The Most Mathematical Sudoku - Numberphile

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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[@sproins]

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

[@ingiford175]

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

[@mehdishakibaii5408]

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

[@kosterix123]

this is the way.

[@mrrobotman5299]

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

[@owenroche5247]

Do you have a link to it?

[@PhilippeAllardRousse]

@@owenroche5247 In the description.

[@WombatSlug]

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]

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

[@lill3lars]

@@owenroche5247it’s in the description under this video

[@Tsunami14]

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

[@longwaytotipperary]

😄

[@ZachGatesHere]

Bobbins!

[@OmateYayami]

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

[@liad88]

@@OmateYayami Yours memory serves wrong.

[@darrenbent7601]

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

[@Yijh]

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]

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

[@thelolman2000]

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!!

[@BrandonWillWin]

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

[@Vendavalez]

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]

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]

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

[@darrenbent7601]

@@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]

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

[@CatCheshireThe]

@@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]

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

[@Tristan_YoloCoaster]

Bobbins

[@matthewgraham2619]

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

[@DeZZie.M]

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

[@olivier2553]

Simon did not have an orange Sharpie!

[@longwaytotipperary]

😄

[@JormaTurkenburg]

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

[@DekarNL]

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

[@kjoonlee]

Normal sudoku rules apply!

[@LorisLaboratory]

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

[@longwaytotipperary]

Ditto! 😄

[@SaintAlecz]

Bobbins!

[@freddupont3597]

hehehe

[@silaslawrence4863]

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

[@omgawesomeomg]

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]

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

[@brenthooton3412]

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

[@emilywilliams3237]

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!

[@Tsunami14]

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

[@Corwin256]

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.

[@runeboas6421]

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

[@akoskulcsar350]

Can't wait for Mark's video

[@KuroroSama42]

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]

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 KZbin 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.

[@grahamania]

Well done Brady! Great Video combining CTC and Numberphile!

[@santimonto26]

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

[@trezl]

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

[@lntermark]

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

[@itskittyme]

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]

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]

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]

​​@@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]

@@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.

[@scat0324]

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

[@emilioherrera6345]

Where's the video with Mark? 😅

[@sdrawkcab190]

Love seeing Cracking the Cryptic on this channel!

[@justarandomdood]

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]

GNU's Not Unix

[@TaohRihze]

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

[@poppyholly1759]

@@joeg451 WINE is not an emulator

[@zadrik1337]

Set Seption!

[@mentalcasanova6420]

It's turtles all the way down.

[@bryananderson9914]

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

[@johanngambolputty5351]

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

[@abydosianchulac2]

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]

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

[@JohnADoe-pg1qk]

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

[@TheFrozenfish]

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!

[@some_gay_enby]

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]

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

[@ejw7247]

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

[@dogwaffles]

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

[@Boonda-p]

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

[@jodyvanliew2514]

Bravo to Simon on the great explanation .

[@paulmaglio9254]

Another great collaboration!

[@skadogg22]

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

[@RealCadde]

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

[@minecafe]

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

[@shashipancholi]

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

[@bristolrovers27]

Nice to see Simon on this channel

[@erichvereen1988]

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]

The people at Numberphile DO understand! ;)

[@TaohRihze]

I guess 45 or so.

[@JormaTurkenburg]

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

[@SpyrosSolda]

​@@TaohRihzeShhhh that's a secret

[@longwaytotipperary]

@@TaohRihze😁

[@math_travel]

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~~

[@ritchards]

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.

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

[@Sandra_and_Nala]

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

[@pardox28]

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

[@numberphile]

Still to come.

[@JeffKotz]

Thanks for the info.

[@longwaytotipperary]

@@numberphilelooking forward to it!

[@Pianoblook]

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)

[@same9643]

The collaboration we all know we needed.

[@Fallub]

I want more Simon videos here please.

[@riccardogilardi3124]

The BEST youtube crossover/collab

[@mountp1391]

Thank you!

[@worstwordmonger]

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

[@davecorry7723]

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!

[@chrisroberts1440]

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.

[@mentalsoup60]

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

[@longwaytotipperary]

This is great!

[@sdetent5787]

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

[@Muhahahahaz]

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)

[@AndrewBackhouse1]

Big fan of both channels

[@tsvtsvtsv]

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

[@walkingwriter4325]

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!

[@ozy1690]

Excellent

[@frankharr9466]

That is fascinating.

[@matthewsaulsbury3011]

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

[@LaGuerre19]

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

[@WAMTAT]

Brilliant

[@avz1865]

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

[@Akatsuki69387]

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

[@-Thauma-]

Thank you❤

[@pyglik2296]

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

[@johngranahan6102]

I enjoy this collaboration

[@humanl4903]

No way a numberphile and crackingthecryptic collab

[@leporid257]

nathan: we're gonna make a sudoku, so a layman can understand my mathematical theory nathan: we're gonna add a very well known sudoku theory. what could go wrong

[@isacami25]

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

[@gmgunner]

I literally just watch that previous video.

[@GeekRedux]

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!

[@flickingbollocks5542]

In Japan they call this puzzle "Latin Squares".

[@BeheadedKamikaze]

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

[@tommyb6611]

mind blown

[@thermotronica]

Holy moly

[@typo691]

Never expected this crossover.

[@FreshSmog]

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]

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.

[@lofomuses]

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?

[@Perplaxus]

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]

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.

[@SomethingVeryGeneric]

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

[@TurtonatorGuy]

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]

all @CrackingTheCryptic videos contain links to play along

[@cloudshaveiteasy]

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]

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]

The site that publishes the puzzles is logic masters germany

[@Scarybug]

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.

[@emdiar6588]

The sound effects are brutal.

[@Hedning1390]

He looks so different I almost didn't recognize him.

[@toto123456ish]

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

[@DidierLoiseau]

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

[@clausewitzianwar]

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]

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]

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

[@NelleShadowblue]

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.

[@bryanleimbach3939]

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

[@Pulsar77]

In the description.

[@ripgordonessy]

SIMON!!! Whooooo

[@delespai5592]

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]

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]

@@RichSmith77 Thanks!

[@jhornerification]

Does this affect the minimum number of clues needed to solve a puzzle (17)?