In the magic square, each row, column and diagonal have the same sum. A magic square with an order of 5 is shown below. Notice that the number that is located in the center of the square is 13. Middle values exist only for the case where n is an odd number. What is the middle value for the magic square with an order of 7?
Each row/column adds to n^2(n^2+1)/2n = n(n^2+1)/2
with n=7, that is 175
The center column forms an arithmetic sequence such that
n/2 (2 + (n-1)d) = n(n^2+1)/2
or, d = n+1
Thus, the (n+1)/2 cell has the value 1 + (n+1)/2 (n) = 1 + n(n+1)/2
So the center column forms the sequence 1,9,17,25,...
the center square. 1 + 7^2/2 = 25
There are, of course, many other ways to form a magic square, where the cells have different values.
To find the middle value for a magic square with an order of 7, we need to determine the number located in the center of the square.
In a magic square of odd order, the center value is always equal to the average of the lowest and highest values in the square.
For example, in a 7x7 magic square, the lowest value is 1 and the highest value is 49 (7^2).
So, the middle value for the magic square with an order of 7 would be:
(1 + 49) / 2 = 25
To find the middle value for the magic square with an order of 7, we can follow the pattern and logic of constructing magic squares.
A magic square of order n is constructed by placing the integers from 1 to n^2 in a square grid of size n x n, such that the sum of the numbers in each row, column, and diagonal is the same.
In a magic square with an odd order (like 5 or 7), the middle value is located at the center of the square.
To calculate the middle value, we need to determine the value that is at the center position. Since 7 is an odd number, the center position would be at the ((n+1)/2, (n+1)/2) position.
For an order of 7, the center position would be at ((7+1)/2, (7+1)/2) = (4, 4).
Therefore, the middle value for the magic square with an order of 7 is at position (4, 4).