Extra footage at: kzread.info/dash/bejne/eql91Leef6fahrQ.html Patreon: www.patreon.com/numberphile

@deepakkpradhan

4 жыл бұрын

Sadly, sharadchandra shankar shrikhande one of the co-authors of the Euler's spoiler paper passed away recently.

@NStripleseven

4 жыл бұрын

deepak pradhan Wow, that's sad.

@leif1075

4 жыл бұрын

Wait i thought BOTH diagonals had to be different but for the 3x3 you have one diagonal as A A A ..at 8:20 isnt that wrong?

@leif1075

4 жыл бұрын

Also at 8:35 you have the same number in the diagonal...that's inconsistent too..cant have all 3s or all 1s..should be one of each..

@RedwoodRhiadra

4 жыл бұрын

@@leif1075 He explicitly says the diagonal restriction is only for the 4x4 cards puzzle and not for the general Latin Squares puzzle.

Moral of story: _Even when Euler's wrong, he _*_still_*_ gets things named after him._ (That's gotta make Matt Parker feel better.)

@electromika

4 жыл бұрын

What a Parker naming system.

@yourguard4

4 жыл бұрын

Even things, which doesnt exists, need a name, so that everyone knows, what you are talking about :P

@rcb3921

4 жыл бұрын

The Euler Square O.O I can't believe that went over my head.

@sumdumbmick

4 жыл бұрын

nah, the moral of the story is that people who name discoveries after people are idiots.

@fredg8328

4 жыл бұрын

@@sumdumbmick Because people don't deserve being recognized for their work ?

4:00 "We don't actually need to match up the diagonals." 4:30 *diagonals match up anyway* The Anti-Parker Square

@PanduPoluan

2 жыл бұрын

So we have Parker (dud), Non-Parker (works), and Anti-Parker (works even in ways not required by original requirements).

@teiermyler4926

2 жыл бұрын

@@PanduPoluan Gold

@mati.benapezo

Жыл бұрын

@@PanduPoluan Is there the Anti Non-Parker?

@aidentoman-sager5527

Жыл бұрын

@@mati.benapezo so it fails even in ways not required? that's just a regular Parker

10:52 No-one brute-forces a problem like Gaston!

@otakuribo

4 жыл бұрын

When he was a lad he did 4 dozen trials every morning to help with the proof, And now that he's grown he does 5 dozen trials on his quest for mathematical truuuth!! 💪

@BlokenArrow

4 жыл бұрын

🤓

@MichaelJamesActually

4 жыл бұрын

K.o.R take my upvote

@talonbraxton8394

3 жыл бұрын

K.o.R are you a Ben and hollys little kingdom fan?

@oz_jones

3 жыл бұрын

Literally egghead Gaston.

Title: Euler Thumbnail: James Grime Me: visible excitement

@screamsinrussian5773

4 жыл бұрын

Euler didn't respond to their calls :(

@sam08g16

4 жыл бұрын

Hotel: Trivago

@darkphoenix0808

4 жыл бұрын

Is that the speaker's name? I honestly don't know

@squidly1369

3 жыл бұрын

@@darkphoenix0808 yes it is he is the best out here I guess I mean his accent presence is awesome 😎🔥

@Triantalex

6 ай бұрын

??

In fact so special that Euler got involved xD We should award puzzles with the 'Euler tried' award

@XHappyKillerX

4 жыл бұрын

The Parkeuler

@XHappyKillerX

4 жыл бұрын

Now that I think about it, I just noticed how the title "Euler Squares" must have been a deliberate reference to the Parker Square, nice!

@NStripleseven

4 жыл бұрын

Yeah, this should be a thing. xD

@salerio61

4 жыл бұрын

There's still loads of awards going for a similar idea of "Erdos tried" puzzles. You even get the choice of accepting the monetary award or a cheque signed by Erdos to frame in your study

@metleon

4 жыл бұрын

Instead of 'college try' we should change it to 'Euler try'.

The youngest of the ‘Euler’s Spoilers’ is no more. He was 103. Indian mathematical genius, Sharadchandra Shankar Shrikhande, who along with his mentor late RC Bose and their colleague late ET Parker disproved way back in 1959 an 18th century mathematical conjecture, passed away at Vijaywada on April 21, bringing curtains to a glorious chapter from the world of statistics and mathematics.

@alveolate

4 жыл бұрын

indian mathematicians are amazing... if anyone has a nice long documentary with a bunch of indian mathematicians, please link!

@amritkumar7488

4 жыл бұрын

@@alveolate there is a documentary on SC Shrikhande tho. I saw it at a college. I don't recall the name. Try googling.

@GerSHAK

4 жыл бұрын

+

@aquibalamLUMOS

4 жыл бұрын

Respect

James Grime: Oiler Spoilers Me, an intellectual: Euler Speulers

@ianmoore5502

4 жыл бұрын

I cannot stop giggling. Thank you.

Squares in order of importance 1. Parker Square 2. Euler Square 3. The Square

@RogueLich

4 жыл бұрын

4. 2^2

@squidly1369

3 жыл бұрын

@@RogueLich lol😂

@alihesham8167

2 жыл бұрын

@@RogueLich 5. 1

14:02 "Never arrange a ping-pong tournament with six team members" -- I first understood "with sixteen members", I went crazy! WTF?!? And then I turn on the subtitles.

The ping pong letters and numbers are adorable

@auroralong5437

4 жыл бұрын

I thought that too until I saw their tiny white pupils and now I think I'll have nightmares....

@mattiacapuano2022

4 жыл бұрын

@@auroralong5437 damn, you're right

@xan1455

4 жыл бұрын

Yay but 4

@MiserableMidnight

4 жыл бұрын

Nooooooooo

@marcushendriksen8415

4 жыл бұрын

Watch #4, it looks like it's teabagging

5:45 I'm mostly here for the twerking 4

@Just_A_Baryonyx

4 жыл бұрын

i noticed that too

@Son-Of-Gillean

4 жыл бұрын

@@Just_A_Baryonyx "Noticed" = fapped

@hamiltonianpathondodecahed5236

4 жыл бұрын

ikr

@Just_A_Baryonyx

4 жыл бұрын

@@Son-Of-Gillean no....

@leadnitrate2194

4 жыл бұрын

it was in this positionerino agadmatorino Hey you're not commenting on Agadmator's recent videos. What's wrong? I really enjoyed your work during the MC Invitational.

This was one of the best Numberphiles in a while for me! James really knows how to give information succinctly and interestingly. Bravo, chaps!

3:33 I realise not only the rows columns and diagonals, but the four 2×2 sub-squares also have one of each rank and suit!

@inigo8740

4 жыл бұрын

That makes it even more like a sudoku! Hooray!

@andersyu4464

4 жыл бұрын

also the middle 2x2 square

@prich0382

4 жыл бұрын

Which surly means that the "difficult" 6 by 6 example surly could be solved by doing the sub 3x3 sub squares no?

@gargravarr2

4 жыл бұрын

It follows by definition, since the other 3 squares of the sub-square are on the row, column and diagonal of the corner square.

@gabor6259

4 жыл бұрын

Also the 4 corners.

James talks about something from Euler, can there be something better?

@cerwe8861

4 жыл бұрын

@Carey Hunt what?

@Pro_Triforcer

4 жыл бұрын

You mean there's a square named after some other mathematician? Sounds almost exciting, but not quite

@kasajizo8963

4 жыл бұрын

Yes, there is something better. Matt Parker talking about squares.

@cerwe8861

4 жыл бұрын

@@kasajizo8963 that's also cool, but like a Parker Square not perfect xD

@cerwe8861

4 жыл бұрын

@Carey Hunt Thanks random guy from the Internet

I love how team member "4" is animated at 5:46

@microwave856

5 ай бұрын

hes a little silly

I always love when different pronunciations clash like one is correcting the other straight away... “ohh it’s a Sudoku” ... “yes a sudoku”

@howard5992

Жыл бұрын

and each time the word " sudoku " is repeated more emphasis can be placed upon that work in the sentence until it can become a very happy shouting match !

That brown paper on Graham's number signed by the very own Ron Graham is just amazing! 0:25

@benjaminlum5894

4 жыл бұрын

Agreed! I'd like that to hang on my wall as well

@jesusthroughmary

4 жыл бұрын

Wow, I didn't even notice, that is too cool

@henriccarlsson9052

3 жыл бұрын

The first thing I noticed also :)

3:14 you think James is sped up here, but actually this is his normal speed, the rest of the video is slowed down

"it's so difficult Euler got involved"

It would have been nice to talk about the link between this and magic squares: say instead of AKQJ and 1234 we used two sets of 0123, and made them into the same arrangement, we could then read off each number as a two-digit number in base 4, then those would be a valid magic square (excluding diagonals) or we could add 1 to every number and it would still work. For a 3x3 example (since I know that one well), [21,00,12;02,11,20;10,22,02] (excuse the formatting) becomes [7,0,5;2,4,6;3,8,1] or [8,1,6;3,5,7;4,9,2] which is a magic square. This logic works for all sizes too.

@HansLemurson

4 жыл бұрын

Wait, so does that mean there are no 6x6 magic squares?

@khaitomretro

4 жыл бұрын

@@HansLemurson No. The assertion is wrong. There are 6x6 magic squares but no 6x6 magic squares that take that form. You always end up with a square that repeats one of the base 6 digits in the rows.

@khaitomretro

4 жыл бұрын

If you can construct a double Latin square then you can use that to create a magic square. Euler's methods for creating double Latin squares can be used to create forms of magic square but won't find all of them, just a subset.

After so many years I still get a smile when I see James Grime

When he described the puzzle, I paused it, got some paper and a pen, and figured it out. And I solved it, hooray! It really is like doing double sudoku, lol. Cheers for the interesting video and fun little puzzle, Numberphile :)

@TheZotmeister

4 жыл бұрын

Check out the 2016 United States Puzzle Championship :)

@helenanevrayeva

4 жыл бұрын

Haha, I was so intrigued so I pulled out a stack of cards for this 😁 I did AKDB first, then it was easy to rearrange for ♠️♥️♦️♣️. Enjoyed it thoroughly!

This video is like a tribute to SS Shrikhande who was part of the "Euler's Spoilers" - a bunch of three people at UNC-CH who disproved Euler's generalisation of this problem - who sadly passed away on the day of the release of this video.

@numberphile

4 жыл бұрын

Amazing coincidence.

@alveolate

4 жыл бұрын

@@numberphile your video --killed him-- satisfied his lifelong ambition of getting obliquely referenced in a numberphile video.

@Alex-xk6sx

3 жыл бұрын

He passed away on April 21, 2020 (at age 102 at that!), not on the day this video was released, though the dates are truly close to each other 😉 May he rest in peace.

@haricashravi3900

3 жыл бұрын

@@Alex-xk6sx that's weird because I clearly remember seeing the news where SSS's death was reported and a few hours later this video released... Could it be possible they had reuploaded/changed the video later?

@Alex-xk6sx

3 жыл бұрын

@@haricashravi3900 Maybe? Waiting for Numberphile to chime in.

Back in high school (late '70s, early '80s), our math teacher had a large, handmade, quilt hanging from one of the walls, with a 10 x 10 Euler square as the pattern. Him telling the story behind is was the first time I heard about Euler.

This lockdown really hasn't cramped the style of the animator. Full marks. I love it.

I like the framed brown paper for Graham's number hanging in the background.

Can we talk about that 4 for a second?

@michaelmatter1222

4 жыл бұрын

4 really went 4 it

@free_h2o142

4 жыл бұрын

4 goodness sake...

@proloycodes

2 жыл бұрын

4 4 a second*

One of your best videos in quite a while. Really enjoyable. James really knows how to explain things. Thanks!

Grime's passion is always very enjoyable to listen to and watch

I love how you never cease to stop making innovative animations

Dr. James Grime is such a joy to listen and watch at. Always with a big smile. We need more enthusiastic people like him :)

11:12 "To be fair, he was a proper mathematician. But he also checked every case." Shaking my head

Classic James. What a mad lad. We gotta have Numberphile live-streams some time.

I love NumberPhile! I watch it all the time. It's one of the only this getting me through lockdown! 😀

@zinniaward8549

4 жыл бұрын

Mood

@esotericVideos

4 жыл бұрын

I do too! I'm a little concerned that they don't seem to be too socially distanced in their videos though. I don't want any of my Maths friends to get sick.

@ragnkja

4 жыл бұрын

esotericVideos I’m sure it was filmed well before the lockdown.

It's great to see James again - I feel like I haven't seen him in a NP video for ages!

@numberphile

4 жыл бұрын

Do you have notifications on for our videos? Bash that bell 🔔

That four day tournament was the greatest event of my life - the first game on the second day was just the bomb!

watching this while currently having in sudoku mood. I suddenly thought of this sudoku variant, 2 sudokus (normal sudoku and wordoku) in one grid following regular rules with the extra rules mention in this video (each cell must have a unique combination of a letter and a number) would be interesting tho (and hard)

5:40 that four was flapping his privates LOL

I love that you've got the paper from the video with Ron Graham hung up on the wall. RIP

This video was a mental rollercoaster ride

What a coincidence....just when the Indian Mathematician who debunked Euler's Theory passed away! P.S. - He died today at the age of 103! His name was Shrikhande !

@numberphile

4 жыл бұрын

Amazing coincidence!!!

@zstanojevic9574

4 жыл бұрын

@@numberphile Also, a video tributing Conway's departure is visibly missing..

@WatchingMyLifeFlashB

4 жыл бұрын

The video showed an Indian Raj Bose as completing it successfully in the 1950's, '54 I believe it was. This Strickhande was he in the '20s that were later disproven until Bose, or was Strickhande later?

James Grime is such a wonderful communicator.

Oh man this remind me of playing around with multidimension Karnaugh maps. I love this channel so much, thank you guys for keeping science available for all

great that numberphile keeps uploading turring the lockedown. love this video.

This reminds me of "The Schoolgirl Problem Puzzle" : In a boarding school there are fifteen schoolgirls who always take their daily walks in groups of three. How can it be arranged so that each schoolgirl walks in a group with two different companions every day for a week (7 days)?

@woodchuk1

4 жыл бұрын

ZaphoD Beeblebrox Isn’t that an instance of a Steiner Triple system of order 15, where there would be (15*14)/6, or 35 triples?

@rosiefay7283

4 жыл бұрын

Let's give Kirkman due credit for this problem. Another Numberphile video, perhaps?

@omikronweapon

4 жыл бұрын

@@rosiefay7283 sounds like one for Cliff. He loves Euler and stuff about taking walks.

14:04 Fs in the chat

@hubert6943

4 жыл бұрын

F

@helloiamenergyman

4 жыл бұрын

F

@tlep2979

4 жыл бұрын

F

@hauphan917

4 жыл бұрын

F

@mementomori7160

4 жыл бұрын

F

This was an excellent presentation as all of yours are. Having taught statistics for years I never thought of using this with setting an Experiment thank you.

James got me interested in teaching myself better math skills that have laid dormant for years.....BIG THANKS!!!!

I bet after it was disproven, Euler's viewers started using the term to describe anything that was given a go but had something wrong in it. As in, "Oh look at that square number magic square Matt Parker came up with, it's such an Euler square of a solution!"

I reckon they should have called them “Speulers”

Just completed one with each row, column and corner diagonal. It's also nice to see the centre 4 are also one of each, as is each corner, including many 4 place patterns like B1, C1, B4 & C4 for example! :)

What a great story - so many twists - a strange pattern - thanks James

In my head I'm just singing to the "ABC Song" by Jackson 5: A B C pair them with 1 2 3. A B C 1 2 3, that's how easy maths can be!

@michaelmatter1222

4 жыл бұрын

LoL

I see Euler and James grime in title, i click.

The four corners also constitute a four card set, as do the central four cards and each four card quadrant, plus others. If you were given all these conditions to meet at the start, it would seem more difficult to solve, but actually makes it easier.

I love this guy. The excitement, the energy, everything

But WHY doesn't 6x6 work??

@renerpho

4 жыл бұрын

An example of the strong law of small numbers (2 and 6 are pretty small). They sometimes do weird things that aren't representative of the general behaviour.

@jacobnugent6895

4 жыл бұрын

@Nhật Nam Trần I agree. why only six? I feel like if six doesn't work, then it should manifest itself again at some point on the number line, causing some multiple of 6 to not work either.

Amazing video ! Thanks for making it ! It infused my enthusiasm of Combinatorics !

James grime is so engaging I love it when he’s in the videos

thanks JAMES

@macaroon_nuggets8008

4 жыл бұрын

your first.

I am a simple man ,I see James. I suddenly love math... Until the video ends.

I feel like those dancing letters and numbers are gonne stay stuck in my mind for quite a long time. I'm not sure whether I should complain about it.

4:25 I like how he managed to get the diagonals anyway even though he didn't need to

I'd be interested in a way of judging "how wrong" a square is, and then seeing how many 6 squares exist that are the "least wrong"

Ping-pong player B did literally nothing and still won the tournament. Impressive.

thank you so much James Grime, finally I´ve understood it!

Throughout history there have been teachers that, through a combination of their passion and understanding for the subject and the way they present it, make learning easy to digest. James Grime is one of those and I envy the students that have studied under him.

I got really into these a couple of years ago. and I found another type of puzzle that is also cool. It's basically the same except instead of an n by n grid with 1 of n items in each row and column you have a 2n by 2n grid with exactly 2 of each item in each row and column. I was trying to figure out how many different possibilities there are, but it's harder to compute than the euler squares.

Omg!! James Grime!! (The earliest I've been)

I love that Graham's number is on the wall

The starter puzzle was something I randomly thought of on a bored Saturday and I couldn't find a single solution, thanks for solving it for me

I’ve had a puzzle like this ever since I was a child, with colours and numbers instead of card values and suits. Never knew it was called an Euler square :)

7:12 Number 2 in third place *logic*: wait, that's illegal!

@waldokind

4 жыл бұрын

Waltlab Channel Zero based?

Now I'm wondering about adding a third dimension to it. You talked about bigger and bigger squares, but what about adding a 3rd component? Perhaps we can make cubes where an element can't share a trait with another element in either rows of the same layer or in its column. After having tried it out with a 3x3x3, it basically seems to be stacks of different solutions for the square version. The additional trait didn't appear to add much of interest, though perhaps that might change with larger cubes. I guess a 4x4x4 could at least include the diagonal rule to make it more challenging (especially since, instead of just 2 diagonal lines, a cube has 22).

In 2012, this channel uploaded a video about a "special magic square" that remains magic after rotation or reflection. But this video provides the explanation. It is really two orthogonal 4x4 Latin squares with the digits 1, 2, 5, and 8: one for the tens place and one for the units place. These digits rotate or reflect to give 1, 5, 2, and 8, respectively, so the Latin square property still holds. So the total of every row, column, and diagonal must be 1 + 2 + 5 + 8 = 16 for both the unit and tens digits, giving a total 160 + 16 = 176, invariant under reflection or rotation by 180 degrees.

What a ride.

14:52 wait, *that* adam savage? or just someone coincidentally named adam savage?

@HanabiraKage

4 жыл бұрын

Adam Savage is a massive fan of Numberphile, so I wouldn't be surprised if it was the actual guy himself.

@screamsinrussian5773

4 жыл бұрын

Yes.

@timothymckane6362

4 жыл бұрын

"I reject your identity, and substitute my own."

@omikronweapon

4 жыл бұрын

I mean, the dude díd just recently do a video with Matt Parker.

@michaelmatter1222

4 жыл бұрын

Some people say it's him, I say it's a Myth :D

This video is delightful!! 💓

That number 4's dance is something.

James 👏 Grime 👏 makes 👏 my 👏 day 👏

14:04 you better don't want a tournement with 12 members (A, B, C, D, E, F, 1, 2, 3, 4, 5, 6), not 16.

@abhijiths5237

4 жыл бұрын

I think he said 6 team members not 16

@jedagelijksebraintraining

4 жыл бұрын

@@abhijiths5237 6 players do work because that is 3x3. Sorry if i missheard.

@andersbendsen5931

4 жыл бұрын

@@jedagelijksebraintraining 3 by 3 is nine. What they said was 6 by 6 won't work.

@brianmarco5873

4 жыл бұрын

@Je dagelijkse braintraining *** wiskunde-puzzels 6 team members with 2 teams make 12. As opposed to 6 player with 2 teams of 3 team members. The ping pong tournament described had 2 teams. I also misheard it as 16 though.

@howardchan3244

4 жыл бұрын

@@abhijiths5237 That's make sense. I am confused for a minute thinking I do not understand the problem.

See the article by Martin Gardener in November 1959 edition of Scientific American where he announced the discovery. Is there any connection to Parker Squares, as E T Parker was the mathematician who used a computer in 1959 to construct the first 10X10 counterexample to Euler's conjecture. Parker worked with Bose, and Shrikhande.

Nothing restores the balance of the universe like a Numberphile video featuring Dr James Grime.

I know probably no one really cares, but I solved it all on my own and I'm really proud.

12:45 I would love to have that thing hanging on my wall! Upvote for new merch!

@manioqqqq

Жыл бұрын

↑

There are more symmetries in your first working example: top middle two, bottom middle two; corner cards, left middle two, right middle - all of them fulfill the rule. And a few more.

What an amazing story. Loved it.

8:44 THE CUNNING SMILE

@GuyNamedSean

4 жыл бұрын

Like a giddy toddler that just pulled a fast one on his dad. I'll never stop loving James's cheeky enthusiasm for maths problems.

3:15 - dr James turned into Mickey Mouse on helium xD

It looks like you can handle this puzzle pretty easily by solving just for suits and just for types, making sure your solutions for both are not isomorphic to one another, then combining them into one grid. Edit: Just watched a bit later where he pretty much explicitly mentions that. My brain is on airplane mode.

3:43 Beautiful! I see that you've done more than Euler asked for, because you also have all four suits and all four denominations in 1) each diagonal broken two & two 2) each 2x2 quadrant 3) the central 2x2, and the four corners 4) the corners of each 3x3 block. (To get utterly magic square nerdy: your square is "complete", in magic square jargon, because any two cards that are two diagonal steps from one another are either two major suits (spades, hearts) or two minor, and either two high cards (ace, king) or two low.)

It's charming that James has a framed bit of numberphile paper in his house.

@renerpho

4 жыл бұрын

And not just any framed bit, but the paper from one of Numberphile's most iconic videos, signed by Ronald Graham himself. :-)

@98081

4 жыл бұрын

I think that's Brady's house.

But can it be done in 3d? I'll try something if I even manage to understand the proof. Edit: ok this is more complicated than i thought

@mementomori7160

4 жыл бұрын

I thought about the same thing, let's try it and make our own theorems

@user-be8ep2zd6r

4 жыл бұрын

for 3d grid n x n x n, do you still use these pairs { (A_1 ... A_n) x (B_1 ... B_n) } only ?

@Adomas_B

4 жыл бұрын

@@user-be8ep2zd6r maybe in 2 dimensions there's 2 parameters, A 1, so in 3 there could be 3, like A a 1

@Adomas_B

4 жыл бұрын

@@mementomori7160 are you in University? If not l, your chances of discovering something new is basically 0%

00:02 James' puzzles always get me going

You get more number combinations by utilising primary colours and mapping rainbows

Matt Parker rehabilitated.

I dont like that droopy bit on the 4 :(

You are the best host of numberphile.💖💖

I particularly enjoyed the organ sound effects for cards example