Frank Puzzles About Fractured Symmetry | Hard Variant Sudoku

Added: 2026-05-15

[00:00:02]Hello everyone. I'm Frank and welcome to Frank Puzzles. And this is today's hard level difficulty puzzle and it's called fractured symmetry by Rab Baron.

[00:00:16]And here are the rules.

[00:00:19]We have normal Sudoku rules apply which means in every cell in the grid place a single digit such that every row every row column and designated nine cell region contains the digits 1 through nine exactly once each.

[00:00:38]We have German whisper lines where adjacent digits along a green line have a difference of at least five. And I call these whisper five lines because a setter came up with that nomenclature and I thought it made sense because it's very easily extensible.

[00:00:54]So as an example since we have a one here these digit must be 6 7 8 or 9 because those are the digits which are five or more away from one.

[00:01:06]And that's an example of how a German whisper/wisper 5 line works.

[00:01:13]We also have palendromes where digits along a gray line read the same in both directions. So for this palendrome line, it's very simple. This digit is the same as that one because it reads the same that way as it does this way.

[00:01:29]Um for this longer one, then you have to have these digits these digits reading the same going this way as it does going this way.

[00:01:45]And that's an example of how palendromes work. We have little killers where digits a clue outside the grid gives the sum of the digits along the indicated diagonal. So therefore these digits must add up to 28. These four digits must add up to 27 and these six digits also add up to 28.

[00:02:10]And finally, we have crop key dots where digits and cells joined by a white dot are consecutive. So for example, if this were say a six, this would have to be five or seven for both of these cells because these two digits are consecutive because there's a white dot between them as are these two. Which means therefore that's what that's an example of how that works.

[00:02:36]And those are all the rules. If you like to play along, there's going to be a link in the description.

[00:02:43]And now I'm going to get started. Let's go.

[00:02:50]Okay.

[00:02:52]So, this adds up to 28 along this diagonal. So and since these are the same digits as these because this must be a palendrome going this way and it's exactly symmetrical for this part at least these three digits must be exactly the same as these three digits which mean and same thing for this these three digits are exactly the same as these three digits.

[00:03:14]So therefore they must add up to 14 for both of them. Since this adds up to 27, this must add up to 27 also because we know these digits have to be exactly the same as these four digits.

[00:03:30]Um, do we color them? H. So, 27 we have at most 8 and nine here, which is 17. So that means these two digits must add up to 10 at least.

[00:03:49]Okay?

[00:03:53]And again these three are the same digits as these three. These four are the same digits as these four.

[00:04:02]Same with these.

[00:04:06]So the question is should we start coloring things? H.

[00:04:12]Um, this has to be 6 through 9 because this is next to a one on a whisper five line.

[00:04:26]These Okay. So, let's maybe color the central box. So, light, medium, uh, shoot, light, medium, dark, green, pink, orange, red, yellow, and blue. So, we know this is yellow, so this must be yellow. This is orange here, so this must be orange there to be a palendrome. We have green here, and we have medium gray here.

[00:04:56]Okay.

[00:05:03]Medium is not the same as yellow. So medium has to be one of these two.

[00:05:10]Um if medium were here, that means it would also have to be there for the palendrome to work, which is impossible because we have a medium already in that color. So this must be medium there.

[00:05:25]Um h green has to be here and here. If this is green, this would have to be green, which is impossible because we already have a green in the column. So, this must be green here. Orange is here and here. If this is orange, this would have to be orange. And that's not possible because of the orange. Orange of the orange already in the column. So, this must be orange there.

[00:05:53]Okay. Um remaining colors in row four are pink, red, yellow, blue. Okay, that means this has to be pink, red, yellow, blue, but it cannot be yellow or blue.

[00:06:10]So this can't be yellow or blue. It's pink or red. This is then pink or red here. This digit is the same as that and it cannot be yellow or blue. So this is pink or red, which means that's pink or red here.

[00:06:26]That pink red pair in row four eliminates pink and red in the rest of the column. So this is a yellow blue pair.

[00:06:34]Um okay, remaining digits in row let's do column four. Column six are green and light. So green and light are here, which means green and light in column five have to be these cells here because we have a green and light here in column four. We have a green and light here in column six. So this must be green or light here.

[00:07:06]So we have definitely green or light here.

[00:07:10]Um so this can't be green because of green in the row. So there's no green possible there.

[00:07:19]Um so these two digits specifically cannot be orange, green, pink or yellow or medium.

[00:07:36]Okay.

[00:07:41]remaining colors in row six. We have light, medium, dark and pink.

[00:07:49]Okay, so therefore this must be light, medium, dark or pink to to correspond and this must be light, medium, dark or pink.

[00:08:03]So this cannot be this cannot be light either place. So this is not light here, not light here, which means this is not light here and this is not light here.

[00:08:15]Okay.

[00:08:21]Um again this can't be it has cannot be it has to be one of the outer corners.

[00:08:32]So red, light, blue or dark is here.

[00:08:38]Red, light, blue, or dark.

[00:08:41]So, this is red, light, blue, or dark here.

[00:08:48]Um, this we don't really have very much information, so let's not color those yet.

[00:08:58]Um, blue is one of these three. Yellow is one of these three, interestingly enough.

[00:09:14]This is consecutive with two other digits. So it must be either 2 3 4 or 678.

[00:09:26]Well, if this is two, that would force this to be a 13 pair, and that's never going to work. So these two digits are the same as these two digits which must be two apart from each other.

[00:09:43]Um so what digits can be here?

[00:09:47]1 and three. So we can't have these are two apart from each other. So they're either 1 3 2 4 35 4 6 5 7 6 8 or 79.

[00:10:01]1 3 is ruled out because that's only four and the remaining two digits would have to add up to 27 minus 4.

[00:10:09]That's 23 which two digits obviously can't work. So this can't be two. Um what about three?

[00:10:19]Oh, this can't be medium because of medium in the column. And this can't be medium for that same reason. This medium also eliminates medium here. Okay. So then this is a green pink dark pair which eliminates pink and dark in the rest of the row. So this is light and medium here which eliminates light and medium in the rest of the box. So this cannot be light.

[00:10:42]This can't be light. Where is light and green then in column five? It has to be here as a pair. So this is light and green. That's what I was hoping to find actually.

[00:10:54]Um remaining digits in column five then have to be blue, red, dark, and orange.

[00:11:10]And obviously this can't be orange because it's that would have to be the same as that and it sees that. So no orange there. And it cannot be blue because of the blue yellow pair in the box. So this is red or dark here.

[00:11:28]This is red or dark. That's red or dark.

[00:11:34]H okay. So again this digit is next to two unique digits. Can't have three. Can't be too four. 27 - 2 and 4 is 21 which two digits cannot add up to.

[00:11:55]Um um so two and four are are eliminated. So therefore this can't be three.

[00:12:18]What about three and five?

[00:12:24]Three and five add up to 8.

[00:12:28]27 minus 8 is 19, which is too big still for two digits. 19 n you can't have 9 and 9 and 9 is the most you could have here. So this cannot be four.

[00:12:43]Therefore, this is 678, which must be next to 1 2 3 which is next to 78 9 here because this is next to two unique digits on a whisper five line.

[00:12:53]So, the blue must be 1 through 4 here.

[00:12:57]So, medium is 1 through 3 and blue is 1 through 4. Interestingly enough, this is then either 57, 68 or 79. And either way we are guaranteed we have a seven here.

[00:13:17]Um this is five 5768 or 79. And one thing we know since this adds up to 27 and these two are both uh the same parody is that this is an even sum. So this must be an odd sum. So this cannot be the same digit. So you can't have pink here and pink here.

[00:13:41]So if you had pink here and pink here obviously that well okay if this were pink this would be red which would make that red.

[00:14:01]H we have a red pink dark triplet in box two and in box six which means the rest of the box cannot be red, pink or dark. So there's no red or dark here. This is not red or dark here which means this is a blue orange pair which eliminates blue and orange in the rest of the column. So this can't be blue and box.

[00:14:28]So this can't be blue or orange. That means it has to be yellow here. So this is yellow.

[00:14:37]Remaining digits in box six then have to be light and what's the other one?

[00:14:47]Uh no medium light and medium.

[00:14:54]H this is the same as that. So it cannot be blue. It's Yeah, we have the same thing here. So this adds up to 14 and this adds up to 14.

[00:15:10]This is a blue yellow pair here in row five.

[00:15:17]Okay.

[00:15:22]H.

[00:15:28]So since this is dark, this must be dark also.

[00:15:35]H, red and pink.

[00:15:45]Oh, so these three also add up to 14, which is the same as these because these are exactly the same as these. It's just we don't know the ordering of this.

[00:15:57]Um, so one of them is between two unique digits on a whisper five line and they must add up to 14.

[00:16:08]So, can you ever have two low digits?

[00:16:14]Um, I guess with nine maybe you would have to have Huh.

[00:17:00]So we know these have to be different digits because they if they were the same they would add up to an even sum and we know this adds up to an even sum.

[00:17:10]So therefore in therefore two even numbers add up to an even sum overall but 27 is an odd sum.

[00:17:18]So let's just mark these as letters right now. So we have a b and c or actually I guess we should make it this a b and c to make it equivalent.

[00:17:34]So C. So this cannot be C. It cannot be A either, right? Because A sees it right there. C cannot be the same as this because we know that these must add up to an odd sum. So they can't be the same digit. So this has to be B. And since it's B, that would have to be red or dark here.

[00:18:02]This is pink or dark. So these have to be the same. And therefore, these are both dark. So bees are dark, which eliminates dark in the rest of the boxes they're in. That makes this pink, which means this can't be pink. It's red. That eliminates red from being here. So this is pink there. This can't be dark here.

[00:18:28]And again, this cannot be pink.

[00:18:31]So there is what matches there dark h interesting.

[00:18:55]Okay. So then we don't need the lettering anymore.

[00:19:04]um dark remaining digits have to be one of these two. Okay. So what happens? So it's one of these two here and one of these two here in box one and box nine.

[00:19:23]This cannot Okay. So dark can't be here.

[00:19:27]Dark also cannot be here because this is these have to alternate between low and high digits and this would be the opposite pair here.

[00:19:38]Um so these can't be dark that can't be dark either. Both of these are So can both of these be dark? The answer is no. If both of these are dark, that means none of these are dark and none of these are dark, which would force this to be dark.

[00:19:58]But then we again this would be the opposite set as this one. So this can't be dark. So therefore, dark cannot be either of these. Therefore, dark has to be both of these, which forces this to be dark over here. So that's full nine darks.

[00:20:15]Pink um cannot be here or here. That's not very restrictive. Can't be here or here.

[00:20:25]Can't be here. Interestingly enough.

[00:20:30]So, pink has to be one of these two.

[00:20:35]Pink can't be here or here.

[00:20:41]What about red? Red can't be here or here. So, red can't be here or here.

[00:21:13]red can't be any of these.

[00:21:16]Red also can't be there.

[00:21:27]Um, so this is definitely dark. So dark is a high digit and it cannot be five because it's next to it's on a whisper five line. So we're guaranteed dark is a high, pink is a low, red is a high, and they must add up to 14.

[00:21:48]The only way that's going to work is if it's six, seven, and one.

[00:21:54]So, red and pink.

[00:21:59]Therefore, pink is one.

[00:22:02]So, all the pinks are one.

[00:22:05]The uh darks are six and seven.

[00:22:12]Um, so we don't know if this could be five.

[00:22:21]This could also be all these digits here. Pink is six and seven. Sorry, red is six and seven. And so is dark. As I said, this 67 sees 67 here.

[00:22:36]So cannot be. This is Oh, we have a 67 pair.

[00:22:42]So, this is seen 67 twice and this is 67.

[00:22:47]So, this is 13 guaranteed.

[00:22:53]First of all, this can't be six or seven. And this is one, which is pink.

[00:22:58]So, that's pink, which means pink can't be here or here. So, pink has to be one of those two. Pink has to be one of those two. Pink can't be here or here.

[00:23:08]It can't be here. So, pink is one of these two.

[00:23:16]Um, so we have a definite 13 here.

[00:23:22]So, this cannot be seven here because if 13 + 7 is 20, 27 minus 7 is another seven and that would have a repeat in that box. So dark has to be six. Since dark is six, red has to be seven.

[00:23:40]That's pretty cool actually some of these things. So this can't be six. It's can't has to be then seven or eight here. And it has to be consecutive with six. So this is seven here. That means and this can't be one. So that means medium has to be two.

[00:24:00]So medium is two.

[00:24:04]This blue is not one or two.

[00:24:07]So it's three or four. This can't be seven. So green or medium is eight or nine. So this is 6 7 and this must be eight. So this is eight here. That's 14 + 13 adds up to 27.

[00:24:23]So this is 8. This is eight.

[00:24:29]Um, orange h.

[00:24:56]Yellow is next to two unique digits on a whisper five line.

[00:25:04]Um.

[00:25:11]Huh.

[00:25:14]So the com it can't be one or two. So if it's it can't be three either because if it's three that would force this to be a 89 pair. So therefore, yellow cannot be low. Yellow has to be a high. So it's eight or nine here. So yellow is an eight or nine.

[00:25:35]Um which is next to three and four on the whisper five line. So one of these two is going to be blue. We don't know which one.

[00:25:47]The remaining digits in row three then have to be 7 9 or five. And five can't be on the whisper five line. This can't be seven because of seven in the column.

[00:25:58]So this must be nine here. Which means this can't be nine here. This can't be nine or seven. So that's five which makes that seven there.

[00:26:07]Um this is next to both three and four.

[00:26:09]So this is a nine. So yellows are nine and this is eight. So yellows have to be nine.

[00:26:17]We don't know what these are.

[00:26:20]So these are nine here. That means this can't be nine. This is eight. Which means blue has to be three. So blue is a three.

[00:26:30]Um this is next to this digit which has to be cannot be it's next to two unique digits on a whisper five line. So this must be three which makes this eight. So light.

[00:26:42]So light gray has to be eight, which means this can't be light. It's green.

[00:26:50]This is three, which makes this four.

[00:26:55]Um, green can't be the four. So orange has to be the four. So this is not orange here. This is blue. This is not blue here. That's orange. So all the all this can't be blue because they are both low and yellow again has to be here. So this can't be yellow, it's blue. This can't be yellow because it's nine there. So this can't be has to be blue which eliminates blue there.

[00:27:25]Um we don't know about medium and light.

[00:27:28]So green has to be not four. It is five. So green has to be five.

[00:27:41]Orange is four.

[00:27:44]Yellow is nine and blue is three.

[00:27:50]And now we just do the rest by just normal sodoku. This can't be seven or not normal sudoku but this can't be seven because of seven in on the next to it on a whisper sorry this is seven which means this has to be one or two and it cannot be one because of one uh in the row in column so therefore it must be two two has to be next to this digit which is 7 8 or 9 cannot be six or eight so this is seven or nine here and now we just do the rest from normal sudoku so we don't need the coloring anymore.

[00:28:26]It gets kind of confusing. So, let's remove these.

[00:28:31]Um, remaining digits in column six are what? Five and eight. And this can't be eight because I have eight in the row.

[00:28:40]So, this is five. That's eight.

[00:28:43]Remaining digits in column four, we have four and three.

[00:28:51]And we don't really have any restrictions there. This digit has to be 2, three, or four to be next to the nine. Remaining digits in row five, we have two and eight.

[00:29:03]Remaining digits in row six, we have two and eight. And this can't be eight because of eight in the column. So this is two, which makes that eight.

[00:29:11]Okay.

[00:29:13]Remaining digits in row seven, we have four, five, 3, four, five. This can't be three or five because it's three or five in the column. So that's four and this is three or five here and we have three or five here. Eight eliminates eight here. So that's two which makes this eight.

[00:29:35]Um remaining digits in column three we have what?

[00:29:41]Three 78.

[00:29:46]Okay, eight can't be here. So this is three or seven. And then we have this can't be eight here because so this must be three or seven because of eight in the row. So that forces this to be eight here.

[00:30:00]Remaining digits of column 7 are 3, five and 9. Nine cannot be either of these because of nine in the box. So this must be nine here. This can't be five because of five in the row. So that's three, which makes that five.

[00:30:15]That means this can no longer be three here. Remaining digits of row two, we have 1, two, and four. This can't be two or four because of two or four in the column. So this is one. This can't be four because of four in the column. So that's two, which makes this four. Okay.

[00:30:33]Um, remaining digits in column 8. Well, this has to be two. So that's two because of the remaining digits in that box. We have one and four remaining. Yes, one and four remaining in column 8. In column 9, we have 2, three, and five. This can't be two. So this is 3, five as a pair.

[00:30:59]That eliminates 3, five in the rest of the column. So this is two here.

[00:31:06]Remaining digits in row one, we have three, seven, and nine. And this can't be three or seven because three is seven in the column. So that's nine which makes this three or seven. That leaves the remaining digit in column one as a one. So this is one which makes this not one. So it's four and one. Four eliminates four here. So it's three and four. Three eliminates three here. So it's five and three. Three eliminates three here. So this is five and three here. So that's seven. Which means this can't be seven. It's nine. Seven eliminates seven in the rest of the column. So it's three and seven. which leaves this as a six. Not a six.

[00:31:44]Uh is a three. Anyways, I don't know how I got a six there. It was just I don't know. Kind of out of it there. Um pretty cool. I I like coloring exercises a lot. And that's actually kind of why I actually chose this puzzle. Um because I was curious about how what type of if it would be a coloring exercise, which it essentially was.

[00:32:08]But yeah, there was a lot of interesting stuff going on around here. Um, how did Okay. Yeah, I determined that this was dark and that basically broke everything apart. So, since we know that this was dark, these had to be two highs and two highs and a low had to add up to 14, which made it 1 six and 7.

[00:32:32]Um, yeah, I went over that kind of quickly. So, the reason why it's 167 is that's the minimum you can have for two highs and one low digit on a whisper five line. Um, with the high digits being with all the digits being unique, right?

[00:32:51]So, if you're guaranteed two highs and one low, the minimum is 167, which is what the this amount has to be. So, since it matches the minimum matches that amount, it has to be those digits.

[00:33:03]that um I went through that rather quickly, but um I guess it's not that hard to logic out, right?

[00:33:12]Um not too bad. I think I would put classify this as average, but maybe I don't know. Maybe it's harder if you I don't I'm not sure what other approach you can really take though other than start coloring.

[00:33:30]Anyways, I hope you enjoyed this solve and I'll see you next time on Frank Puzzles. Take care.