Note: A magic square is a ‘n x n’ square grid (where ’n’ is the number of cells on each side) filled with distinct positive integers in the range 1, 2…, n2 such that each cell contains a different integer and the sum of the integers in each row, column and diagonal is equal. The sum is called the ‘Magic Constant’ or ‘Magic Sum’ of the magic square.

- Numbers used in the Magic Square
- Number of ways we get the ‘Magic Constant’
- The Yantra Itself

Let’s discuss them all.

Numbers used in the Magic Square

Per definition, a normal magic square of ‘n x n’ will have numbers with the below specifications: –

- Numbers are in sequence
- Numbers starting from 1
- Up to n2

Figure (A) shows the ‘Uvasaggaharam Magic Square’ known as non-normal magic square.

On initial look it seems it has some random numbers.

- Numbers are out of sequence
- Numbers are starting from 0
- Up to 3n2–1

Here are the numbers in ascending order — [0,5,10,15,20,26,27,28,31,32,33,36,37,38,41,42,43,46,47,48,54,59,64,69,74] which doesn’t give any pattern. But when we take the difference of the consecutive numbers (m — m-1) we have beautiful palindrome number sequence — [5,5,5,5,6,1,1,3,1,1,3,1,1,3,1,1,3,1,1,6,5,5,5,5]. Plotting a line graph in Figure (B) which is symmetric on ‘Y’ axis, meaning there is a sequence/pattern followed.

Trying a different approach, write all the number from 0 to 74 in group of 5 and highlighting the magic numbers give the ‘Glide Reflection Symmetric’ Figure ©

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