Sudoku Adventure #1191 - "Like Two Drops of Water" by SennyK

本站添加: 2026-05-27

[00:00:00]Hello. Let's continue our Sudoku adventure with like two drops of water by Seni K. So we have normal 6x6 Sudoku rolls. That means in each row, each column and each 2x3 box, we are placing the digits 1 to six exactly once each.

[00:00:14]We also have these gray lines in the grid. These are palendrome lines. So they read the same forwards and backwards. So if this was 2 35, we would want to read 2 3 55 532. So that this reads 2 355 532 and this reads 2 355 532. Tell you a little secret that just means these two are the same digit.

[00:00:32]These two are the same digit. These two are the same digit. So it's basically just a way of drawing clones in the grid. All right, that's palendromes. Um we also have these German sums. So let's give an example first. So 2 6 3 1 54.

[00:00:51]So what we need to do is starting from the clue we always include the first digit in the sum and then we could keep including digits until the difference is less than three. So 2 to 6 is difference four. So that's included. We include the six. 6 to 3 is difference three. That that's at least three. So we include it.

[00:01:08]But then 3 to 1 is 2. And so that difference is not at least three. So we stop and don't include the one. So we would include the 2, six and three. We sum them up. they sum to 11. That does not match the 14. So that is not a valid way to fill this row. Right? So we need whatever the German sum is to sum to 14 and include digits uh from here moving forward until um we reach a difference of less than three. So hopefully that's clear.

[00:01:42]Um and that is it. Those are the rules.

[00:01:44]There's a link in the description if you'd like to try the puzzle yourself.

[00:01:47]and I'm going to get started right now.

[00:01:51]Okay. Um, interestingly, these three and these three are the same digits, just different orders. But the the difference of three is going to be preserved between these two, right? So, like this is let me actually use letters here.

[00:02:06]This is A B C. This is CBA. And so the difference AB here is the same difference AB here. The difference BC here is the same BC difference here. So actually, yeah, this for the sums, they're the same order. Um, and so whatever is included is included. Now, 16 is is a pretty big sum to reach. Um, one way we can think about that is we know that that all of the digits 1 to six sum to 21. And so 21 - 16 is 5. That means we're missing digits that add to five. Meaning we're only missing the five or we're missing say 1 4 or 2 3. So we can only be missing one or two digits. So we know that this sum reaches at least here. Um which also means that the 14 sum reaches at least here.

[00:02:55]So um 14 has an audi of seven which can still be achieved in two digits.

[00:03:06]So we we know these two have to be different because if these two were the same wait do they have to be different?

[00:03:12]If they were the same then actually we could we could get away with them being the same. I think it's just this would be too lower than this or something. I don't know. Or one of them would stop and the other wouldn't. Okay.

[00:03:29]So, we know either we have a five here or these two add to five. So, this I mean it's it's not much to say. It's just not six. But um same thing here. I don't really like that marking.

[00:03:46]Is there another way to think about this? So the Audi's of the 15 are going to be six, which technically could be 1 2 3. But I don't actually think that works cuz if this is 4, 56, there's no way we're including all three of them in the sum.

[00:04:01]We don't have a difference of that much.

[00:04:04]So, um, we might be able to use that kind of strategy to think about this a bit more closely cuz we need to get really big here. And we know that we're going to have to alternate low, high, low, high, low, high. Right? So, four and 1 2 3. We need to if we want to keep summing, we got to get to the 456 range.

[00:04:22]Um, and then from the 456 range, we got to get back down to the 1 23 range in order to have a difference of at least three. So, we know that these four cells are going to have two highs and two lows. So the absolute maximum sum is this which is 16.

[00:04:39]The problem is we could include one more digit.

[00:04:42]So it doesn't have to be this maximum I don't think.

[00:04:47]Yeah. What this is saying is that we're missing the four which is possible. If we were missing the five, is it actually possible to use all of these in a sum?

[00:04:55]So we're missing one high. So these would have to be the highs. These would be a four six pair and then these would be the 1 2 3. Now I'm concerned about wherever the four goes, right? If if our line went all the way through here, I'm concerned about the four because in order for the four to keep including to to be included in both directions, we'd have to be surrounded by ones in order to be a valid um German sum.

[00:05:21]Right? If I if I make this a two, this difference is two, which stops the sum before we reach the four. If I make this a two, then we stop. This is a difference of two and we we stop right here. So I I just don't think this can be a five on its own because wherever the four ends up, it would be surrounded by ones, which isn't possible and wouldn't actually sum to the correct thing anyway. So actually, I believe our only choice is to Yeah.

[00:05:47]And for another for a similar reason, a 23 pair doesn't work because now our only low left is a one and we need we need two lows. So this is a 14 pair and we don't know which way this goes.

[00:06:00]Unfortunately, this is also 14 just because of the palendrome.

[00:06:05]Um but it means that we're going to have a 23 pair and a 56 pair somewhere.

[00:06:16]Oh, what about the two three pair? So where's where does the three go? Right.

[00:06:22]If we put the three here, it would have to be surrounded by sixes, which is no good. So, these are not threes. These are either the two or the five or the six.

[00:06:32]So, one of these is the three. That makes these two five six by the way.

[00:06:39]And we know it we know it involves the two.

[00:06:42]So, that can't be a two, I guess.

[00:06:46]Um, does it matter?

[00:06:54]So, if the three were here, we'd go, let me just do it one below just to have scratch space. If the three were here, we would go six here, and then we'd go two here, and then five here, and okay. And then we wouldn't want we would need the uh four next to it to stop the sum. The one would not stop the sum. So we need the four and then the one. So this is one way to that this row fills. Let's go down one here and say what if the three were here. Well then this would be the six. This would be the two and this would be the five. And from the three we could go to the one or the four to stop. So unfortunately that's not all that interesting. But these are our two options. So this is three or five. This is two or six. This is two or six. And this is three or five. And then the one four is correct.

[00:07:44]Okay, so we can actually move this up here. Oh, so this is just a two six pair. That's that's handy.

[00:07:51]Um, this is 35.

[00:07:55]Okay, we can get rid of these.

[00:08:00]So this is three or five.

[00:08:04]Now the 14 is it gonna end it? The biggest we could make this is a 56 pair adding to 11 with two more adding to uh 13. So we do have to use this one which means it does have to be a 35.

[00:08:21]Um does it have to be a 35? No, not a 35. But let's think about the two options. If we start with three, this is six. This is two. That adds to 11. So we need three more.

[00:08:35]We can't we can't do that. We can't get three more.

[00:08:41]It's not possible. Okay, so we better be the five. Unless I'm wrong. We better be the five. Uh, yeah, the five, the the two. Sorry, I got confused for a second.

[00:08:50]The five, the two, and the six.

[00:08:52]This adds to 13. And then we'd have a one after it. So that's what we have to do. So we have 5261.

[00:09:01]That makes this 5263.

[00:09:04]And then this is a 34 pair. Perfect.

[00:09:08]Now, we can't do one four because that four would get included. So, this is three and this is four. All right. I don't think I need these green anymore.

[00:09:15]That was fun. All right. Took me a little bit to think through that. This is going to be a 256. That can't be two, six, five. That makes this a five or six. Can't be a six. So, these are both fives. The palum, right? That's two.

[00:09:28]That's six.

[00:09:30]Oh, the three could be next to one or four, unfortunately.

[00:09:37]All right, this is 134, which is That's not one. That's not three. That's not four. All right. Should we think about the 15? That's all that's left. I wonder how much Sodoku we can do first.

[00:09:48]Um, we know five is one of these two.

[00:09:52]Not immediately helpful. Six is one of these two.

[00:09:57]The two is one of these two. I really don't think we have I mean, I guess I could put the 134 up here. That's not a three. And we can put the 256 up here.

[00:10:06]That might help later. All right. 15.

[00:10:11]What's the absolute minimum number of cells to get to the 15? Um, if we do, if we did a five six pair, that's 11.

[00:10:23]With the five six pair, oh well, we can't use the Okay, in these three, we can't use the five, which is even worse.

[00:10:28]We'd have to be four six pair with a Yeah, that's not going to work. That's not big enough. First pair would be 10.

[00:10:33]We need five more. We can't do that in three. So we're doing it at least. We're doing it in these four because after the five, the four would break it. So these are going to add to 15, which means these add to right. We could have thought about the Audi's as well. These add to six. So this is a two. That's five. That's six. That's a five. Uh next to five, we cannot put a three. So that's a one. That's four. That's three.

[00:10:55]Um and so this is a pair and we should know the order. Yeah. So this is going to go to high, that's six, and this is going to be three.

[00:11:01]And I'm really hoping that adds to 15.

[00:11:04]Yes, it does. 6 + 3 is 9 + 1 is 10 + 5 is 15. All right. Places the six there.

[00:11:10]Um, these digit. Okay, this one's a one.

[00:11:14]These two digits are the two and the four.

[00:11:18]I believe the only thing really other than Sudoku is this palendrome.

[00:11:23]This is not a one. This is 3, four.

[00:11:26]Um, these are from 1, two, three, four.

[00:11:28]That's not one. That's not three. All right. So what is our deduction here?

[00:11:35]Okay, this is interesting. So this is a 1/4 pair because of the column, but this digit goes here. So this is also a one4 pair. So one of these is one, the other is four. They both touch this guy or they see this guy. So through the box row through the column, right? And so this can't be one or four because if it was one or four, these would both be the same, which is not possible. So this is a three. That gives us the four and makes both of these a one which makes that a four. And there's our one four pair I was talking about. That's four and that's one. That's two and four. Two and three. And we're done. Very cool puzzle, Sy. I enjoyed that.

[00:12:12]I was trying to hold that sneeze until after I stopped recording and it didn't work. All right.

[00:12:17]Anyway, I did enjoy that. That was very fun. Uh the the way this palendrum interacted with the 14 and 16 sum was really fun to think about. And this 15 ended up uh really resolving things nicely. And then the ending with this this palendrome was unexpected. All right, cool. Well, how'd you do?