What is a magic square matrix?
Table of Contents
What is a magic square matrix?
A Magic Square is a n x n matrix of the distinct elements from 1 to n2 where the sum of any row, column, or diagonal is always equal to the same number. Examples: If the prime diagonal and secondary diagonal sums are equal to every row’s sum and every column’s sum, then it is the magic matrix.
What is the sum of a magic square?
The well-known magic square below has the property that the three numbers in each of the three rows, the three columns and the two diagonals all add up to the same number 15. This number is called the magic sum of the square….Age 11 to 16.
| 2 | 7 | 6 |
|---|---|---|
| 4 | 3 | 8 |
What is magic square formula?
[1] X Research source You can find this number by using a simple math formula, where n = the number of rows or columns in your magic square. So, for example, in a 3×3 magic square, n = 3. m = n [ ( n 2 + 1 ) / 2 ] {\displaystyle m=n[(n^{2}+1)/2]} . So, in the example of the 3×3 square: sum =
What is the magic constant or magic sum of a magic square of size 11 in python?
| 46 | 8 | 16 |
|---|---|---|
| 44 | 12 | 33 |
| 28 | 26 | 11 |
| 5 | 37 | 31 |
| 48 | 9 | 15 |
How do you complete a magic square?
There are five easy steps.
- List the nine consecutive numbers in order.
- Add them up then divide by three.
- The very middle number in a consecutive number list is the number for the middle square.
- Apply the rules in the magic square solution diagram.
How does a magic square work?
A magic square is an n x n square with a whole number written inside each cell, so that the sum of the numbers in every row, in every column and in each of the main diagonals is equal. This number is called the magic number. The main diagonals are those that stretch from corner to corner.
How do you complete a magic square in math?
Magic Square Solution
- List the numbers in order from least to greatest on a sheet of paper.
- Add all nine of the numbers on your list up to get the total.
- Divide the total from Step 2 by 3.
- Go back to your list of numbers and the number in the very middle of that list will be placed in the center of the magic square.
How do you find the magic constant in a magic square?
The magic constant of a magic square of nth order can be found by dividing the sum of 1 to n2 by n; namely, the magic constant = n (n2+1)/2. Magic squares are called “magic squares” in English.
Why some matrix is called magic square?
Magic squares are called ‘magic’ because each row, column, and diagonal in the square has the same sum, called the magic constant. It takes a great deal of skill to be able to arrange numbers in a square to make all the rows, columns, and diagonals have the same sum.
How do you identify a magic square?
This is a magic square, if we see, the sum of each row, column and diagonals are 15. To check whether a matrix is magic square or not, we have to find the major diagonal sum and the secondary diagonal sum, if they are same, then that is magic square, otherwise not.