Sriramachakra

Let M be a magic square of order 4 and let it be represented by matrix as follows:

${\displaystyle M={\begin{bmatrix}a_{11}&a_{12}&a_{13}&a_{14}\\a_{21}&a_{22}&a_{23}&a_{24}\\a_{31}&a_{32}&a_{33}&a_{34}\\a_{41}&a_{42}&a_{43}&a_{44}\\\end{bmatrix}}}$

The numbers in each row, and in each column, and the numbers that run diagonally in both directions, all add up to the number 34. M is called a strongly magic square if the following condition is satisfied:[5]

For all m, n such that 1 ≤ m ≤ 4, 1 ≤ n ≤ 4, we have

${\displaystyle a_{m,n}+a_{m,n+1}+a_{m+1,n}+a_{m+1,n+1}=34}$,

where it is assumed that if a subscript exceeds 4 it is replaced by 1 (wrapping around rows and columns).

For example in a strongly magic square M the following must be true.

${\displaystyle a_{23}+a_{24}+a_{33}+a_{34}=34}$ (taking m = 2, n = 3)

${\displaystyle a_{24}+a_{21}+a_{34}+a_{31}=34}$ (taking m = 2, n = 4)

${\displaystyle a_{44}+a_{41}+a_{14}+a_{11}=34}$ (taking m = 4, n = 4)

One can easily verify that the magic square represented by the Sri Rama Chakra is a strongly magic square.

• Pandiagonal magic square

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