### Magic Square Party Trick – Numberphile

- by
**Theodore Winn** - 3 weeks ago
- 100 comments

Right, Brady, I’m gonna give you a mathematical gift. I’m not give you many mathematical gifts, I give you a very special one today. And, ehh now, to make it extra special, I often ask people when I do this. It’s one of my party tricks. Er…their age. But that feels a little impersonal. So, would you wanna give me a…err…arbitrary number between 21 and 65? What would you? What would you like? Brady: 42. Matt: 42!? Ahh, nerd! Ok! Right, so 42…42…42…40… I guess smaller… I guess here is…2. Right…there’s more I’m just…I’m starting with those digits. I’m gonna put a 5 in a… There I’m gonna put a 3…ahh…actually I put a 3 there and 6 there. I’m gonna change it as I go. That’s gonna be a 9, that’s gonna be a 10, 22, 23, 24, and 12! And what I’ve done for you there, if you err…double check all the numbers in the top row would add up to 42, if you go through and check those. The second row would add up to 42. And all the columns add up to 42, the diagonals 42, the opposite… I mean all 4 in the corner add up to 42, each 4 in the corner…it’s a magic square. I love magic square, one of the reasons I love this a lot, and to they that…that… For you Brady, that’s a gift magic square based on the number 42. Matt: What can you think? Brady: Now, make one for…58. 58, ok, this number of 58, this one is gonna be wildly different…at 58. So, I’m gonna put a 5 there, I’m gonna put a 4 there… I’m gonna put a 3 there, I’m gonna put a 6 there, I’m gonna put a 1 there, 8, and that one would be 38, and then… 39, and then 40, and there you are! Incredible amount of mental arithmetic later I’ve managed to… You look unimpressed, I gotta be honest. Brady: What I am… the first time I was impressed… now I think maybe you just using a pro-forma… Maybe, maybe all I’m doing is if you gave me the number “n”, then I’m going through, and I’m doing these all exactly the same every single time, and so I fill in those… And this is easy to remember, this is the multiple of 9. fifty-four, thirty-six, eighteen, seventy-two Then remember I’ve put 9 down there, 10, 11, 12… and then I do n-21, I do n-20, I do n-19, and I do n-18. And that is a magic square! The problem, of course, and the reason they get a bit suspicious for big numbers is you could look at this one here, and you go, “Wait they’re all quite small, what’s this?” What’s these massive 30s and 40s going on? They’ll be a little bit unimpressed. So, even though you gave me 58, out of no where, you look at this and be a little bit suspicious. Brady: So, that’s why age is often good. Matt: Age is often good, cause they tend to be in around the 30s and 40s is perfect, anything too big starts to go awry… Brady: What if they give you small? What if they give you like 8? Matt: Actually, that’s why I said between 21… So, age is very good, cause then, if someone said 21, you’ll have 0 there, which I’m kind of ok, whether you don’t mind 0, it goes 0, 1, 2, 3, anything smaller you get negative numbers. So, the square still works, if you gave me a tiny number, so, if you gave me something like emm “8”, then I would have, in that spot there, I have to subtract 21 off 8, then I have a -13 hanging out there. If I gave you a million? If you gave me a million, you’ll have massive massive numbers…

Here's a thought: Along with uploading these, you could upload another video of the complete, unedited interview (unlisted of course) for the hardcore numberphile fans like myself

0:25 42 42 Thoughty2

#python, just could not resist :p

n = 42

count = 0

square = [[0, 1, 12, 7], [11, 8, 0, 2], [5, 10, 3, 0], [4, 0, 6, 9]]

offsets = [(0, 20), (2, 21), (3, 18), (1, 19)]

for offset in offsets:

square[count][offset[0]] = n – offset[1]

count += 1

for List in square:

print List

Can you guys do a video of the graphic function y=x^x?

I have one of these squares that Matt made and signed for the number 32, from his show stand up maths at the Edinburgh fringe last year 😀

the four corner numbers also add up to whatever the number is

the four corner numbers also add up to whatever the number is

the 4 corner numbers also add up to the chosen number

That was a Parker Square of an attempt at making me believe there wasn't a trick behind that.

it's epic

and so the ParkerSquarepocalypse begins…

If ever this question has been answered pls. comment. okay heres the question:

what is the sum of

…(-3)+(-2)+(-1)+0+1+2+3…?

How did you know I was 42?

is there an easy way to regognize these numbers ?

Make a video on the function of a rubber duck!!!

at 0:09 it sounded like he said "potty tricks" instead of "party tricks" LOL

Could you do a video about algebra (zheng/fu/wu and fang cheng) and magic squares in china? its very interesting

"look at him think!" xD

can you see Brady's mind cogs, Matt?

i have question about number 3.

if i take number, that can be divided by 3 and sum up its digits, it will give me number that can be divided by 3. why is that?

i was expecting a parker square in this video.

I always watch Matt Parker in 0.5 speed. It's hilarious.

Quanotations

classic parker square

I love that every comment is about the Parker Square.

So this is the actual complete answer for life, the universe, and everything:

22-01-12-07

11-08-21-02

05-10-03-24

04-23-06-09

There's a youtuber called 42 😉

What about this?

3 7 3 3

3 3 7 3

7 3 3 3

3 3 3 7

I'm going to print off that n Magic square and memorise it, thanks Matt Parker!

Well that's a bit of a Parker square…

The answer to life the universe and everything is 42

I think the number at 3:33 on top was supposed to be 1,000,000,000.

Actually ages don't "tend to be" around thirties and forties! Come on.

If the magic number would be a millon it would definitely be a parker square

Please arabic😢.

His reaction to a 42 being a number of choice is priceless 🙂

just watched one of your shows in Leicester and just wanted to know, do you even lift bro?

Can just put 2s all over the place in case of 8

But I'm 19… Does that mean I can't come to matt's parties ? 🙁

all the numbers add to a billion, and you said a million… bit of a parker square

the first one was an indian magic square

42 equals 42.0 !!!!!!!!!420 IS REAL !!!!!!!!!

sadly this only works without repeats above 21+12 =33 otherwise two entries are the same.

But with 32, 33 and 34 numbers repeat themselves, right?

That 3 was a Parker Square of a 3

I have just two words this video…

Read More

W H A T I S S I X T I M E S S E V E N

#ParkerSquare

I was more impressed with the Parker Square.

Watching this exactly one year later! 😀

497 500 506 490 1993-borns like

505 491 496 501

492 508 498 495

499 494 493 507

Is there a video proving 1+1=2?

Classic Parker Square!

How to get beat up at parties trick

"Wow, I just turned 21! Now I'm finally old enough to…. have a magic square built around my age. Yep."

https://scratch.mit.edu/projects/158053442/

calling someone a nerd on a numberphile video is not an insult, but a compliment

Ahh, When we used to trust Matt Parker with Magic Squares. What Nostalgia.

is there a Nerd's Magic Square tshirt?

I saw a magician once combine this trick with another trick to create a magic square of a number that an audience member secretly thought up.

But if the trick fails, then it will be a Parker Square of a trick.

How does exactly a Parker Square work?

well 11 + 8 + 5 + 10 does not equal 42 it equals 34

34 is the perfect number to do this with, because you'll have the numbers 1-16 in a 4×4 grid, and, you can write them in order in a seemingly random sequence. I tried it. It looks more impressive.

I don't think he's qualified to talk about magic squares.

You are crazy

And bad😵💩

Number sudoku

But the mid-left and mid-right boxes don't work!!

You can't just do some boxes but not all

One thing I find interesting is that when he shows the magic square in the graphic, the 4 square that is one row above the center and the one below the center add up to the number (I'll say 42) but the 4 square that is one column left of the center and one right of the center does not. Would be interesting to see if it is possible to make it so that those would add to 42 as well.

Before I start watching, is it another parker square?

Is that a Parker Square?

Well, I use my personal method called par position that combines position of a number assigned to a letter, which I call 1432

A 1 2 3 4

B 5 6 7 8

C 9 10 11 12

D 24 25 26 27

Using my position algorithm I get

1 8 11 25

26 10 5 4

6 3 27 9

12 24 2 7

Is this going to be another Parker square

A magic square should contain distinct numbers, so n should be >= 34.

What about the squares at the sides? i.e. 11+8+5+10=34 in the 42 square, do those not count?

That’s not a parker square, but that is a parker 3.

Parker Square-ish when he explains it

Parker’s square

This magic square method was invented by the greatest MATHEMATICIAN OF ALL TIME SRINIVASA RAMANUJAN

This is my favourite membership video. So funny to see Matt dig his own hole

13 box fill only odd numbers and gets answer 42 how get

thankyou

This was my favorite trick when i was younger i was always curious about it seeing as i loved math

The guy is pausing the vid to get the answers

I was stuck on some homework and this helped alot

Hi! 35 not

Parker square of a video

Not all the 2×2's add up to the number.

Although this method is an awesome trick to show your friends, it has 1 flaw. What happens when the number you are given is the same as another number after you subtract it? Do you tell them to say a different number?

You can try 34 and you will find it more amazing.

Did You Notice All The Ones Add Up To Six And Six Times Seven Is 42

It still works for numbers <21

(Parker Square. PAAAAAARKEEEEERRRRRR SQUAAAAAAAAARRRREEEEE!)

Hi! I've done another pattern, (4 lines of square) : (n-20) – 8 – 12 – 0, 11 – 1 – (n-21) – 9 , 5 – 17 – 3 -(n-25) , 4 – (n-26) – 6 – 16, so I think there should be a lot of patterns.

Parker squares are better, just random numbers that add up to random amounts. They're a bit ugly but anyone can do them so much more inclusive.

That is a PARKER SQUARE!

The squares [2×1 2×2; 3×1 3×2] and [2×3 2×4; 3×3 3×4] don't add up to that sum

One of the best memories in our college days… As math majors we really enjoyed solving magic square.

If ur maths teacher gave u a qr code then stop

Dude, you do look like Monty Python =)

Matt: Tell me your age.

Person: 42.

Matt: I will make a magic square out of it.

Person: Are you a magician?

Matt: No, I'm a mathematician.

Person: Then what trick will you be doing?

Matt: Gimme a piece of paper.

Person: Here.

Matt: [

draws a magic square]Person: thanks. [

looks suspiciously]