This Trick Can Help Unlock Impossible Sudokus

** TODAY'S PUZZLE **
Tonight's sudoku has received umpteen recommendations in recent weeks. Apparently it's the ultimate "nabner" puzzle (a nabner line cannot contain two consecutive digits anywhere along it): it's called Someday We'll Meet Again and it's by Twototenth (not Vera Lynn or Johnny Cash!).
We don't want to spoil anything but do give this a go - it's a quite extraordinary construction with so much fascinating logic. We're looking forward to the comments on this one!!
Play the puzzle at the link below:
app.crackingthecryptic.com/su...
Rules:
Normal sudoku rules apply. Gold lines are "nabner" lines; ie they cannot contain repeated digits and no two digits along a line may be consecutive. Eg If a line contains a 2, there cannot be a 1 or 3 anywhere along the line. Any two lines that cross each other will each proceed straight through the intersection. The inequality points to the smaller of the two digits it separates.
** NEW SUDOKU HUNT JUST OUT **
Join us on Patreon (for as little as $2) for a brand new sudoku hunt (called Lines & Shapes) - it was released on 1 Septmber. Closing date 20th September :)
/ crackingthecryptic
** NEW GAS PACK: VOLUME 2 IS OUT **
The new GAS (Genuinely Approachable Sudoku) pack is out on all platforms here:
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60 original puzzles by Clover, Bill Murphy and Philip Newman!! Earn party hats and dinosaurs with these brand new puzzles!
▶ SUDOKU PAD - Use Our Software For Your Puzzles ◀
You can input classic sudoku puzzles into our software and help support Sven, the programmer responsible for the wonderful user interface we all use to play these puzzles everyday. The app also comes with 12 handmade puzzles from us:
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ALSO on Amazon: Search for “SudokuPad”
▶ Contents Of This Video ◀
0:00 Theme music & introduction
2:02 Glyn's Painting
2:52 Happy Birthdays
3:45 Join Us On Patreon!
4:15 Rules
6:15 Start Of Solve - Let's Get Cracking!
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(Please note to use our real names rather than 'Cracking The Cryptic'.)
▶ SUDOKU PAD - Use Our Software For Your Puzzles ◀
You can input classic sudoku puzzles into our software and help support Sven, the programmer responsible for the wonderful user interface we all use to play these puzzles everyday. The app also comes with 12 handmade puzzles from us:
iOS:
apps.apple.com/us/app/svens-s...
Steam: store.steampowered.com/app/17...
Android:
play.google.com/store/apps/de...
ALSO on Amazon: Search for “SudokuPad”
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[@Mayank3083]

Something to lookout for in 4 cell nabner lines is if it has any 2 of 2/5/8. It means then you know the other 2 digits on the line right away. Think of 3 sets, 123 / 456 / 789. By having any 2 of 2/5/8 on the line, you knock out 2 of the 3 sets and from the remaining set you will have to pick the extreme digits. Eg- If you have 5 and 8 then it knocks out 456 and 789. So your nabner line would be 1358

[@turun_ambartanen]

Yes! It's easy to see which digits are impossible if you use the numpad on the computer.

[@Qazqi]

I know you've done the placeholder approach in the past and then feared doing it again due to some people perceiving it as bifurcation, but it is clearly not bifurcation and it's probably best to just accept that those people won't see reason when placeholders make sense as a technique. I'm glad you decided to try that approach again here. For anyone who thinks this is bifurcation, consider that when you discover your guess was wrong, you normally undo to the split and continue on the other path, pretending the first path never happened for the most part. With the placeholder, you *are* constantly progressing the puzzle with everything you do afterward. If you get to the end and the solution is wrong, that is still the same amount of progress as guessing right. Simply take one more step to flip all the digits and the puzzle is done. There's no undoing at any point, only forward progress toward the solution. If guessing right would have gotten you to the solution, guessing wrong is guaranteed to get you to the solution the exact same way, but with the one extra relabelling step at the end.

[@RichSmith77]

I agree completely. Another conceptual exercise could be to imagine you were filling in two grids simultaneously. Every time you enter X in one grid, imagine you also enter (10-X) into the other grid too, in the corresponding position, and keep both grids perfectly in sync. Clearly the logic being applied as you fill both grids is identical, and the second grid is always the (10-X) symmetrical mirror of the first. Ignoring the single inequality clue, you're going to end up with two valid solutions for the nabner lines. Then the inequality clue simply tells you which of your two solutions is the correct one. But now realise that you can save yourself the effort of filling in two grids as you progress, because the second grid is always instantly derivable from the first grid. So just keep track of your progress in one grid, but just imagine there's a virtual mirror grid. Then at the end, if it turns out the inequality doesn't work in the grid you have been filling in, simply derive the second correct grid from it, by performing the transform X ➡️ (10-X).

[@travisporco]

in fact the placeholder is just a kind of pencil mark. You could imagine that the software let you enter things like (1,9) or (24,68), i.e. both pairs of possibilities--but keeping them carefully separate. You could just do the exact logic Simon did. Once you hit the > sign, you could just eliminate whichever of the pairs was falsified in this kind of pencil mark. The only reason to do it the way Simon had to was simply the limitations of pencil marking in the software.

[@progandy]

@@travisporco Letters would be another option, but then it will be more difficult to apply the logic you learned with numbers.

[@badrunnaimal-faraby309]

My only gripe is that the disambiguation doesn't affect any of the logic and is only near the end of the solve path to bring up issues like this. Even if principle prevents you from providing a single given digit, it would hurt no one to put the disambiguating clue earlier in the solve path.

[@RichSmith77]

@@badrunnaimal-faraby309 I guess it's a deliberate decision, so as to make the puzzle harder for anyone who isn't familiar, or prepared to use, placeholder digits or letters. Without knowing that "trick", it does make the puzzle a lot harder.

[@eepopgames2741]

I for one loved the stretch from 1:02:00 to 1:09:00. Simon always thinks of those moments as us yelling at the screen about the thing he missed. And yes, there was something he missed that putting the 1 on the nabner line in box 9 removed 2 as a possibility from it. But I wasn't yelling, I was rubbing my hands together excitedly as I know in moments like this Simon is going to bounce across the grid to pull a rabbit out of a hat like he did in box 2. Its like watching a magic trick, you know its coming, you watch with rapt attention thinking you have got it all figured out and then the actual magic is completely unexpected.

[@terracottapie]

I think you mean 1:02:00 to 1:09:00. Your links go to the intro to the video from the second minute, and the reviews of the puzzle.

[@xlittlep]

I agree with you, except I knew that he was going to perform some incredible feat of logic outside of the solve path, that I would get to enjoy. I think the reason why Simon doesn't like to go full "Pencil Mark" is because once his central pencil marks are on the grid, those cells essentially become invisible to him. It's as if those cells are resolved as "solved" by his scanning skills. It was an incredible solve, especially for someone who admittedly struggles with Nabner line puzzles.

[@warlok333]

🎉 I always love seeing how Simon inevitably comes around to the same conclusions in a puzzle by completely circumventing the solve path! It gives me bonus insights into the mind of a world class puzzle solver that normally wouldn't be seen.

[@bbgun061]

Yes, he always gets the solutions in the end. But missing that logic made a lot of things more difficult for him in the meantime. (Note that I would do far worse if I were solving it. I'm merely looking over the shoulder of a giant!)

[@iceberg54321]

Well, when it takes you 15-20 minutes instead of 15-20 seconds to get the 1, you darn sure look to see anything that gives you.

[@bobh6728]

If Simon could spot the obvious wins I see after he gets a digit, the video would be under an hour. If I could find the difficult logic that Simon finds, I would actually be able to solve the puzzle. We would make a great team!!! Two examples: After he found the 1 in box 9, it eliminated the 2 on that line where he had just said it can’t have both 2 and 3. That would give him the 2 in box 7. Also, in box 2, several times he stated then that 4&6 couldn’t be one the one line because of the 5, but the other line also has a 5 placing a 4,6 pair in the box. EDIT: I wrote this comment while watching the video just before he called himself a numpty for missing the 4,6 pair.

[@dustinnyffeler8624]

I'm the same way. I've often thought if I could just sit off screen with a laser pointer to point out the easy wins. It would make him so much faster. At least we know he's human.

[@Cid0484]

I'm seriously confused how a logical thinker like Simon can overlook the fact that a 4 cell nabner-line with 5&8 on it can only go with 1&3 while he has it twice at the same time 😂

[@asleepappeal]

@@Cid0484 It's because he is thinking of way harder things. He sometimes forgets to do the easy stuff because it's so much fun to crack the hard parts that would give the rest of us a hard time. I don't care about him getting stuck for 5 minutes in a 90min video when I would be stuck for hours in the very beginning lol.

[@mtoner100]

Exactly. I can easily see the paths forward, once he explains some logic that would have never occurred to me... I think I agree, he misses the easy stuff because his brain is looking at it from much higher up than the average person's. 😜

[@btf_flotsam478]

I would also note that the line of inquiry he was pursuing at about 38:00 would have led him to conclude it is _impossible_ if he spent a bit longer thinking about it (would the 2 and/or 8 either go in the same row as the 2468 set, or on the same nabner line as the lines with a 1 or a 9?)

[@francescomarchisotti]

I’m really happy to finally see Simon solve a puzzle using placeholders. He hinted at the technique a couple of times before but never actually used it because he was afraid of people calling it bifurcation, but fear not Simon, we all are each other favorite’s people, we’d never accuse you of that!

[@windybeach2184]

I’ve seen him use it with colours or letters but never for the entire puzzle like this :)

[@TwotoTenth]

Always a pleasure to see one of my puzzles end up on the channel! (No apologies necessary, Simon, it's an enjoyable solve even if it's not your very cleanest.) For what it's worth, I try to avoid using placeholder digits in setting puzzles of this style, because I know not all solvers like using them and I want to make sure the puzzle can still be done without. But I have no issue with anyone using them to solve, especially in this case as it led to some extra drama regarding whether there would be a 3 in the corner. As you point out, nabner logic (as well as German Whispers, Renban, and Between Lines, among others) doesn't distinguish between X and (10-X), so the logic is completely valid. (I set enough ambiguous high/low puzzles that I'm now accustomed to just coloring one set green and the other red, and scanning for "green 2-8" instead of 2 or 8. But that took a lot of getting used to.)

[@QuarkTwain]

What if the inequality sign was placed in box 1 instead of box 3? Say, if it was in row 2 between column 2 and 3? That would allow the high/low question to be resolved early, but all the solving logic would still be the same. Perhaps that takes some suspense out of it.

[@bbgun061]

Is it fair to use Simon's logic at 37:46? Can I as a puzzle solver assume that there are no superfluous clues? That seems like something that Simon is getting from his long experience of solving such well-made puzzles. I can imagine that a lesser puzzle setter might leave a superfluous clue by accident. (Or an especially devious one might leave one in as a red herring...)

[@Kyufoxy]

@@bbgun061 Honestly, no. Unlike uniqueness such an assumption can break the puzzle. In this situation though you don't even need to assume anything, you can disprove it: if you put 1 and 9 on both lines and create the quadruple of even digits in row 5, you force both 2 and 8 on lines that have 1 and 9. Just one of them breaks a line already.

[@davidrattner9]

Just absolutely loved this from you!! Outstanding! Wonderful setting!

[@colej.banning2419]

​@@bbgun061I don't think any of Simon's actual deductions are predicated on that logic, though; so far as I can tell, he only uses it to abandon a line of investigation that he doesn't expect to be fruitful, which is perfectly legitimate.

[@dolevsacher8612]

I did a similar thing, but instead of guessing a 1, I used the letters {A, B, C, D, E, F, G, H, I} to represent 1 to 9 or 9 to 1 (E is 5 either way). It's an identical solution but somehow feels more "mathematical". You can solve the whole thing with letters and the inequality disambiguates if it's the A=1 or A=9 case. Absolutely beautiful puzzle!

[@malvoliosf]

Actually, I think that is the better tactic. When you write a big number, that should be an assertion, not a hypothesis.

[@dommaster661]

Nice Idea, that help with the thinking of both ways simultaneously. It's follow the same way of it can be both but makes less thinking and no spaghetti because there are half of possible Digits (Or Letters) than before, also same logic.

[@FryGuy1013]

I just pretend that it's a placeholder 1 in a funny font that looks very similar to the 1 in the correct font.

[@dolevsacher8612]

@@malvoliosf I wouldn't say it's a better tactic, but more of a stylistic choice, I think. After all, it's still equivalent to the placeholder method

[@DarshitMehta06]

It feels way harder to think of things like how to find non consecutive 'letters' from I, H, G say.... instead of 9, 8, 7

[@Emmibean77]

Simon, please give yourself (and your wonderful brain!) some grace and kindness. You managed to unlock a brilliant way to solve not only this puzzle, but all puzzles involving these lines. Even when us viewers watch these videos and catch things before you see them, I cannot imagine any of us actually want you to berate yourself. I know it’s easy to say as someone who isn’t posting my solve attempts to half a million people. But your audience is rooting for you, and does not expect you to solve every puzzle flawlessly! I hope you appreciate the incredible feats your brain has brought about over all of your years. And remember that the best comments come from kindness. A spectacularly brilliant man often reminds me of that!

[@drewskavich]

When you know what to look for, it's painfully obvious. However, when you've yet to reach that point, and you're facing 20 crisscrossing lines of an anti-type with which you are not yet expert, there is no shame in not instantly seeing something. You solve devious puzzles every day, and you're competently narrating your thoughts as you go along. Be kind to yourself. You appreciated the beauty and logic once you saw it. That's not an insult to the setter. Wonderful puzzle. Admirable solve. Thank you, once again, for sharing these remarkable puzzles with the world.

[@studgerbil9081]

I used to believe he was toying with the viewers. There are several examples in every video where he pencil-marks an impossible digit right next to the cell that makes it impossible. Over the years, we've all learned that this is just how he thinks. Simon was never built for regular sudoku. As he once said, "It's Mark for the GAS and Simon for the torture." He's an amazing logician.

[@Playmaker6174]

The ultimate nabner construction actually made it here, and I’m relieved that I got to experience this treat very early on. To be honest, I was a bit hesitating and didn’t lean on the trick that you used in the middle of the solve Simon (with that trick, I probably could’ve gotten row 123 and col 789 a bit faster), but I eventually overcame that part at the end without the trick so I wouldn’t really feel ashamed of myself much. After all, when it comes to coloring like this, I’m just used to doing so on the entire grid instead and then resolving all things at once satisfyingly :) (also don’t feel bad at yourself for missing certain points Simon, I did struggle for a short while too, nabner is just hard to scan in general)

[@cathybryant5119]

I did solve this using placeholder digits. I made that decision earlier in the solve than Simon and, for once, solved it slightly more quickly than he did. It is really quite amazing how quickly these lines become very constrained. This was really an amazing puzzle. Simon, don't beat yourself up for missing the obvious. The number of times I miss the obvious, such as: not filling in the total in an arrow puzzle when I have all the digits on the line; not filling in a 9 on a German Whisper when I have a 4 beside it; not filling in the missing digit in an otherwise full renban line. I could go on and on, but you get the idea. I'm just glad I'm not filming myself when I miss these - I applaud your bravery at doing live solves every day on video.

[@CrankyOtter]

I think Simon’s hardest problem with this puzzle is not having an established way to pencilmark or otherwise notate nabner line possibilities. It’s not a problem with the logic it’s that without decisive (yet flexible! X OR 10-X) notation, he solves all the logic at least twice.

[@hamishwatt2475]

I feel as though Simon has held off on using placeholder digits until now, and they could have helped in several solves in the past. Glad to see him put this into his bag of tricks and also the immense delight from the stream of digits discovered shortly after going down this path was wonderful.

[@MatthewBouyack]

Yes!! Simon, I don't know if there's already a name for the technique you describe at 45:34, but I've always called it "perfect bifurcation" (because it will succeed either way) and it's probably my favorite technique for solving semi-symmetric puzzles!

[@user-kt2jr1ys5d]

Please don’t beat yourself up Simon, thank you for going through and helping explain the logic of sudoku and helping me become a better solver. There are rare times where I do see the next move ahead of time but I know without your logic skill, I wouldn’t be in that position to be able to see it in the first place. Thanks again for the great solves!

[@troy.s]

Wow! Wonderful solve. One thing that jumped out at me, was at 1:02:00, a little cleanup after placing the 1 in R8C8 would have saved that 7-8 minutes of poking around the grid. Not often I shout at the screen, but this was one of one of those times.

[@elLooto]

What jumped at me was once 5 and 8 are on a 4 long line, the other two digits must be 1 and 3. This happens in box two at 55:30. Simon missed it twice (your timestamp is the second miss), and was suitably embarrassed by it a few minutes later.

[@erikbreathes]

it absolutely amazes me how simon always finds some absolutely mindboggling workaround so he doesnt have to follow the most obvious line of thought

[@Jalo1138]

I feel like, a really helpful way for me to conceptualize the “highness or lowness” is to imagine that the digits are the absolute value of the distance from 5, concluded by the inequality symbol confirming which digits are higher than 5 and which are lower.

[@clairerichter2863]

Oh Simon, you know we love you, "warts and all"(simple misses). You're too clever so please don't apologise. Your complex logic spotting is sublime. You made a sick day Sunday all the better.❤️

[@Jodawo]

If you want to be able to do nabner lines, then this is the video to watch. Simon breaks the secret in this video. When using the nabner line constraint, you are focusing on too many possibilities to keep straight. With this new understanding of how to deal with this constraint, you could now simplify the solving of such a puzzle. This technique has been used in puzzles where high and low being identified is important. It does take Simon a while to see it but once he does his knowledge of that constraint goes up exponentially. For those solvers out there, this is a technique you should have in your toolbox.

[@xlittlep]

I wondered if he could have performed the same logic by switching to the alphabetical letters A to I, where A could be either 1 or 9. It makes it less intuitive to perceive which letters are "even" or "odd" but at least the puzzle would not feel bifurcated in any way.

[@Jodawo]

@@xlittlep I had a puzzle I created and I found it best to use letters instead of colors. The reason was I needed to symbols for the direction of the constraint. I ended up using circles and green shaded cells. I tried using different shapes but that would make me use three because of overlap. Aesthetically I did it using the circles and green shaded cells because it gave it its best look. Since I used color in the grid it made it difficult to use color for the puzzle. I'm assuming that is why solvers did not give it a high rating. That puzzle also broke up into numbers 1-9, 2-8, 3-7, 4-6, and 5. I ended up using A and B to signify high and low but not knowing which would be which until a certain point in the puzzle. I did see it solved by Panthera in the way that Simon solved this puzzle. She used the placeholders. When she got to a point when the puzzle broke she knew she would have to switch the numbers. Fortunately for her she chose correctly the first time unlike Simon. If you want to take a look at the puzzle, I was talking about, it is on Logic Master Deutschland called "Between The Edges" by Jodawo.

[@Paolo_De_Leva]

Yes, finally Simon used *placeholder digits* again, after teaching us how to use them, a very long time ago... 👏👏👏 I hope he will teach the world how to use this extremely powerful 💪💪💪 technique *systematically,* whenever it can be applied‼ Indeed, *placeholders* can be used in many other kinds of puzzles, including those based on *German whispers, German whispers+renbans,* and *rotationally symmetric* ones. In short, all puzzles that have two (or four) valid solutions if you ignore the *disambiguator,* provided these solutions can be obtained from each other with a known *transformation.* In this case, the disambiguator is the inequality sign, and the transformation is: *_y_** = 10 - **_x_* *Placeholders* are the best way to simplify your notation. And they are by definition mono-furcation (not bi-furcation). They are not based on a "guess." Each placeholder is meant to represent two digits (in this case, either itself or 10 minus itself). They should be used more often‼ In dozens and dozens of previous CTC videos both Simon and Mark got *heavily* bogged down by their complex notation, that could have been *hugely* simplified by using placeholders.

[@Jodawo]

@@Paolo_De_Leva I think they refrain from using it because of the explanation on why it's not bifurcation. In a sense what they're doing is going through a long chain until they find it either works all the way through or it breaks and they have to switch the numbers. I don't think it's bifurcation but others may have trouble with telling the two apart.

[@Paolo_De_Leva]

@@Jodawo You are perfectly right: _"Others may have trouble."_ But that's also exactly the reason why they should teach this technique to the world *systematically.* And by the way, I explained this technique millions of times in the comments of previous CTC videos, and I can tell you that, luckily, *most* people agreed with me (not statistically relevant information, though, because it was obtained from a non-randomly selected sample of people...).

[@myfyrmadocjones]

4:50 Family Fortunes is called Family Feud in America I think. Not sure about the noise though. The UK programme is based on the American version.

[@steve470]

Yeah, but Feud has a very different strike sound than Family Fortunes. When Simon did his impersonation of the sound, I was immediately reminded of the wrong-answer sound effect from Where in the World Is Carmen Sandiego?.

[@Raven-Creations]

Very nice puzzle. After getting started, I realised I'd be stuck with pencil-marking both high and low possibilities in each cell. Programmers know that swapping two values requires a third (your 0s at the end). Rather than continue by choosing one digit, I switched to using A-I (although I retained 5 instead of E) This allowed me to arbitrarily set the scissor cells in C2 to ABCD and the ones in C3 to FGHI. Doing this made it easy to fill the grid, and when I got a D in R1C8, but A, B, and C could not go in R1C9, I knew D could not be 4, so had to be 6. The remapping from letters to numbers was just a matter of changing A to 9, B to 8 etc. and the rest was just finishing off. Considering how easy it was doing it the way I did it, it was very frustrating watching you suffer for so long to make any real progress, and quite a relief when you switched to using placeholders. I dread to think how long it would take without using placeholders. It would be possible, but it would be so hard to see what was obvious with the placeholders. @ 49:34 - "It feels like I'm being asked something about 7s and 9s" - and you'd have got somewhere if you'd pencil-marked 8 onto the line in box 9. That now can't have 7 or 9, so in R7 the second 79 must go in C5, which means R8C6=8, which puts 8 on the line in C4 in box 2. @ 57:55 - "I'm stuck again" - On the line with the 8s in box 2, it can't have 9,8,7,6,5, or 4, so the last two digits are from 123, and must therefore be 13. @ 1:02:44 - "I've a feeling it's not going to do as much as I need it to" - Clean up your pencil-marks and it's obvious. 2 cannot go on the line, so R7C3=2, removing 1 from R7C4, and making R6C1=1. For want of a modicum of discipline, you flounder around for ages looking for something new, instead of just following the flow. @ 1:08:38 - "Sorry, I am trying" - Yes, very trying 😄 @ 1:09:26 - "It almost makes me want to turn off the video" - Noooo! Moments like this are priceless - realising your errors is how you grow. We've all had moments like this, you just get to have them on camera for all the world to see. Your mistake near the end was caused by you not tidying up your pencil-marks when you placed the 3 in R2. Consequently, you thought the pencil-marked 3 was valid.

[@GeHeum]

One helpfull secret about length 4 nabner lines is to think in pairs of adjacent numbers: For example if you have a length 4 nabner line from which you know there cant be a 7 on it then there must be precisely 1 digit from each of the pairs (1,2), (3,4), (5,6), and (8,9). Another possible use for pairs: if you have a length 4 line with a 6 on it the other 3 digits must be chosen by picking exactly 1 digit from the pairs (1,2), (3,4) and (8,9).

[@GeHeum]

The generalization is hopefully obvious, although it would take me many words to properly convey. But in this puzzle making pairs of adjacent numbers gave me a lot of digits instantly

[@henrystern339]

My way of thinking about 4 cell Nabner lines is that they are made up of the following {123, 345, 567, 789} Maybe this is obvious to some, but it helps me to think about them.

[@dranben]

I loved this solve! A very different approach than what we usually see, and not afraid to break a "rule" because it has solid logic behind it. Thanks Simon!

[@lizzzylavender]

Oh. My. Goodness. This puzzle was incredible. I got a little intimidated seeing the long video but I really wanted to try it after the praise in the description, and whoo boy am I glad I did. I got 79:58 which is damn near exactly Simon's time, which is very exciting as I'm usually much slower than Mark and Simon's solves. But wow, what a gorgeous puzzle.

[@xlittlep]

One of the best solves I think you've ever done, Simon! What an heroic effort!

[@davidrattner9]

Great solve Simon. Thoroughly enjoyed watching how went about this!!

[@martysears]

This was a fascinating watch. Not just the outstanding nabner construction (I hope Zetamath is watching!) but also a lot of Simon’s ponderings and considerations about the psychology of the setting. Around 17 minutes, saying which lines looked like they were important in the mid-solve of the puzzle, which ones looked like they were definitely intended for the break-in, and which ones looked more like later add-ons. I love these kind of almost telepathic insights he has. And then around 37 minutes, realising that he was pursuing the wrong line of enquiry because Twototenth would never put a redundant line in the puzzle. That’s next-level solving. Obviously no logical deductions could come from that, but he certainly used it to help steer him in a more useful direction. Great stuff!

[@emilywilliams3237]

I agree - this is one of the (many) things I enjoy about watching Simon's videos.

[@SSGranor]

To answer Simon's question at the end, I did the puzzle with a high/low (and also odd/even) shading strategy and needed no placeholders. And, I was able to finish in just over an hour.

[@puritan7473]

Simon "It's very possible I've missed something on a line somewhere" 🤣😆🤣 I will not not forget that for a while!! (while forgetting 2 can't be next to 1 and 6 can't be next to 5 so 2 lines are forced!) Edit, so glad you didn't turn off the video. You should not feel bad for missing the odd thing when you just see so easily incredibly difficult logic that I struggle to understand!

[@agoristtaxadvice]

Absolutely brilliant Simon to just do the "guess" on one of the oranges and go through.

[@john-paulwallcraft9362]

Plot twist, Maverik is Mark.

[@GlaucoHass]

Running with a lawn mower above his head

[@raysouth1952]

Excellent solve Simon, and an excellent puzzle to boot! I like it when you miss things because it makes me feel better about my own ineptitude, and of course because I can get in a good bit of shouting, provided I notice, which I didn’t this time!

[@solfeinberg437]

Instead of coloring 2468 and 13579, just color one 24 and 79 and the other 68 and 13, then keep solving the puzzle. You're either right, or you'll get a contradiction at the > sign. If that happens just reverse everything 123456789 becomes 987654321, i.e., 1 & 9 switch, etc. 5 stays 5. Much easier to think about that way.

[@longwaytotipperary]

Holy blinking guacamole!!! What a ride!!! Watching this was my thrill of the day!!

[@davidrattner9]

Sounded like something Robin would say....""holy..." 😀. Wonderful ride it was.

[@longwaytotipperary]

@@davidrattner9 🤪

[@bass2564]

I feel this is one of those cases where not only is ok to guess, you actually _should_ just go ahead guess that "green is low", Any logic will work exactly alike regardless of that guess being right or wrong, and if the inequality works out to be the wrong way around, in the end, you can reverse that guess by subtracting each digit from ten. This makes pencil marking an entire order of magnitude easier. (EDIT: just got to 42:12 in the video 🙂)

[@MikaelMikaelMikael]

Oh yeah, this was essential. Before I tried it, the puzzle felt incredible hard. After I did "the trick", it was a walk in the park. And of course I made the wrong pick initially, so I had to flip all of the digits in the late stage, when I'd got to the upper right corner. So I had a moment of dread, but it was correct in the end, wheew.

[@LiquorStoreJon]

WELL, This looks mighty challenging!

[@GlaucoHass]

I wonder if it is possible to make a puzzle forcing Simon to go through the intended path. It's outstanding how he can recovery from not seeing things he revealed by taking a completely different route. It gives me hope to continue, when I'm stuck.

[@EdoTimmermans]

Beautiful way to solve the puzzle! And Simon, having a conversation with you would be a great party, as long as there would be no music and alcohol causing distraction.

[@MrFrederuco]

Simon, don't beat yourself up too much. I can't count how many times I have done a puzzle with kropki dots that have a negative constraint, and I spend 10 minutes trying to find the next step, and it is the stupid negative constraint. Love your channel, and my wife enjoys watching how giddy you get when you find the next bit of beautiful logic in a puzzle.

[@daleomiller]

I could *feel* your frustration at times, and I know that affected your ability to see some things. Never apologize for that. I learn from you with every video I watch.

[@danemaple1657]

i think what simon is saying at around 23 mins is that if the inequality wasn't there, you could essentially flip all 1s with 9s, 2s with 8s etc and end up with the same solve, just with the opposite igh low number in its place, and the inequality in the corner cements only 1 of the 2 outcomes, making it unique.

[@faeself6510]

I'd absolutely love to be at a party and have someone get excited about a puzzle.

[@unobic]

Simon, no need to apologize since no time was wasted. Each puzzle is a lesson and you do not waste time if you learn something new.

[@joejoesoft]

In the states, we have Family Feud. There's a wrong answer sound effect, but it's just a buzzer. It's not like the Family Fortune sound effect.

[@eva3662]

I was so proud of seeing R1C6 20 mins before you, but then you went on a mental breakdown that made you want to turn of the video out of embarrassment for not spotting it 😂 felt good about myself for 20 mins though, worth it

[@MrJungle123]

Ooo. A nice early 'start of solve'. Lovely.

[@TheClawNinja]

It blows my mind that this puzzle solves based on the given information. Great job to the setter, and to Simon for that solve!

[@colleenscottcarmello5103]

**** Simon: "I don't know why, my brain didn't understand it, see it, concentrate on it in the right way".. Welcome to my world Simon.. sometimes these sudoku's make my brain stop on the tracks haha.. You Did Great.. Too hard on yourself! After all, your name is Simon.. you're brilliant!!

[@emilywilliams3237]

I have posted comments on several videos (well, comments on comments, actually) arguing that placeholder techniques are not always necessary in puzzles with high-low polarity considerations as the main thing. My thought in countering (strong - too strong, in my opinion) criticism of you or Mark for using coloring and pencil marking in puzzles such as German Whispers is that there should be a way to solve the puzzle without place holding, and I prefer to watch a video in which the non-place holding method is used. I still think that - BUT I think that this puzzle was an ideal place to show how the place holder technique allows the solve to be easier to explain, for sure, and in fact easier to achieve. For myself, I prefer coloring and pencil marking - but this video was brilliant and I am glad you took this approach, Simon. (In fact, as I have also said before many, many times, you should solve these puzzles using techniques that are satisfying to you and that allow you to enjoy yourself - your pleasure is very contagious to me!) Thanks for this video!

[@davidrattner9]

I always cherish what you write and how you write it. 🙂

[@emilywilliams3237]

Thank you, David. 😊@@davidrattner9

[@karlwaugh30]

What a puzzle. I managed 45 mins and did a similar guessing orientation thing. Lovely stuff

[@ukdavepianoman]

A much simpler explanation around 23:00 is that without the inequality sign, a solution "X" could be found but there is nothing in the nabner lines to rule out 10-X i.e. swap 1 with 9, 2 with 8, etc. (5 being invariant). I used placeholders early on (much easier) but still found it quite tough. Using placeholders is no different mathematically (logically) from using colours or letters. It's absolutely not bifurcation because the logic of both solutions (without the inequality) is identical (as Simon said). Bifurcation is if you have guess a number (usually from a pair) and it leads e.g. to a contradiction, when you wind back and choose the other number, the subsequent logic is completely new.

[@tdbraun6837]

That was very entertaining!!

[@RichSmith77]

I often wonder, when Simon reviews the comments on Logic Masters Germany before attempting the puzzle, does he not run the risk of seeing spoilers for the solution path? Or are they generally a lot better at avoiding spoilers than the typical KZbin comments? Edit: Even an unintended hint may be let slip, no?

[@SSGranor]

LMD has a feature called "hidden comments," which can only be seen by people who've entered a correct solution to the puzzle. Generally, when someone makes a spoilery comment there, they'll leave it as hidden. And, as the constructor of a puzzle, you have the ability to both edit other people's comments or to hide them. (Though, to be fair, I've never needed to do either for reasons of spoilers.)

[@RichSmith77]

@@SSGranor Oh, that makes a lot of sense. Thank you.

[@matthewhi1205]

Simon you are awesome. Don't think that line can be seen so easily.

[@andremouss2536]

From Simon's blindspot around 59:00, I found a little trick on four cell nabner lines : you should look at digits separated by three. For example, in the left line in box 2, there is a 5 and an 8, so there cannot be 4679 and thus the two remaining digits are 1 and 3.

[@delta3244]

Adding on to this, I find a useful rule to memorize is that a 4-length nabner with a 5 on it either has [1 and 3] or [7 and 9] on it, and whichever one it has, the last digit will be on the other side of 5. For example, a 4-long line with 5 and 8 on it is a 1358 line because 8 is on the same side of 5 as [7 and 9], but 8 is not 7 nor 9. (edit: forgot a determiner)

[@biaberg3448]

SO fun to watch !

[@echterkeks6900]

when Simon put the 1 in box 9 and not delete the 2 from the nabner.... i'm a little bit yelling at my monitor BUT you did still do a fantastic job on this puzzle

[@stuarttierney6709]

Did it! Took nearly two hours but still happy :). Really fun puzzle actually.

[@Mennoo_]

Amazing puzzle and absolutely an amazing solve! Love how you showed this technique, which some people would write of as bifurcating, but definitely is not. I would could the technique 'symmetric solving'. Cause you make use of some sort of symmetry. The symmetry can either be in the mapping of the digits on the solution (in this case flipping 1-9 to 9-1). But it can also be used on grids which are (mostly) symmetric in its clues, and in that way solve the grid until the point where the unsymmetric clues define the final solution. In a certain way you solve the grid 2 times by solving 1 and recognize the structure to change the grid to the other option. For example, I used this technique on 'Hiding Spots' by Xendari, which was featured on CtC on June 2 2023, where I solved the grid making 1 assumption, until a point where the unsymmetric clues in b3 (couldn't be mirrored around positive diagonal) determined the orientation of the digits. (And spoiler, I made use of the technique while setting my very first puzzle 'Thinking in Circles')

[@playeurz]

The 1 in box 9 stared at me for a good 15 minutes 😅 amazing as always Simon :)

[@markp7262]

1:07:01 finish. I didn't use placeholders, I just colored the "high" and "low" digits different colors. It was definitely more tricky, but I got there in the end.

[@stuartharris2165]

Family Fortunes in the US is Family Feud

[@MasterAries7]

Family Fortunes is called Family Feud in the states, but having just checked the states version has a much harsher noise.

[@LarkyLuna]

The way to not "bifurcate" would be to create shading for the 8 non 5 digits and get adjacency rules for all of them Or just define 1 as a symbol that represents that ¹⁹ like it was done in the video Very good insight Relaxing a rule and solving for it then reintroducing the constraint is a valid way to solve math problems, specially when you proved that both would be solved by it

[@LarkyLuna]

P.s. i went back and swapped every digit lol Using a temporary digit like 0 to replace everything was neat

[@Adrian_Grey]

I tried doing this by coloring high vs low and solving with the ambiguity and I got pretty far but eventually got stuck and went for placeholders anyway. Definitely the way to go here. Made the puzzle so much clearer.

[@Orenotter]

For nabners we've not got a feel. It's hard to get used to this deal. The logic is sound But the digits flip 'round And the three in the corner's not real!

[@flobiish]

@45:00 Yeah, superficially it seems like it might be bifurcation to "guess" a digit, but (and I didn't need the explanation personally) you explained well why it's not.

[@G.Aaron.Fisher]

26:02 for me. I don't think I've ever been this much faster than Simon before.

[@MegaMinerd]

The way I find it easier to understand the logic at 11:00 - 5 eliminates 4 and 6, forcing 2 and 8. - 2 eliminates 1 and 3. - 8 eliminates 7 and 9. - The final digit of the line has no fill.

[@milotdauti6991]

dont worry about the 6 :) you are not stupid! dont beat yourself up :) we all love you :) You are so amazing and a joy to watch! Thank you for everything : )

[@mentalmike]

That was a great puzzle and a great solve! With the misses in logic, because they're typically few and far between I find them funny rather than frustrating (hope Simon does a bit in retrospect!). The box 2 logic I happened to spot straight away as soon as the he placed the 5/pencil marks that the 4/6 could be place at around the 55 minute mark and then SImon got my hopes up 10 minutes later by looking at 4/6 in that box only dash them quite superbly by missing that they couldn't go on the other line 😄Plus I think we all enjoyed box 9 that past Simon remained blissfully unaware about. Precise logic to put 1 on the line: check. Logic going all over the grid to eventually remove 2 from the line: check. Whereas us laymen just spot that 1 and 2 are consecutive 😁

[@timcotton1782]

When I reached the point at which a 4 is forced to be on one side of the inequity, and recognized that it couldn't work that way, requiring the polarity reversal, I did not, as Simon did, treat the greater than symbol as "irrelevant". I reversed it, allowing for 7, 8, or 9 in R1C9, which simplified the final construction prior to polarity reversal of the entire grid.

[@rentalcustard]

The reaction at 1:09:30 is so satisfying after 10 minutes of shouting at the screen! I do hope it's with a measure of irony on your end, Simon, because the fact you missed this logic was _more_ than compensated for by the exquisite logic in what you did see, and your communication of that logic. Instantly seeing the stuff everyone else struggles to see and then missing the "obvious" is a Simon trademark and it's immensely entertaining.

[@MattYDdraig]

28:04 Used the exact same short cut as Simon, even to the point of incorrectly choosing the 1 from the 1/9 pair in r1c3 and the use of 0 for cycling to the corrected answer. Fortunately for me, not having the pressure of doing it on video or trying to explain every step of the way makes filling the grid a lot easier 😅

[@doublepudge465]

When you pulled up the comments from Logic Masters Germany. I noticed someone called ‘3good5you’ …. I wonder if it’s the same person who creates troll levels in Mario Maker …. What a coincidence that’d be. 2 of my most watched categories of video on KZbin. Sudoku and MM, coming together in the weirdest of ways 😂

[@adipy8912]

Me too😄 Do you watch CarlSagan and Geek?

[@AndrewMooreMar]

I had the exact same thought

[@RasperHelpdesk]

Pretty sure it is, I've seen a few MM folks in the sudoku world

[@Qazqi]

I never noticed this, and I don't know if we could ever get a trolldoku beyond what little we've had, but I'd love it. One of the only things that comes to mind is Everything is Wrogn. Maybe it would be possible to create a fun trolldoku with new software innovations like Chameleon has been doing with Fog of War etc.

[@doublepudge465]

⁠@@adipy8912yeah. Carl mainly. Seen pretty much every video 😂 Geek, on and off. (But love the interaction between the 2 of them)

[@gyan1010]

~38:00 the way to prove there is not both a 1 and a 9 on the line in r4 without claiming the short line in box 6 is there for a reason, is because if they were both on the line then where would you put 2 or 8 in box 6 after you form the evens quadruple in r5?

[@PaulAndHisUkulele]

When Simon knew it was a 1 or a 9 (and then went for the 1), I had the same logic but called it 19 and coloured it Green. I knew the four below it would 6789 if it was a 1 or 1234 if it was a 9 so I coloured them Purple. If purple was high, green would be low. And Vice Versa. Now I also knew in the same row, column or box, if calculated a 19, it couldn’t be a Green but instead would be the opposite, a purple 19. With this, I stepped nearly identically through the path Simon followed… … it took me about four hours to get through! It took me nearly as long to work out the mechanism of how nabner lines worked, and then it was just a matter of selecting the two options for each cell and green/purple colouring… By the end, I found out whether green was bigger than purple or purple was bigger than green thanks to the top right inequality. Superb puzzle.

[@HunterJE]

The "arbitrarily pick a placeholder and then fix if it breaks on the inequality" approach was clever but I wonder if could alternately be useful to keep the pencil marks as is but extend a shading system with two shades for "same direction" across all cells? Like make all the blues green and all the oranges purple and extend that shading with each of the two colors meaning "we don't know which but we know the cells of this shading are either all high or all low"

[@MarkBennet10001]

Use placeholders, or letters (as I do often with German Whispers), or colours - the techniques are logically equivalent. Psychologically they may differ, but they record the same information.

[@AndrewMooreMar]

I'm pretty sure Simon has done that in the past, labelling the cells as "extreme", "medium", etc. with the same reasoning, that some people would get confused/upset by the placeholder. I guess both approachs work, and I personally am happy watching Simon constructing the logic either way.

[@michaelanderson5961]

I solved it using distinct color shading for both odd/even and high/low. It was doable but I think harder to parse out then picking a specif path and correcting at the end

[@joeg451]

During the stretch from 1:02 to 1:10, you could also ask where 4 and 6 go in column 4. They are both basically naked in that column.

[@neillrobbins7508]

Bloomin marvellous!

[@chrism4551]

My goodness...the first time that bifurcation was not really bifurcation! Possibly the puzzle of the year

[@Taeolas]

Quite a challenging puzzle. One thing that would help, the app description doesn't include the example defining "consecutive". Since I usually jump straight to the app, and hadn't used Nabner lines in a long time, I misread the consecutive limitation and had no idea how to start. I used the letter method in the end to keep things settled and found it worked well for my way of thinking, once I got used to the idea that "G" is consecutive to "F" and "H" and so forth.

[@pardox28]

1:23:56 was my time. I took my time but glad to see that I was still under the length of this video. I have all my numbers assigned to colors and was able to use the colors to solve the puzzle. Once I was able to see that it has the case of having 1s and 9s, 2s and 8s, 3s and 7s, and 4s and 6s as possibilities for squares, I was able to visualize when a particular color I had ruled out other colors. A pretty nice puzzle which is great. I've found a lot of puzzles this week way to difficult for me.

[@jaydenbenston2869]

i think one way of solving without placeholders is by using shading but denoting the extremes and midlings of each pair. Like 1 and 9 are extremes and 4 and 6 are midlings.

[@HunterJE]

Simon went further back than needed to fix the double-wrongness that came up towards the end-that happened at 1:19:15 when he made that old easy mistake of extrapolating options from resolved pencil marks, specifically seeing the 39 and 29 pencil marks in row 2 and assuming that meant r2c9 had to be from 239 and not seeing that the 39 was already resolved by the placed 3 and in fact the remaining unplaced digit was 5.

[@CauchyIntegralFormula]

34m32s. I did the same thing you did, which was to break symmetry and tell myself "if the inequality's the wrong way then I'll flip digits". And indeed it was the wrong way. Luckily, 0 works as a placeholder value for swapping numbers

[@Gonzalo_Garcia_]

28:45 for me. Fantastic puzzle, loved it!!

[@brenthoskisson6979]

I love that there is a 3 in the corner whether it is right or wrong.

[@titusadduxas]

1:07:51 - I decided to guess the high/low split and sods law came into play of course! Didn’t take long to switch the digits around at the end though and I got 3 in the corner twice!

[@leefisher6366]

45:45 - Though I do understand this, you could make it 'simpler' by putting a '4' in that 1/9 square. Why? Well, because the digit is 4 away from the central 5. If four larger, it's a 9, if four lower, it's a 1. Likewise, the 2/8 pairs are 3, the 3/7 pairs are 2 and the 4/6 pairs are 1, to get resolved when you hit the inequality.

[@crab0traps0now]

Always a delightful surprise when I can see something that Simon can't, such as the logic unfolding at around the 48 minute mark without the aid of filling in a place holder in r1c3. Sadly, this is a rare occurrence!

[@joekerr3638]

The 46 pair in box 2 is incredible.

[@stevesebzda570]

Sounds like Family Feud . Yes, they are funny outtakes (and answers on them). Hysterical , you're right. I think Richard Dawson started it, I'm not sure (he was the host for a long time anyway).

[@ckdo1974]

1:17:10 -- There's no good reason not to use the inequality - just pretend it is the other way round: The corner digit must be greater, i.e. 7, 8 or 9.

[@oloflundqvist278]

The fact that you see the 7 in box 5 reaching into box 2, but you don't see the 5 next to it reaching into box 2 is hilarious to me

[@Froggysrevenge]

41:20 - 43:50 Simon describes an entire puzzle being bifurcated, with the little greater than disambiguating at the end.

[@josephrion3514]

18 minutes in good find. You place the five in box six in the middle row. Which places the five in box five in position one. On the short so good.

[@andremouss2536]

21:00 By not considering simply the converse, Simon skips the obvious fact that the center low nabner line contains 1379.

[@olleicua]

The line in box two that you were embarrassed for not seeing more quickly also took me quite a while. You shouldn't feel so bad. This was a hard puzzle. I also took forever on several deductions that were arguably more obvious (that you had no trouble with).