The Most Mathematical Sudoku

The Most Mathematical Sudoku - Numberphile

Рет қаралды 211,935

4 ай бұрын

Simon Anthony (from Cracking the Cryptic) shows us an incredible sudoku set by a mathematician. See the Phistomefel Ring at: • A Sudoku Secret to Blo...
More links & stuff in full description below ↓↓↓
Cracking the Cryptic: / crackingthecryptic
See Simon crack the puzzle at: • A Difference Of Square...
Another Numberphile video about Sudoku: • 17 and Sudoku Clues - ...
Thanks also to mathguy_12 (Nathan Hallmark) - see his research at: repository.flsouthern.edu/ite...
Patreon: / numberphile
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Our thanks also to the Simons Foundation: www.simonsfoundation.org
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Пікірлер: 320

@mrrobotman5299 5 ай бұрын

I remember watching Simon's solve of this. It was beautiful watching him work it out.

@owenroche5247 5 ай бұрын

Do you have a link to it?

@PhilippeAllardRousse 5 ай бұрын

@@owenroche5247 In the description.

@WombatSlug 5 ай бұрын

I do as well. It was a thing of beauty. My mind does not work like that very well, but I love how he's able to tease such things out of these more difficult puzzles.

@owenroche5247 5 ай бұрын

@@Nope-w3c probably should checked there first lol. Thanks!

@lill3lars 5 ай бұрын

@@owenroche5247it’s in the description under this video

@sproins 5 ай бұрын

*after hours of complicated maths* : "Well, 3 can't go there"

@ingiford175 4 ай бұрын

Thats three in the corner, three in the spot light...

@mehdishakibaii5408 3 ай бұрын

@@ingiford175 I was thinking about the exact same thing as you said when I was reading @sproins 's comment :))))

@kosterix123 2 ай бұрын

this is the way.

@Tsunami14 5 ай бұрын

No mention of The Secret, so we now know Brady is not one of Simon's favorite people.

@longwaytotipperary 5 ай бұрын

😄

@ZachGatesHere 4 ай бұрын

Bobbins!

@OmateYayami 4 ай бұрын

I think it was done in the 1st video though. If memory serves right.

@liad88 4 ай бұрын

@@OmateYayami Yours memory serves wrong.

@darrenbent7601 4 ай бұрын

That is because he is not with his favourite people. LOL

@Yijh 5 ай бұрын

Amazing to see Simon on Numberphile. Very good pair of videos showing that Sudoku can be a lot more interesting/intense/difficult than the bog-standard ones everyone is familar with.

@sabinrawr 4 ай бұрын

Simon's joy is infectious. Can't ever get enough!

@Vendavalez 5 ай бұрын

The only thing I wish had been done better in this video is doing an introduction to variant sudoku. Even people who are very familiar with sudoku as a game may not be familiar that those are even a thing and may be confused by the grid. For those who are indeed confused, variant sudokus are regular sudoku puzzles with custom rules/hints on the board rather than numbers. If you follow those hints you should be able to get some numbers until you have enough to solve the puzzle as a regular Sudoku. Some of those custom rules have become popular and a lot of puzzles use them and some may only be used for a single puzzle and then never again.

@backwashjoe7864 4 ай бұрын

Thanks for the background! The origins of those extra rules was confusing, but now much less so, and I like the video even more! :)

@RossReedstrom 4 ай бұрын

And following those rules - applying logic to get the first number, is referred to as the "break in" of the puzzle.

@darrenbent7601 4 ай бұрын

@@backwashjoe7864 Simon has a lot of fun on CTC solving the puzzles. It really is joyful. It is refreshing to see a solver have so much joy, even if he is totally confused at the start of the puzzle. It takes a few sessions, but there is a natural rhythm to his solves, even the epic movie length solves.

@eugenetswong 3 ай бұрын

I'm confused. Is a variant required to do what he did in the video?

@CatCheshireThe 2 ай бұрын

@@eugenetswong Not in the first video, which is a property that applies to all standard sudoku grids and variants that use standard sudoku rules. This one is an extension of that property but does require variant rules since it depends on sums of values to work, and in normal sudoku the actual values of the numbers don't matter, only their positions relative to each other (you can take any normal sudoku and say, swap all the 1s with all the 2s and it's functionally the exact same puzzle, but that is not possible in many variants).

@4evafcn 5 ай бұрын

I'm disapointed... 2 videos about set theory and simon doesnt mention scrable bags once... :D

@Tristan_YoloCoaster 5 ай бұрын

Bobbins

@matthewgraham2619 5 ай бұрын

Without it, this video is as useful as a chocolate teapot.

@DeZZie.M 5 ай бұрын

They made a tiny cameo I believe, they were on the table on his left!

@olivier2553 5 ай бұрын

Simon did not have an orange Sharpie!

@longwaytotipperary 5 ай бұрын

😄

@BrandonWillWin 5 ай бұрын

Simon’s sudoku solving was S Tier lockdown viewing for me a few years ago

@thelolman2000 4 ай бұрын

Since watching the video four days ago I have spent hour and hours over on Simons channel. Have learnt so much about the various sudokus and have downloaded their app and tried so many myself. Four days seems such a long time ago now!! Thanks for all the fun and knowledge Simon!!

@DekarNL 4 ай бұрын

Simon lulled me asleep countless nights. His voice and logic are relaxingly hypnotic.

@JormaTurkenburg 5 ай бұрын

This is just the kind of crazy shit I love seeing on KZfaq. Also great to see Brady and Simon collaborating.

@SaintAlecz 5 ай бұрын

Bobbins!

@freddupont3597 5 ай бұрын

hehehe

@kjoonlee 5 ай бұрын

Normal sudoku rules apply!

@LorisLaboratory 5 ай бұрын

Every time Simon explains things, its fascinating, even if ive heard it before. Great video! 💗

@longwaytotipperary 5 ай бұрын

Ditto! 😄

@omgawesomeomg 5 ай бұрын

Watching CtC I always thought the minds of puzzle solvers should also be really good at math, since proofs are also puzzles in way. Nice to see these worlds collide.

@kevray85 5 ай бұрын

One of my all-time favorite puzzles from the channel. Thanks for hi-lighting it!

@brenthooton3412 4 ай бұрын

4:55 "and look at what we're left in the corner" oh Simon you tease! you know we can't have a 3 in a circle leading to a three-cell arrow

@runeboas6421 5 ай бұрын

Why didn't Simon do birthdays today?! :O

@Tsunami14 5 ай бұрын

This was easily one of my favorite CtC puzzles. So glad to see this was featured!!

@silaslawrence4863 Ай бұрын

So happy to see this colab! Bloody love cracking the cryptic

@Corwin256 4 ай бұрын

I still remember his solve of that puzzle ages ago. I think of it often. Simon is the one who taught me how utterly beautiful sudoku could be.

@emilywilliams3237 4 ай бұрын

This puzzle - any sudoku puzzle, actually - brings so much pleasure to me as a viewer when I watch Simon or Mark (from Cracking the Cryptic) - and I always learn something. Excellent feature here!

@scat0324 5 ай бұрын

A teaser towards the end of Mark with some brown paper - so more collab to come!

@emilioherrera6345 5 ай бұрын

Where's the video with Mark? 😅

@grahamania 5 ай бұрын

Well done Brady! Great Video combining CTC and Numberphile!

@santimonto26 4 ай бұрын

The video was amazing, it was the perfect balance of detail and explanation for the depth of the topic. I love understanding what's behind the games I love. Would love to see the accompanying video on further details, ray-tracing and DLSS

@itskittyme 4 ай бұрын

I remember watching his puzzle videos a few years ago, and they were still easy / solvable at the time. And then you could gradually see them getting tougher each week, with less and less numbers filled in from the start. Then at a certain time, the first puzzles started to appear that had no pre-written digits at all. That's the moment I stopped trying because it started to go over my head. So it's funny now to see this Numberphile video, showcasing how much further they went down that rabbit hole with the empty puzzles since then. This one goes way over my head xD

@jwolfe01234 4 ай бұрын

It's not clear to me what their target audience is any more. Simon still goes into excruciating detail explaining basic concepts while solving puzzles that are effectively impossible for people who aren't already experienced-to-expert level solvers. Mark is somewhat better in that regard but seems to be following Simon's lead in doing more of that. But their videos get tens of thousands of views, so what do I know.

@fakjbf3129 4 ай бұрын

My favorite innovation has been Fog of War puzzles where you can’t even see the whole grid. I actually find them easier to solve than regular sudokus because the limited view focuses you onto the next step rather than being distracted by clues that aren’t useful until later on.

@tanyaegorova3149 4 ай бұрын

@@jwolfe01234I'm an avid viewer, but I'm ridiculously bad at maths, so it kind of scratches my itch for a nice sudoku/logic/maths puzzle game without the frustration of trying and failing to solve it. Thinking about it, Numberphile and Sixty Symbols videos kinda do the same

@thefacethatstares 4 ай бұрын

@@jwolfe01234 He gets people in the right mindset, which is that ANY puzzle is possible for newer sudoku solvers, even the super hard ones, if you just take it one step at a time and record your deductions in a visually clear manner.

@trezl 4 ай бұрын

So cool to see 2 of my favorite channels teaming up!

@KuroroSama42 4 ай бұрын

In my experience, these "more complicated" sudoku just end up being much easier than a normal one. Adding more rules just means adding more constraints, so you have more ways to narrow down answers. Basically, you're adding more equations to your system, but not more variables. More to look at, but more straightforward answers. This one doesn't seem to follow that though.

@RichSmith77 4 ай бұрын

Adding new constraint rules allows the setters to create puzzles that have far fewer (or even no) starting digits, which means the difficulty can still be as hard as any standard sudoku. You should check out a video or two on the Cracking the Cryptic KZfaq channel. They have some incredibly inventive puzzles that are far more interesting than the vanilla sudoku puzzles you see in newspapers. They always provide a link to a web page where you can try the puzzle first. And if you get stuck, you can watch part of the video until you get unstuck.

@lntermark 4 ай бұрын

Never expected to see Cracking the Cryptic on Numberphile, but this is great!

@sdrawkcab190 4 ай бұрын

Love seeing Cracking the Cryptic on this channel!

@some_gay_enby 5 ай бұрын

Why is the bottom right square completely taken away when it is only cancelled out once with the arrow/green? The second part is still there

@msolec2000 5 ай бұрын

Before removal it is 2 red/1 green, if we remove both colours like the other cells in both sets, it is left with red at the circle of an arrow, which can now be cancelled with the green cells on the arrow proper

@jodyvanliew2514 5 ай бұрын

Bravo to Simon on the great explanation .

@johanngambolputty5351 4 ай бұрын

Never anticipated seeing Simon here, but its a joy :)

@akoskulcsar350 5 ай бұрын

Can't wait for Mark's video

@Boonda-p 5 ай бұрын

Damn no mention of chocolate cake, maverick, 3 in the corner or secret!

@justarandomdood 5 ай бұрын

In Sudoku (and the previous video), Simon and Mark have often called this S.E.T., which stands for Set Equivalence Theory. But did y'all know that the word "Set" in "Set Equivalence Theory" actually stands for something as well? It stands for "Set Equivalence Theory" 😋😋😋

@joeg451 5 ай бұрын

GNU's Not Unix

@TaohRihze 5 ай бұрын

I guess with what we learned, is that Equivalence Theory then is a zero sum game.

@poppyholly1759 5 ай бұрын

@@joeg451 WINE is not an emulator

@zadrik1337 5 ай бұрын

Set Seption!

@mentalcasanova6420 4 ай бұрын

It's turtles all the way down.

@bryananderson9914 4 ай бұрын

CTC on Numberphile!I love when my separate hyperfixations combine.Crossovers are the best

@ritchards 5 ай бұрын

I remember one of the earliest puzzles they looked at involving those two squares, which had the trick that unless you knew about that relationship, it was nigh impossible to crack.

@chrisroberts1440 5 ай бұрын

I like the killer sudoku as the values of the numbers matter as opposed to them just being symbols. I do the ones with no starting clues in the cells, normally a couple of minutes at a time while I wait for a process to complete on some software I use at work.

@paulmaglio9254 4 ай бұрын

Another great collaboration!

@math_travel 4 ай бұрын

I used to just solve Sudoku as a puzzle. This was my first time seeing Sudoku approached mathematically like this. I am grateful for this. Still, I will enjoy solving Sudoku itself. thanks~~

@Sandra_and_Nala 4 ай бұрын

Yes, more of Simons sideview :D so different and refreshing!

@pardox28 5 ай бұрын

Is there a link for the video that Mark appears in? Or is that video coming out soon?

@numberphile 5 ай бұрын

Still to come.

@JeffKotz 5 ай бұрын

Thanks for the info.

@longwaytotipperary 5 ай бұрын

@@numberphilelooking forward to it!

4 ай бұрын

I love hearing Brady's enthusiasm. I miss his 2 guys talking podcast with Grey.

@bristolrovers27 5 ай бұрын

Nice to see Simon on this channel

@minecafe 4 ай бұрын

6:33 I said "beautiful" at the same time! XD

@Fallub 4 ай бұрын

I want more Simon videos here please.

@Pianoblook 4 ай бұрын

Great collab, and fun to see you exploring the math of games & puzzles! I'd love to see a video about using 'Hat Guessing' logic as a way to try and beat the game of Hanabi. Check out the paper called, 'How to Make the Perfect Fireworks Display' (although hanabi afficianados have come up with even more clever algorithms since them)

@erichvereen1988 5 ай бұрын

What the people over at Numberphile don't understand, is that between Simon and Mark, they can probably created a few dozen videos from all the secrets they know! ^_^

@numberphile 5 ай бұрын

The people at Numberphile DO understand! ;)

@TaohRihze 5 ай бұрын

I guess 45 or so.

@JormaTurkenburg 5 ай бұрын

Let's gooo @@numberphile and bring back HI! 😂

@SpyrosSolda 5 ай бұрын

@@TaohRihzeShhhh that's a secret

@longwaytotipperary 5 ай бұрын

@@TaohRihze😁

@sdetent5787 4 ай бұрын

I could watch this chap (and maybe a friend of his) solve puzzles for hours. Beam!

@RealCadde 4 ай бұрын

WHAT? Simon in a Numberphile video? Never would have thunk it but now that he is, i am stunned it took this long.

@tsvtsvtsv 4 ай бұрын

the whole added dimension is like a really complicated version of that lights out game. seems like the color cancellations work similarly

@Muhahahahaz Ай бұрын

7:05 the thing I didn’t realize about attempting a “normal” solve here, is that what we saw is literally the entire puzzle! In other words, the entire puzzle starts “blank” and you have to fill in every single number! I thought maybe they removed the seed numbers for the purposes of this demonstration, but no… Every single number must be determined via the various rules, and whatever algebra/geometry/set theory you can come up with! (So yeah… Never gonna be solvable the “normal” way lol)

@skadogg22 4 ай бұрын

whoa I just realized this is Simon from Cracking the Cryptic!

@same9643 4 ай бұрын

The collaboration we all know we needed.

@ejw7247 4 ай бұрын

This is the crossover I’ve been waiting for my whole life

@mountp1391 4 ай бұрын

Thank you!

@matthewsaulsbury3011 4 ай бұрын

Wow! This is amazing! I like mathematics and sudoku!

@longwaytotipperary 5 ай бұрын

This is great!

@walkingwriter4325 5 ай бұрын

I enjoyed watching both of Simon's videos, but this one made the Phistomefel Ring proof look like child's play (ha ha). Well done!

@AndrewBackhouse1 4 ай бұрын

Big fan of both channels

@frankharr9466 5 ай бұрын

That is fascinating.

@dogwaffles 3 ай бұрын

"Let me start" is the best kind of phrase.

@ozy1690 4 ай бұрын

Excellent

@riccardogilardi3124 4 ай бұрын

The BEST youtube crossover/collab

@WAMTAT 5 ай бұрын

Brilliant

@shashipancholi 4 ай бұрын

Mark: appears on Countdown Simon: appears on Numberphile Coming soon: CrackingTheCryptic help solve a Millennium Problem using sudoku

@abydosianchulac2 5 ай бұрын

I'm sorry, this was the _first_ puzzle that person had set?! Edit: And I'm sorry, he's just turned 22 and he's doing his PhD? Wow, didn't know those folks actually existed.

@ladislavseps4801 5 ай бұрын

Define puzzle. It was first sudoku, but i would argue Phd thesis in mathematics is lot of puzzles and solutions..

@JohnADoe-pg1qk 5 ай бұрын

No, it wasn't. There is a comment from @mathguy_1243

@TheFrozenfish 5 ай бұрын

That's the level of complexity / difficulty / beauty a sudoku nowadays has to have in order to have a chance to appear on CTC! :D A few years ago with the appearance of the first Miracle Sudokus it was already magical, but today… my oh my… unless the setter intentionally makes the puzzle "approachable", you are going to have a very hard time trying to solve it - which many people like!

@davecorry7723 4 ай бұрын

I thought this was a set of new rules, such that in all sudoku, the number on the bottom-right corner equals the sum of those three nearest green cells. It's not. I realise that I've no idea what this is about. So I'm going to get drunk, in this beautiful, cold, winter's Wednesday night. Thank you, Numberphile!

@lofomuses 4 ай бұрын

at 00:40 and 00:51 -- what are the sounds that I hear in the background? The graphic is changing, but via some sort of noisy machine?

@FreshSmog 5 ай бұрын

As a programmer, what will this change in terms of algorithms to solve sudokus? The typical way is to recurse through the single sets looking for single solution cells and making guesses if none are found. Does that mean we should additionally check these cages from every orientation?

@mentalcasanova6420 4 ай бұрын

Take a look around at some of the solvers out there, they are getting incredibly advanced, though I'm unsure at the completeness of them compared to the many variant rules being developed every week.

@-Thauma- 4 ай бұрын

Thank you❤

@worstwordmonger 4 ай бұрын

Simon didn’t even share the secret he only shares with his favorite people, unbelievable

@johngranahan6102 4 ай бұрын

I enjoy this collaboration

@pyglik2296 4 ай бұрын

Amazing. Starting solving the sudoku without putting in any numbers!

@BeheadedKamikaze 4 ай бұрын

Where can we see the video that you filmed with Mark (pictured at 7:33)?

@isacami25 4 ай бұрын

uff. i haven't seen a video of cracking the cryptic in ages. that's always a rabbit hole for me lol

@avz1865 4 ай бұрын

I got Jumpstart by the first few seconds. It's Simon!!!!

@GeekRedux 5 ай бұрын

Love seeing CtC on Numberphile! But where's a Numberphile video featuring Mark? We see that video clip at the end... C'mon, don't do him dirty like that!

@Perplaxus 4 ай бұрын

The mathematics of solving single solution puzzles are fascinating. If you could do a video on other solution strategies that would be really cool. I want to see more interesting ways to solve things - that can be for more traditional math things too. Anyway thank you and happy 2024

@Pulsar77 4 ай бұрын

Search for 'The Sudokult Discussion' on youtube. It's a video series on advanced sudoku techniques by Rangsk and Philip Newman, two people who are very active in the Cracking The Cryptic community.

@LaGuerre19 4 ай бұрын

When Cracking The Cryptic does a crossover with Cruising The Cut, we'll finally have (CTC)²

@gmgunner 4 ай бұрын

I literally just watch that previous video.

@tommyb6611 4 ай бұрын

mind blown

@SomethingVeryGeneric 22 күн бұрын

At the end theres a video trailer of Mark on the right, where is that video in the description, I haven't seen it!

@mentalsoup60 4 ай бұрын

The laugh at the end is about exactly how I laughed when it clicked

@humanl4903 4 ай бұрын

No way a numberphile and crackingthecryptic collab

@thermotronica 5 ай бұрын

Holy moly

@Akatsuki69387 4 ай бұрын

I don't know why but the cages sound made me laugh so hard I almost choked on my water.

@typo691 4 ай бұрын

Never expected this crossover.

@flickingbollocks5542 4 ай бұрын

In Japan they call this puzzle "Latin Squares".

@TurtonatorGuy 5 ай бұрын

Does anyone know what this type of sudoku puzzle is called or how to find a website or app that has them? I kinda want to try it...

@_thth 5 ай бұрын

all @CrackingTheCryptic videos contain links to play along

@cloudshaveiteasy 5 ай бұрын

If you're looking for an app, CTC made one for most types of variant sudoku, with puzzles set by really talented constructors, it's linked under all of their videos!

@conorpappas3871 5 ай бұрын

And more concretely, this type of puzzle is called a "variant" sudoku, as it includes rule variants. This particular puzzle includes "arrow", "killer", and "renban" variants, and you can find apps and puzzle sets devoted to exploring those rules. Logic Masters Germany is a great resource to find puzzles of all types. Its the most popular forum on which puzzle constructors post their works. Finally, CTC has two books they have put out if you're looking to do some puzzles on paper.

@moytta122 5 ай бұрын

The site that publishes the puzzles is logic masters germany

@Scarybug 5 ай бұрын

Cracking the Cryptic has website links for every puzzle, and those sites have software to support all those sudoku variants with great tools for marking them as you solve.

@delespai5592 4 ай бұрын

Could someone explain how the square in the bottom right position was cancelled out by the green squares sitting under the arrow? As I understood it, that bottom right square had three instances of itself (one green and two red), while the green squares along the arrow would only sum to one of those instances.

@RichSmith77 4 ай бұрын

You're correct, it was two instances of red and one instance of green. But you can cancel out the one green instance with one of the two red instances, leaving a single red instance. That remaining red instance, in an arrow's circle, can then be cancelled with the digits in green along the arrow, the same as he did with the other arrows.

@delespai5592 4 ай бұрын

@@RichSmith77 Thanks!

@matteopascoli 5 ай бұрын

There’s Maverick at 2:23 !!

@emdiar6588 4 ай бұрын

The sound effects are brutal.

@zakdentes2139 4 ай бұрын

@Numberphile, Wouldn't what you've said about the gray arrows with circles in this video imply that the numbers in the gray-circled cells could never be 1 or 2 (because no two other distinct numbers in the set from 1 through 9 could sum to either 1 or 2)? And also that the number circled in the extreme lower-right corner (with the gray arrow that is three cells long) would have to be 6 or greater (by similar logic)? These would seem to be worthwhile axioms of Sudokus to mention further if correct... Or do the gray arrows and other symbols drawn on the sudoku grid in this video only apply to a particular Sudoku puzzle, or perhaps family of Sudoku puzzles?

@mathguy_1243 4 ай бұрын

You are correct in both aspects! That logic about how arrows work is exactly correct and those arrows do only exist in particular puzzles in which the creator places them :)

@bryanleimbach3939 4 ай бұрын

That looks like a fun puzzle. Where’s the link?

@Pulsar77 4 ай бұрын

In the description.

@toto123456ish 5 ай бұрын

Shouldn't we keep the bottom right cell in the red set at 5:22 if we remove it only once?

@DidierLoiseau 5 ай бұрын

It cancels out with the 3 green cells at the bottom right, covered by the arrow

@clausewitzianwar 5 ай бұрын

Just to be slightly more explicit than the other reply: We removed once because the cell was shaded both red and green, leaving one red shading left. We removed it the second time because the 3 arrow cells had the same sum as the 1 red cell.

@howmanyrobot 5 ай бұрын

Just to be even more explicit than the other replies: It was in the Green Set 1x and in the Red Set 2x. So we cancel them out and end up with it just being in the Red Set 1x. However it's also the circle on an Arrow Sudoku clue, and all three of the cells that make up the arrow are in the Green Set. By the rules of Arrow Sudoku, the digits on the arrow sum up to the digit in the circle, so by removing the arrow cells from the Green Set and the circle cell from the Red set, while the distribution of digits is unknown, the *sum total* of both sets is still the same.

@toto123456ish 5 ай бұрын

Thanks @DidierLoiseau @clausewitzianwar @howmanyrobot5652 It is perfectly clear now.

@NelleShadowblue 4 ай бұрын

I finally understood! We cancel out two red cells each with, one green cell located in the same position, and three green cells that are related to the location.

@My-Say 4 ай бұрын

I've been writing Sudoku solvers in programming for a few years and it is my understanding that a person could prove P=NP in solving them fast enough. Does this now open that door or no? What kind of solve time would we need?

@Shadow4707 4 ай бұрын

Do you even understand what P and NP are?