MATT PARKER: 1, 68, 44, 28,
41 and 64
And so you, ok that's quite a nice magic square,
except it doesn't work.
If you add them up you get different numbers in different directions,
If I go through now and square all of these numbers,
that becomes a magic square.
or rather it becomes a semi magic square.
So this is so close to being a magic square of square numbers.
So all the rows add to the same number, all the columns add to the same number.
No one has ever found
a magic square that works properly both diagonals
and all the numbers are square numbers.
It's an open question in mathematics.
And so people actually compete. There are sorts of squares we haven't found,
so people try to find a 4-by-4 magic square with cube numbers,
or, you know, a 7-by-7 magic square with square numbers, right?
and so there are prizes for all the ones we haven't come across.
Just last year someone found the first 7-by-7 magic square with all cube numbers,
and they won a prize, they won 500 euros.
It's alright, I mean, you know and fame, and mathematical...
you know!? BRADY HARAN: What's their name?
MATT PARKER: I can take... yeah... BRADY HARAN: They're famous... MATT PARKER: Let me check my notes, ehh
Yeah, that really famous guy, ok!
Now in mathematics the word "fame" means
something slightly different to what it means to everyone else.
Eh, in maths means, "fame" means
every century someone will look your name up in obscure book.
So I thought, you know what, I could try to find one.
So I wanted to try and find the proper magic square, with all square numbers
cause there's 1000 Euros for that one, and that's what I'm after.
[3-by-3 or..?]
3-by-3, I'm a purist. Do you want to see what I've found?
Right, here's the one I found.
29, 1, 47, 41, 37, 1, 23, 41, 29
Alright! So there's my fella.
There are a few problems with this one.
For start, it does work! So, if I go through by square all of these,
And then I check the adding-up
The total of this square is 3051.
And it works for all the columns, it works for all of the rows.
It only works for one of the diagonals.
So this diagonal here works.
This diagonal here doesn't work.
and so it's semi magic square.
Also, as you may have spotted, some of the numbers are in there more than once.
So, you see there's two 41's, there's two 29's, there's two 1's!
Some people would say that makes it less of a magic square,
BRADY HARAN: I would say that!
MATT PARKER: You would say that, you are with the vast majority of humans in that...
BRADY HARAN: You can just put all the same number in it.
MATT PARKER: No, yeah ok, so no that's very good point.
So a magic square all the same number over and over
would still technically be a very disappointing magic square.
And so I mean, to be honest, it's a bit like:
You know, you always think your children or your pets are the greatest in the world
and you put a lot of videos of them up online.
For me, everyone else is like:
"It's not a very nice square, is it? Don't, should we tell Matt?"
"He seems so excited about it."
You know what? I am excited about it. This is my square!
And so I will admit I'm looking at it through rose-tinted square glasses.
But I like it, it's a semi magic square with repeated entries,
and it got square numbers in it and...
My find. BRADY HARAN: Has it got a name?
MATT PARKER: That hasn't got a name, I don't want to call it the "Parker Square",
because it doesn't work properly, it would be like: "Oh, that's a classic Parker Square."
or someone would do something that's almost right, but not quite, they would...
"That's a real Parker Square kind of move." So I'm not calling it the Parker Square!
BRADY HARAN: Matt, you know the video is called?
MATT PARKER: I'm calling it, oh, for crying out loud...
The first time you name something after me,
and it's something that's not quite right!
You know what? Maybe it'll become the mascot,
for giving things a go!
People suspect one may exist or may not, I don't know, but they can't rule it out.
But it's generally agreed:
it's not achievable with our current computing power
or our current number theory to be able to find one of these...
But I gave it a go, right? And of course, I didn't find it.
I found this. This adequate...
-You know, it's like...you know? BRADY HARAN: I'll tell you what, Matt.
I don't think this is our best Numberphile video,
but it was a Parker Square of a Numberphile video...
MATT PARKER: Stop trying to make Parker Square a thing!
[he he he he...]
ROGER BOWLEY: Or this diagonal, or that diagonal they add up. Or this little square in here. They all add up to the same number.
Which is 176.
JAMES GRIME: The magic hexagon, if it exists, has to be of size 3.
So it's three layers, you've got the one in the centre, you've got your second layer and your third layer...