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Magic Square Party Trick – Numberphile

Magic Square Party Trick – Numberphile


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…

Author Since: Mar 11, 2019

  1. 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

  2. #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

  3. 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 😀

  4. 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…?

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

  6. 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?

  7. 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

  8. 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.

  9. 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.

  10. 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.

  11. 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

  12. 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?

  13. 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.

  14. 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.

  15. 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

  16. 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 ]

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