Magic squares
Magic squares are among the Mathematical amusements.
The sum of the first k natural numbers is
A magic square is a square array of integers from 1 to n² is said to be of order n.
The sum of the integers from 1 to n² is 
So in a magic square the numbers in each row column and diagonal have the magic sum
This is to be a magic square. Each row, column, and diagonal is to add to the same number.
How can this magic square be completed?
Solution:
Odd Square Matrix
finding 4 corners Value D C A B
for matrix 3 x 3
3 x 3 odd square matrix
Sum is 15
Sum is 6 ( Number can be repeated and use only1,2 & 3)
Sum is 18
5 x 5 odd square matrix
Sum is 65
Numbers 1 to 25
Start 1 -- --- I First Row middle
Complete 25 -- --- Last Row middle
Number Entering Method
L shape
diagonal / if ends with no columns then L shape
diagonal / if ends with filled column next to the Row ↓
we can use this method for odd number matrix like 3,5,7,9,11,13,.....
step by step images
Step 1
7 x 7 odd square matrix
Sum is 175
9 x 9 odd square matrix
Sum is 369
11 x 11 odd square matrix
Sum is 671
13 x 13 odd square matrix
Sum is 1105
15 x 15 odd square matrix
Sum is 1695
17 x 17 odd square matrix
Sum is 2465
19 x 19 odd square matrix
Sum is 3439
21 x 21 odd square matrix
Sum is 4641
10 x 10 EVEN square matrix
Sum is 505
I TRIED UP TO 21 X 21 MATRIX
TRY MORE LEVEL
