Uncovering the Mystery of Magic Squares

[soeren]

Magic Square

Hello,

Don't know, which forum, so i put it to general...

Yesterday i saw something like an magician on an exposition, showing some math to angle for attention.

He asked the audience to give him a number between 41 and 100. So he got the 47.

He worked out a magic square _very_ quickly.

It was that one:
4 18 14 11
15 10 5 17
9 12 20 6
19 7 8 13

You see, that the horizontal lines, the vertical lines, and all possible 2x2 - squares have the sum of 47...


How did the magician do that?


I've found some links here:
http://mathworld.wolfram.com/MagicSquare.html
http://en.wikipedia.org/wiki/Magic_Square

But i don't know how to adapt the instructions for constructing an squad with doubly even order to other sums of the lines, etc ..


Can someone please help me?
It would be great :-)


greets
Soeren

 

[snoble]

Could he just have a handful of these such squares (I have no idea how he found them originally) and then just be adding on squares of all ones? Then all you would need is one for 41,42,43,44 and you'ld have the squares for 41 and up. You already have the square for 43 now right?
3 17 13 10
14 9 4 16
8 11 19 5
18 6 7 12
If you rehearse enough I imagine you can recall and add the numbers as fast as you can write them. Just a guess... no idea how you find the other 3 squares

 

[soeren]

Then all you would need is one for 41,42,43,44 and you'ld have the squares for 41 and up. You already have the square for 43 now right?

Yes that's an interesting idea...

45 = 41 + 4*1
46 = 42 + 4*1
47 = 43 + 4*1
48 = 44 + 4*1
49 = 41 + 4*2
...
100 = 44 + 4*14

He said that it would be much easier to do with 48.
Does that fit?


thanks for your answer!

greets
soeren

 

[soeren]

any suggestions how he found these squares for 41, 42, ... ?

Or does someone of you know the other squares?

greets
soeren