Magic squares - brain teasers ???!!!

Magic squares are the arrangement of numbers in n X n cells such that addition along the horizontal or vertical or diagonal direction yields same sum. Think it is difficult to solve. Actually it is pretty easy if you know the trick. Let me see...
8 1 6
3 5 7
4 9 2

This one is a magic square with sum equal to n(n*n + 1)/2 = 15

What about n=7, 9, 0r 57....think it is a problem nope...


take a small bit of paper and say for n = 3, draw the cells. Since n is a odd number here, start populating it from the uppermost - middle square starting from 1

X 1 X
X X X
X X X
Now, fold the paper vertically. We find that, S33 comes above diagonally over 1. Fill it up as 2.

X 1 X
X X X
X X 2

Now the second fold is horizontal. So, S21 will come diagonally above 2. Fill it up as 3.

X 1 X
3 X X
X X 2
Ouch!...there is a 1 already. Fear not! Since vertical fold would still yield the place of 1(S12) as the possible location which is already filled, go to the cell just below 3. Fill it up as 4 and lo!!! I can fill up till 6 in one shot.
X 1 6
3 5 X
4 X 2

Now, a horizontal fold does not yield any cell and a vertical fold yields the cell S33 which is already occupied by 2. So, go to the cell below 6 and fill it up as 7. Horizontal fold. Fill up 8 at S11. The remaining S32 will be filled up with 9 (you can fold and check).

8 1 6
3 5 7
4 9 2 Voila!!! There is your magic square.
You can follow this procedure for any value of n.
Note:
1. n=odd; start in the middle upper most cell. n = even; start at S11
2. Alternate horizontal and vertical folds.
3. When no cell is available, go to the cell below.

If I have left anyother rules mail me at vind@siu.edu
I tried and got this:
17 24 1 8 15
23 5 7 14 16
4 6 13 20 22
10 12 19 21 3
11 18 25 2 9


Enjoy!!!!

  ¶ 1:44 PM