Sudoku Adventure - "Ratio Count" by gdc

[00:00:00]Hello, let's continue our Sudoku adventure with ratio count by GDC. So, we have normal 6 by 6 Sudoku rules. That means in each row, each column, and each 2 by 3 box, we are placing the digits 1 to 6 exactly once each. We shall have these ratio lots lines. So, a digit in a circle counts the number of adjacent pairs along its line that have a 1 to 2 ratio. 1 to 2 ratio just means one is exactly double the other. Uh the example given, we'll go use this line for it, is 3 2 4 2. Now, that doesn't mean that we're ignoring this circle here.

[00:00:33]But, if we were 3 2 4 2, how many pairs of digits do we have with a 1 to 2 ratio? These don't. These do. 4 is double 2, and these do. 4 is double 2.

[00:00:42]So, that's a count of two um 1 to 2 ratios on this line. So, any either of these twos could have been circled. And that would have fulfilled our that would have uh fulfilled our our lot there.

[00:00:55]And that's it. Those are the rules.

[00:00:57]There's a link in the description if you'd like to try the puzzle yourself, and I'm going to get started, right now.

[00:01:04]Well, the number of pairs on a line is 1 minus the length. And so, the circles can't ever be more than 1 minus the length. So, that's 1 2s, and then this is 1 2 3.

[00:01:16]So, this is a 1 2 pair here, making this 3 4 5 6.

[00:01:25]Um yeah, so how would this be two?

[00:01:31]Cuz if it was two, this this could be four. It would have to be. We This would have to be 1 to 2. This would have to be 1 to 2. But, this can't be a 1. So, this would be four, but then now what do we put next to the four? 3 5 and 6 are not 1 to 2 ratio with four. It would have to be a two, and we'd repeat the two. So, actually uh this is a one.

[00:01:47]And this is not involved. This this doesn't do 1 to 2. We'd have to have a two here. So, these don't use the five.

[00:01:53]In fact, they have to be 3 6.

[00:01:56]Okay, so then that's 4 5, and this is a two. So then two has to go to a one or a four, which then goes back to a two.

[00:02:04]That makes that a three.

[00:02:06]So this has to be one to two links and that's six and then that makes that a three and then that makes that a six.

[00:02:10]Nice. That's three and six.

[00:02:13]This is going very smoothly. This is 2-4-5.

[00:02:16]This is 1-3-6. That's not a six. All right.

[00:02:20]What here?

[00:02:22]Um I think it's possible we could do two here with a four here and a one or a four here.

[00:02:29]All right, what else? What about this guy?

[00:02:32]Oh, if this was a one, then one of these would have to be a two, but the two is gone. So this is a two, making this a 1-4 pair.

[00:02:39]So 1-4 pair means that's not one. And so this is 3-5-6.

[00:02:44]The 3-6 looks in, making that a five and this is 3-6.

[00:02:50]What now? Uh 1-4 1-3-4 here.

[00:02:53]The three can only go here.

[00:02:56]So that's not a three. This is a 1-4.

[00:02:58]This is a 1-4, but not a one. That's four and one. That's a four. That's a one. That's a four. We get five and four.

[00:03:06]That's a 3-6-1.

[00:03:07]That's a three.

[00:03:09]Uh we need five and six here. This is six. This is five.

[00:03:12]All right, these two digits are 4-5.

[00:03:16]Uh that's not a four and these are I'm just going to do as much Sudoku as I can before I think about the remaining circles.

[00:03:22]I think it's just this one.

[00:03:24]Anyway, these are 1-2-5. That's not one.

[00:03:26]All right, I think we do have to think about this one then.

[00:03:28]Um oh, if this was one, one of these would have to be two, but they can't be.

[00:03:32]So it's a two. That's one and six.

[00:03:35]That's not a two. That's not two. That's not one.

[00:03:38]Two So both of these pairs need to be ratio. So that's a four. That's a five.

[00:03:42]That's five, two and four. We get the five, two and one and suddenly we're done. Wow, under three minutes.

[00:03:48]That was very smooth. Cool puzzle, GC.

[00:03:50]Um yeah, I think the the big realization I had right at the start and it's in box one, fair enough, was this one-two pair, right? Just blindly penciling these that made this one-two pair. And then I realized two couldn't work cuz it would have to be 242. It's kind of like a chain of black dots.

[00:04:08]Um, it it is a chain of black dots. Like if you're used to chains of crop key dots, it's like that um, if it were two and that just won't work if you start with two in a um, in a 6x6 at least. In a In a 9x9 you can't cuz you can do 248. But in a 6x6 um, a chain of three black dots has a uh, um, has a two in the middle with one four surrounding it. It's the only way to do it.

[00:04:34]All right. Well, how do you do?