A Sudoku Secret to Blow Your Mind - Numberphile
Simon Anthony (from Cracking the Cryptic) reveals the Phistomephel Ring - a hidden feature of ALL Sudoku puzzles. Second video is here: • The Most Mathematical ...
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Cracking the Cryptic: / crackingthecryptic
Another Numberphile video about Sudoku: • 17 and Sudoku Clues - ...
Our thanks also to the legendary Phistomephel.
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Second video is here: kzhead.info/sun/m5x6pdCfopyvfJs/bejne.html
Now, can you use the same trick to prove the shape of the Earth, and how it would relate to the fake alien invasion of 2030?
I'm so glad to see this collaboration, but here's a small correction: Phistomefel was not the first to realize the phenomenon of set equivalence in sudoku, nor even the specific arrangement discussed as "Phistomefel's Ring". He is a terrific setter, and is deserving of all his fame. It's also true to say that Phistomefel's discussion of this relationship was hugely influential, so I also don't at all object to the phenomenon being named after him. I just wanted to correct the record. No need to worry yourself about this detail.
I just wanted to mention that the flickering red and green squares are a bit uncomfortable* to look at, because they are blinking so fast. (*I don't have epilepsy)
Was it your intent to discriminate against the colourblind by choosing to use red and green in the way you did? As colourblindness is a physical disability, in many jurisdictions it is illegal to discriminate in such a way. Were you aware of that?
@@Ggdivhjkjl Interestingly, Simon himself is colour-blind. I can't remember what type of colour blindness he has.
It's so weird to see Simon from a different angle and not sitting in his chair with his guitar in the back. It's almost like he's a real person or something.
Is that his setup in Cracking The Cryptic?
@@wyattstevens8574 yes, he seems to be in some kind attic room. There's a window to his right-our left-through which we can sometimes hear his nemesis Maverick taking off from a nearby airfield to buzz the recording 🤣🛩
Took me 2 min before I even realised it was Simon, I was thinking that the lingo was eerily similar to CtC... 😂
I know right
Same with the microphone. It's subtly different, but different enough that it's almost eerie to me....
The Phistomephel Ring is a sudoku secret, but not the sudoku secret that Simon only tells his favourite people
As you can tell, Numberphile watchers are obviously not Simon's favourite people.
He has a marvelous proof to solve all Sudoku puzzles, but KZhead videos are too small to contain it.
I was waiting for him to say it😭
But the secret is 45, not 42, 45!!!
But some of us are in both sets 😂.
Never in a million years would I think my two favourite channels would collaborate like this, and yet here I am, wonderful!
Haha when I saw the ring in the thumbnail, I just knew they'd bring in Simon to explain it.
@@tiarkrezar Yeah me too, I can't recall the number of times I watched him explain it over and over again in his solves
Considering the probability of a collab, the number of possible candidates, and frequency of video uploads, I’d assume the expected value to be much less than 3.6525*10^8 days
I've heard Simon explain this relationship so many times and in several different ways but it always fascinates me!
Your mind will be really blown when you learn one day that Simon's "Maverick" is none other than Mike Patey playing the long con collab setup.
I just need everyone to know that my mailman recommended this video to me
He needed you to see it post-haste
Because this video is pushing the envelope
Thanks for letting me know
Was not expecting Simon on numberphile! What a great surprise.
I was like, Yea,I know that. I saw it in cracking the cryptic. Then I see Simon on the screen...
@@phs125Same 😅😂
Omg I didn't recognize his voice and everything until I read this comment, a couple minutes in.
@@phs125 Yep... looked at the thumbnail and though the same, open the video and look and behold it was Simon :D
It's great to see Simon Anthony reveal one of his skills --- not only can he type into his sudoku app (so loudly that we can hear him), he can also write in Numberphile's approved way of marker pens on brown paper.
[3] "Oh wait that's meant to be a four." *clack* *clack* *clack* *clack* *clack* *clack* *clack* *clack* *clack* *clack* *clack* *clack* *clack* *clack* *clack* *clack* [4]
i can literally hear his clack clack sound rn after reading ur comment :")
Mechanical keyboards for the win
I bet he felt squirmy not being able to de-highlight the common cells.
@@brenthooton3412 Someone really needs to invent the un-highlighter (lowlighter?) that dissolves highlighter marks
This guy who explained the ring seems pretty clever. He should start his own KZhead channel for this kind of stuff.
Nah, it could _never_ work. Might as well say he should build his own app or something.
What and put like 2 hour solves of really difficult sudokus with different variant rules? No chance that loads of people would love that.
You really think people would watch a KZhead channel where he and maybe another guy, just do sudokus for every video? Nobody would watch those two!
@@TheThursty100 What if they also did cryptic crosswords? Nah, that would only make it worse!
@@TheThursty100 Maybe it could work if sometime, there was a 3 in the corner!?
I've heard this explanation from this man so many times, and still I watch this video in full for just one more time!
This was even slightly different because there were no scrabble bags & tiles
I notice that Numberphile viewers don’t get told ‘The Secret’ - he really does save it for his favourite people!
Phew, was worried they'd give away the secret here. Still gotta be a friend of Simon and Mark to learn that one.
Shhhh!!!
Soylent Green is people!
Then, the same can be done with blues? Rather than 'left 2 column and right 2 columns', the same can be done with 'top 2 columns and bottom 2 columns'. So 'left-right blue' should be equal to 'top-bottom blues'. If 'left-right blue' contains three 9s, so, too should 'top-bottom blues'. Etc. I just tested it with their first example, and it holds.
Can we find the pattern in KenKen?
@@rogelioortiz3003yes but the reason the classic phistomephel ring is so useful is that a lot of digits are cancelled out in the process, and its 16=16 instead of 27=27. It's a very efficient design. You could take any 3 boxes and already know they are equal to any 3 rows or columns. The trick is to maximize the number of digits that contribute to both sets, because those cells can be disregarded. However, if you have too many digits contributing to both sets, it will simplify so far that it doesn't show any new information.
Normally in these situations, it's traditional to say "Wow, I can't believe this crossover!" but this one... this crossover makes a lot of sense. Really cool to see how far the proof on this has come: I've followed CtC for years, and I remember how involved the old versions of this explanation were, but this seems so simple and elegant. Great video!
How about "I can't believe I'm seeing 12tone comment on a Numberphile/CtC crossover video"?
I mean, that crossover also makes a lot of sense @@MarcusTheDorkus
I hope you don't mind me taking partial credit then! I'm the one who came up with this particular explanation, completely by accident while I was playing around with SET. It's a really nice way to get rid of the double-counting that we did before, which makes it quite a bit harder to follow. Let alone that mind-bending explanation I don't even remember which was used before some very smart people came up with SET.
I'm glad one of us reads username, otherwise I would have missed this was @12tone Thanks @@MarcusTheDorkus
I hadn't watched for a while and was half expecting Simon to start talking about Scrabble bags
Now this a great collab! Love to see Simon featured here. Glad he didn't tell everyone the REAL secret of Sudoku here.
Of course not. They are not his favorite people!
Simon on every video “I’m sorry for explaining this again, I’m sure most of you are tired of hearing this” and here I am watching a video of just that
I can't believe Simon didn't take his bags of scrabble tiles for this one! I remember a while back James Grime said that he didn't think sudoku was proper maths and he didn't like them ... there are plenty of puzzles on the Cracking the Cryptic catalogue that definitely prove him wrong now!
Yeah, those computer-generated puzzles tend to leave a bad taste in the mouth for so many people.
At 4:28 you can see him holding something that looks suspiciously like a Scrabble bag. I guess the rest of it got lost in the edit.
@@hugobouma I feel like there's going to be a follow-up video on Numberphile2, as it seems like there would be tons of these equivelances within the geometry of a sudoku puzzle and that to sepcifically focus on this one surely means there is something else about this specific one that didn't get mentioned in this video and that is still to come.
@@MrDannyDetail There are a huge number of them, yes. If you look back at the proof of the Phistomephel Ring, it doesn't require anything about the specific shapes. You can take any two pairs of _k_ (not necessarily 4) non-intersecting rows/columns/boxes and the same will work. I think the point is that the Phistomephel Ring is visually nice, so composers use it and solvers look for it. If you designed a sudoku that could only be solved by applying the trick to, e.g., row 1, row 4, box 8 versus columns 2, 5 and 6, probably nobody would find the trick.
That's because the scrabble tiles are no longer needed! In the old explanation, you had to double-count the corner cells of the ring, and then remove them once, which is a somewhat complicated action, and the scrabble tiles help people make sense of that. In this explanation, which I am very proud to say I came up with first (or at least, I hadn't seen it before I posted it on the CtC discord server), you don't have any double-counted cells anymore.
Genuinely can't believe that Simon got through this explanation without once saying the words "Scrabble bag" (
I don’t think most of Numberphile’s viewers would understand the reference
I saw it in his hand at one point in the video. I guess it was cut for concision.
Exactly 😂
@@milliams Bobbins 😅
That is why I couldn't understand the explanation this time.
It's SIMON! I've seen him explain this on CtC so many times. My own sudoku skills have greatly improved. Once in a while I even solve a puzzle faster than Simon does. If that happens, it usually means he paused to explain some things to the audience.
I clicked on this video thinking it was a Cracking the Cryptic video and was shocked to see the classic Numberphile format!
It warms my heart to know that speedrun explainer legend Bismuth also watches both CTC and Numberphile
@@ProfessorPlusGut Mark and Simon are speedrunners of a sort.
Simon explaining the Phistomephel Ring over and over in his videos and really perfecting and honing the explanation... was all leading to this very moment.
I have been doing sudokus for 20 years, and could never find "the" trick that would get me over the top. I just used this successfully, I think this is it. Thank you!
I love how elegant and simple the explanation is. Is one of those things you wouldn't have guessed in a lifetime, but after you've been told, you inmediately think you should have.
Absolutely love Simon and CTC! What a nice surprise to see him featured on another of my favorite channels!
I have seen Simon explain this more times than I can count, and I still listen to it all the way through every single time. There is something magical about it!
Ditto!
I love this. I've done sudokus daily for the last 20 years. I particularly enjoy super hard ones where I have to use advanced techniques to solve them. It doesn't happen very often, but it does happen. This needs to be added to the sudoku wiki, wish i would have learned about this a long time ago lol
but how the ring helps in solving the sudoku itself? Okay I get it they'll have the same exact numbers, but how, while solving the sudoku, will this information come in handy. Could i take a look at one of the smaller squares and say, hey that number must go here in this ring?? How exactly is my question.
@@abhijeetbadole5078 if you can solve the 4 corners and center ring you win because you can't actually screw up the rest of it unless you break basic rules of the game. try this, fill in the 4 green corners and red center ring with notes of possible numbers for those cells given the games current state and basic game rules. now for the green corner cells, check the red center cells for the same number. if that number is not part of the possible red numbers discard it. do the same for the red center cells as well. keep doing this step as you solve bits of it and it will remove quite a handful or two of numbers and allow you to more easily solve the puzzle. you don't NEED to solve just those cells but utilizing those cells reduces the possible number state of other cells by quite a bit and thus you don't need to look into the future as far/much.
@@abhijeetbadole5078 I've only found it useful in checking my work. If I try to solve it using this method, it's either too niche to attempt or, in cases where I am able to get 4 corners or the ring, it really doesn't do too much to help solve the puzzle. I'd love to see someone use this to solve the puzzle, maybe pick up on a new strategy, but so far I just see proofing after the fact, and not really an applicable method to _solve_ the puzzles themselves.
You can solve any sudoku without advanced techniques. You need only the very basic techniques and trial and error.
0:26 “is this a secret that can help you solve sudokus?” I guess Brady isn’t one of Simon’s most favorite people since he didn’t immediately get told THE Secret! 😂
And that is?
@JC20XX obviously a secret.
@@JC20XX one of those IYKYK type of things… you can watch almost any of Simon’s solves over on cracking the cryptic to be brought in to the inner circle
It isn't
@@jackyhyurane7362Depends on the sudoku. There are quite a few puzzles that absolutely need the Phistomefel Ring to solve. And there are even more that need one of the 2 main variations of the Ring (called the "Expanded Phistomefel Ring" and the "Mid-Grade Phistomefel Ring", due to the Ring in question either lying on the edge of the grid in the Expanded version or in between the edge and the classic Phistomefel Ring in the Mid-Grade version); and there are *_even more_* that require some other sort of Set Equivalence Theory.
Many people said it already but I have to say it too: I’m extremely happy and pleasantly surprised of this collaboration of my two favorite channels. More Simon & Mark content on Numberphile would be greatly appreciated!
As a long time CtC and Numberphile viewer, when I saw the title of this video, I thought, oh Simon's going to get a kick out of Numberphile doing a video about this. Then I saw his face lol
Although Simon is one of favourite people and someone whom I see on an almost daily basis, it is so so weird to see Simon in this setting 😂
I love how much the proof of the theorem has been refined over the years
he makes it seem so easy and obvious
I think I'm being really silly, I don't understand the logic of why removing the overlapping cells would mean the remaining cells in the green and red match
@@JD-ee4dfBecause the overlapping cells match since they are the same number, and since each set is made out of the same numbers, therefore the remainder must also be the same: Sort of like if you had two sets of numbers 1-9, and you took out the 5s, the remaining sets are still identical
@@Kass401 That helps, thank you!
This technique is super useful, because you can optimize away numbers from the red circle or green squares, if you know its not contained in the other. more specifically, if you have a full red circle, but some empty green squares and you know that the number 5 does not appear in the red circle, but in one of your green squares, you have a cell with the remaining possibilities of 5 and say 6, you know by eliminating 5, that the only possible value is 6...
This is so strange, I've been watching Numberphile for years, and I just got into Cracking the Cryptic last month. Glad to see Simon on here!
It’s so great to see Simon in a Numberphile video!! The Phistomephel ring is something that blew my mind when I first learned about it and it’s wonderful to see more people understand it too :)
So happy for Mark and Simon! They deserve this recognition.
For a second I thought a new Cracking the Cryptic episode came out. Then I realized it was a Numberphile video. Great job, Brady and Simon! Simon and Mark knows a lot of other amazing variant Sudoku facts and secrets.
The funny thing is that if you move the green 4x4 squares of the Phistomefel ring one step inward diagonally, and the you move the red ring cells to the perimeter of the grid (so that e.g. on the top row, the leftmost, the rightmost and the three middle cells are red, and the same way for every row/colum of the perimeter), the equivalence still holds.
Yeah true. That's just the magic of the whole "set equivalence theory" that has been going on in sudoku. It's all about just defining things that all have the exact same digits (like 5 rows or 5 boxes of sudoku do), and then removing the overlaps.
It's equally true, but less useful when you're constructing a sudoku puzzle because it's harder for the solver to spot. The beauty of this ring over the other combinations is _specifically_ that this grouping is very "neat" and easier to recognise because it's one connected set of squares.
This makes me so happy seeing simon on here. Ive been watching him for a couple years now and love him and marks videos!
Stumbled onto Simon about a year ago. Occasionally I would watch him. I've been doing sudokus now for a little over 5yrs. Love Them!! I started out using them as a way to keep my mind sharp and stimulated. I would randomly attempt the difficult ones..and all though I would resort to placing all possible numbers in each cell😢 and slowly removing them. I would eventually solve them...but this technique/"secret" is awesome. Gives me confidence to try the more difficult ones. You have definitely gained a subscriber 👍🏾
I'll have to implement this into the Sudoku solver I've written in VB. My goal is to create a solver that does not need to use brute force. I have felt there must be some sort of pattern such as this and am happy to have learned it here. I feel every 81 box grid should be solvable with logic if there are at least 21 givens.
Yes, but bear in mind it is most usually and usefully used with variant sudoku (many less givens and extra rules etc). It applies to standard sudoku as well of course, I’ve just never seen it used to assist in the solving of a standard. Would be interesting to see one though.
He has a video where he solves a classic sudoku that a computer couldn't solve using set theory.
@@BuildChamp The program I designed solves the hardest known Sudoku in about 1 second, but it does test possibilities that are 50/50, and this always seems to result in a solution. I guess we can call that "brute force" because it somewhat isn't using logic. It simply saves the board solution thus far using logic, creates a list of all 50/50 possibilities, then starts testing each one, resetting back to the previous logic-filled screen on each failure and eliminating that attempt from the list. I'll have to check out this other video.
@My-Say when I say the solver couldn't solve it, I mean he turned off the bifurcation methods. I believe the puzzle is called "Steering Wheel" on Logic Masters.
Wait, are the visuals implying that Phistomefel is a young German dude, and not an dusty old man who spends his time in between heaps of scribbled papers, as I've imagined?
I believe he did a video where he showed himself setting a puzzle a long time ago. Something involving Thermometers and the Phistomephel ring. I want to say it was like a Patreon thing from way back in the day. And he looked like college age or just out of college back then.
Haven’t you seen his interview on Memeristor’s channel.
No way! I saw the thumbnail and immediately thought it was a new Cracking the Cryptic video, got confused about the short runtime, then saw it was Numberphile, and then see Simon in the screenshots. What a little rollercoaster of emotions.
What an incredibly great video, with a very clear description of one of "our" secrets. Great job and well done, Simon!
This is a crossover I wasn't expecting!!! I love cracking the cryptics channel!
First I thought "a bonus ctc video?". But right after, I saw the Numberphile logo on the thumbnail. It's so cool to see Simon from this angle. Another cool thing is that Phistomefel has been mentioned a lot this week.
Glad to see people still watch Numberphile and Cracking the Cryptic. I expected this to be an old video but this was just uploaded yesterday!
0:08 stunning visuals as always, keep up the great work
Simon Anthony is great. He really appreciates the beauty of Sudoku and is a terribly great solver.
I have been waiting for this ever since it was hinted at in the comments of that CTC video!! I'm very excited to see it's finally here :)
Simon AND Numberphile? What a perfect match. Great video.
It is so weird seeing Simon outside of CTC but it's always a pleasure listening to him ❤
Great to see Simon here explaining a really fun solving technique! Can’t wait for Mark’s Video on a different topic- looks it’s something to do with little killers!
Clicked on this thinking “I already know about this from Simon on Cracking the Cryptic, but I’m down to watch a Numberphile video. And what a pleasant surprise to see Simon is the one explaining it here!
Amazing, cracking the cryptic is a phenomenal channel. Glad to see Simon here
Good ole Simon, he only teaches the secret to his favorite people, but he will teach phistomefel’s ring to anyone
This is the cross-over I never expected but love!
Used this in yesterday's solve on Cracking the cryptic, very cool to see Simon here!
I have never seen this channel or the other and my brain is tickled! Thank you
So happy to see simon on the channel!
it's awesome to see Simon on this channel!
As an avid CTC and numberphile watcher, this collab warmed my heart❤
I have heard Simon explaining the Phistomephel Ring so many times, and I will never get tired of it
First Mark is on Countdown and now Simon is on Numberphile?!?!
If you round pi down to 3, then the Numberphile logo is a 3 in the corner.
Love this collab. Brady and Simon work so well together in my brain.
Oh boy! This collaboration! Much clearer explanation then the first time encountered
Simon’s “off-sider” Mark is currently on a big run on the BBC show Countdown. If he can pull off an Octochamp or a series win in a few months then it may offset his recent loss at the (UK) Times crossword championship, losing a title he had held for a number of years.
Channel 4, not BBC.
I never expected a Numberphile x Cracking the Cryptic video ! Wow
This video came up in my notifications and I was baffled, "why is there a new Cracking the Cryptic video at this time of day?" Turned out to be an even rarer treat.
A collab of two of my favourite channels, made my day!
The crossover I never expected but am so excited for 😁
It would be fun to see a video on the group theory behind Sudoku, especially extending the idea of equivalence classes. You could introduce orbits and stabilisers and so on.
How dare you make my year in the first 4 days!!! - best collaboration ever!!
When I read the title I thought of Cracking the Cryptic, but I never expected to actually see Simon here. What a nice collab!
THIS is the crossover i have been DYEING for thank you Dr Haran and Simon! This is so exciting I got up and did a little lap around the house and had to explain to my wife why it was so cool
I just love Brady's astute questions. I was about to write that the Phistomephel Ring is just a special case of a much more general phenomenon, when Brady chimed in with the perfect question. Alas, Simon didn't really answer the question adequately, although he did provide another special case.
This is an iconic mashup! Love both these channels
Two of my favorite creators on KZhead, and what a great concept to cover
This was very fun - an excellent explanation. And Simon is just as relaxed and relaxing in his own Cracking the Cryptic videos as he appears here. This is absolutely brilliant. (I will note that Phistomefel spells his name slightly differently than it appears here ...)
It seems like the Phistomefel spelling is correct in the video but incorrect in the description. That's fortunate, because the description is much easier to edit.
And he still insists he'd be no fun at parties! Lies!
@@spatulamahn Is that "fun", or is it "phun"?
wow. I saw a Numberphile video that i actually already knew all about, considering i've been a fan of cracking the cryptic for a year or two, and thought "i wonder who they've got to explain this..." Turns out, it's going to be explained by the same man who i already learned it from :D
Thank you Simon for this video! When I watched it several days ago I doubted that the Phistomephel Ring would be of much use to me but today I used it to solve a difficult (for me) sudoku.
OMGGG!! SIMON FROM CRACKING THE CRYPTIC!!! My absolute favorite puzzle channel!! So glad for this collab
Crossover moment
I'd never think cracking the cryptic would do a collaboration with you! Wow!
It’s been a long time coming
Two of my favourite worlds collide - cracking the cryptic doing a collab with numberphile!!!! Just perfect!
Most impressed - and especially that the pattern can be applied in other column/row/square selections. I've worked out some algorithms for generating and solving this puzzle but this is a new idea - so once I've digested it properly I'll see what I can do with it. Nice one chaps!
After it was proved some time ago that a classic sudoku requires 17 digits at least, but there are variant sudokus sometimes with no digits at all, it makes me wonder about a "Entropy number" for each clue where there's a way to calculate exactly how much logic is added to (or restriction is placed on) the grid by that clue. Like an arrow sudoku with an arrow that covers 3 cells in one box has a greater "weight" than one with 2 cells or one that crosses into another box (allowing a repeat digit). Is there a way to quantify that numerically?
Well, just some thoughts to go with yours on what I know about the set of puzzles, I think it's important to understand the general nature of these puzzles first, then you can start to quantify things like your proposed "entropy number": 1a. Any given puzzle, it either has one solution, no solutions, or more than one solution and we are not interested in the latter sets 1b. If a puzzle is extremely sparse, for it to only have one unique solution, the set of tactics needed in order to begin the puzzle is very small in count because there is a completely restrictive set of information. C1. Sparse sudoku puzzles have low "entropy number" 2a. If a puzzle is almost completely filled, assuming that the puzzle has one solution, the set of empty cells is small in number. 2b. Given a small set of empty cells, there must also correspond a corresponding small set of tactics needed in order to finish the puzzle C2. Full sudoku puzzles have low "entropy number" etc.
Wow. Two of my favourite channels combined. Simon should have told them that he only tells his friends the secret number.
This is possibly the most exciting channel colab to see of all time
Love seeing Simon explain the Phistomefel Ring. Set Equivalency Theory does not work well for every puzzle, but when it does, it makes for some cool eliminations and solving. Great video.
Seeing Simon from a different angle is so weird! Been watching him every night since over an year now!
Ah! What a great crossover! Love both these channels.
How wonderful to have Simon in a Numberphile video! And like Simon says - you ARE brilliant, Brady, with quite an eye for brilliance too. I'd be very proud that my children grew up with even half your zest for knowledge. Thanks for all your hard work.
A minute into the video I started thinking "They should have gotten Simon to explain this!" I hadn't even noticed it was him, he sounded different. What a lovely surprise!
Brady's observation at the end was on point - we've used this for years to crack lots of puzzles by knowing full rows and deleting the overlaps. The same ring logic applied to those horizontals is applied to the verticals and thus the blocks of 10 top and bottom center and at the sides are all equivalents (you 'delete' the ring instead of preserve it).
Simon‽ What are you doing in my numberphile video‽ 🤣🤣🤣
The crossover we didn't expect yet we all wanted
Yay Cracking the Cryptic! I'm a big fan, and Simon just mentioned you, Numberphile. Your back catalog looks marvelous. So count me as another viewer of yours! Have a marvelous day, all...
Let's goooo, crossover Love cracking the cryptic
What I’d give to talk to Simon at a party
Huge fan of both channels, so to see Simon on Numberphile is a huge dream come true!
Love both channels and love the collaboration.