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!! 💪
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
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.
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.
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.
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 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.
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.
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.
@Aleksandr A. Adamov 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?
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 :)
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!
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.
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 !
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?
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.
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 !
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.
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.
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!"
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)
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)?
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.
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.
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).
i’m interpreting this knowledge as more evidence that 6 is a volatile mathematical aberration. A 6-pointed star can’t be done without 2 lines because of how it interacts with the numbers 1-5, and a double latin square of size 6 can’t be done, which I’m guessing is for similar reasons. Plus it’s the sum AND the product of the first three natural numbers… it’s like it’s more highly divisible than any number was ever meant to be. Its connection to the beastly and arcane is pretty fitting
The rules don’t work out for a 6 by 6 Flat Torus, unless you Nash-isometric-embed it, with extra curled up squares/corrugations, into something like a Hévéa Torus. Hey, don’t knock it, they do those tortuous sleights of hand in String Theory all the time. 😀 As a fun-filled alternative: One might be able to make a 6 by 6 square work, if the surface was a special (holographic-like) 2D section of a 6D Calabi-Yau manifold. If nothing else it would be an interesting little exercise.
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! :)
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.
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.)
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 :)
I got to learn about latin hypercubes last semester in order to determine a reasonably random uniform selection of a multidimensional variable selection. I had to create 200 points distributed through 5 dimensions down the 'diagonal'. Then randomly swapped values between points along the same dimension. Ie n=2,x=2 swaps with n=10,x=10. The reason to do this was interesting. It meant that we could do a constant set of tests for whatever number of variables we came up with to test. The variables were being chosen to run a simulation between a parasite living off a population and succeeded or failed if they reached equilibrium or died/became unbounded.
@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.
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.
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.
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.
@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.
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
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.
It's interesting how Euler could come with some of the most important and famous math contributions in history, and also many times just guessed stuff whimsically.
