kss-d blogGeR: tHe MAgiC $qu@rE

kss-d blogGeR: tHe MAgiC $qu@rE: "The other Day I was reading a novel when I encountered a interesting and catchy word.........yes......u got it..... Magic Square..... ..."

tHe MAgiC $qu@rE

The other Day I was reading a novel when I encountered a interesting and catchy word.........yes......u got it.....
 Magic Square.....
For those who don't know what a magic square is......let me tell.......
It is a square in which numbers are put according to it's order, whether it is of order 3 ie 3*3 or similar.
 and the special quality of that square is -- The sum of the no. whether added vertically, horizontally or diagonally remains same , provided the nos are not repeated.
  
HERE IS AN EXAMPLE OF 3*3 MAGIC SQUARE ----

So, I thought of making 1.  There i saw a order 4 magic square. So, no was filled in it from 1 to 16.

And if we total the sum then it comes by formulae....   n(n+1) /2  =  16(16+1) /2 =136
This is the sum of 16 boxes in a square. So the sum of 4 of them, which gives sum of any row or column is 136/4= 34.
This is the magic sum.
So, I applies this logic to find out magic sum for order 3 square.
It comes out to be 15.(give it a try........or check out above pic).
And after that what i was supposed to do was ----  find out those set of 3-3  nos. which give sum 15, and which can be fitted in the square to met the condition.
So i come up with these conditions or u can say equations........

1. 9+5+1
2. 9+4+2
3. 8+6+1
4. 8+5+2
5. 8+4+3
6. 7+6+2
7. 7+5+3
8. 6+5+4

 So these are the eight equations which are needed to fill the square.......   ;-)
U can look the symmetry which i used while forming them........It gives some ease.......

If we analyze the equations......then we get that
No. 5 has been used 4 times.....so it must be in center of the square.(coz we get 4 eqns with 5 as a common no which can only be in centre )
similarly no.2 has been used 3 times(6,8 and 4 also),,,,  so it(they)must be somewhere in corner of the square....

if we put no. 5 in center and proceed by filling other nos acc to the eqn........we find that we have made a magic square........It's easy........

This method is also applicable to squares of other order ...... but it will be cumbersome one for higher orders.......or for the special one.....if u wish to make.....like one that  ALBRECHT  DURER  made..
HERE IT IS........

JUST HAVE A GLIMPSE OVER THIS AND U WILL BE AMAZED............HE HAS MADE SUCH A MAGIC SQUARE ..........U CAN ALMOST FIND THE MAGIC SUM - 34......IN EVERY LINE.......EVEN IN 2*2 SQUARES..........OR THE KITS SHAPE U CAN SEE(2+10+8+14,6+12+14+2) ......OR SIDES OF RECTANGLES(5+9+12+8,3+2+14+15)....
AND IT ALSO DIPICTS THE YEAR IN WHICH HE MADE THIS 1514(CAN U SEE??).....AND HIS INITIALS ARE ALSO THERE ( 1 FOR A and 4 FOR D )......
SO IT'S NEXT TO IMPOSSIBLE FOR US (NORMAL) LIKE PEOPLE TO MAKE SUCH LIKE ART........BUT WE AS A STARTER CAN MAKE SIMPLER ONES.......

WHAT DO U SAY, GUYS?