your systematic way. Cause when you do those cross boxes, you can only have two choices. And so I’m learning a whole lot myself.
Alright, well, some of you I see some comments here, Howard and Philip, you missed the video, so I’ll go ahead and I’ll just quickly review what we came across here. So the first thing we did was to find the cross-box double doubles. We found a couple of them here and here. The five, nine here in row eight I eliminated because it’s part of a five, six, nine triple combo that is row emanating down here. That’s going to prevent the link.
So we focused on the four, five cross-box double-double. We were looking here and here at this four, five, and then we started to look along rows. What I did is I looked along the row here and here this way. And then I looked back the other way to try to find an in-box, double-double that shared one of those numbers, either four or five.
Ultimately we found this five, six double-double here that we could use in box nine and row seven was our linking row that we linked to the two double-doubles along row seven here. And that allowed us to eliminate five, the common number from this space right here up in box three.
And then we did the logic here of if this is a four, this is a five, which makes this a six, which makes this a five, or this is a five. So these other end points that are not linking, these are the, what I’m starting to call, the elimination end points up here in row three and down here in row eight. One of them is going to be five, one or the other. We don’t know which one, but in all cases, five is eliminated from the space where I have the green X. Anybody else have any questions about it?
And you might add that putting in the five there or putting in the nine there solves the puzzle quite quickly.
Actually, you’re right. Thank you. I had forgotten that I had done that. Yeah because it’s a five, nine double-double, once you eliminate five from that space you’re good to 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. So happy solving. I’m Chad Barker, your Sudoku Professor.