MagicSquare

The word Magic in Mathematics will attracts every one.

The magic square is an arrangement of numbers in a square grid such that sum of numbers in each row, column and diagonal will obtain the same result.

The sum which is obtained is called

**or magic number.***magic constant*
It is possible to construct a normal magic square of any size exept 2*2.

Mathematical formula to obtain magic constant:(SumOfNumbers/NumberOfRows)

:N(N+1)/2*R

R - number of rows or column.

N - total number of blocks =R*R.

MagicSquare (5*5)

__Method 1:__
steps to be followed to obtain the magic square.

*First number in the magic square should be inserted in the middle block of first row.

*Next insertion is to be made in a block as indicated by the arrows in the above figure.(5*5)

*Insert the remaining numbers by following the indication.

*By following the above procedure, if you get a block which is already inserted then insert the number below that block.

*Follow the above procedure to obtain complete magic square.

Method 2:

We can obtain magic square numbers by using simple mathematical formula.

Formula to obtain

*I*_{th}row and*J*_{th}column number:

__=n ( ( I+J-1+ ( n/2 ) mod n ) +( ( I+2*J-2 ) mod n ) +1__
Try this out

let us consider a magic square of order n=3

let I=1 J=1

=n ( ( I +J-1+ ( n/2 ) % n ) +( ( I+2J-2 ) % n ) +1

=3 ( ( 1+1-1+ (3/2 )%3 )+ ( ( 1 + 2*1 - 2)%3 ) + 1

=3(2) + 1 + 1

=8

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Try this:

Hope you like :)

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