 # Magic Square – Definition, Facts, Examples | How to Solve a Magic Square?

A magic square is a puzzle the addition of numbers in every row, column, and diagonal are the same. Every magic square has an order which is nothing but the number of rows x number of columns. Check out the rules to form a magic square and the steps to solve the magic square puzzles in the following sections. You can also find the questions on number patterns on this page.

## What is Magic Square?

Magic squares are square grids with a special arrangement of numbers in those grids. The numbers are special because every row, column and the diagonal sum is the same number. No number is repeated in the magic square.

While arranging the numbers in the grids, see the sum of numbers in every row, every column and diagonal are equal. The smallest magic square possible is 3 x 3. The number of elements in the magic square is the multiplication of the square order.

Example: The sum of numbers in all rows = 15
The sum of numbers in all columns = 15
The sum of numbers in both diagonals = 15
Therefore, it is a 3 x 3 magic square.

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### Interesting Facts about Magic Square Puzzles

• We need to have 3² = 9 or 4² = 16 or 5² = 25 different numbers are required to form a magic square.
• We can frame multiple magic squares with the given set of numbers.
• The number of elements in the magic square is its order.
• The order of a magic square N x N means it has N number of rows and N number of columns.

### Steps for Forming a Magic Square | Magic Square Rules

Students can get the simple guidelines to form a magic square in the below-mentioned sections.

• Get the set of numbers to be inserted in the magic square.
• Using the trial and error method, place the numbers in the square grids.
• Remember that the sum of numbers in every row, every column, and diagonal are equal.
• At last, check the condition is satisfied or not.

### Magic Square Puzzle Examples

Question 1:
Check whether the following is a magic square or not. Solution:
The important rule to say a square grid is a magic square is the sum of numbers in every row, column and diagonal is the same number.
The sum of elements in first row = 9 + 6 + 3 + 16 = 34
The sum of elements in second row = 4 + 15 + 10 + 15 = 34
The sum of elements in third row = 14 + 1 + 8 + 11 = 34
The sum of elements in fourth row = 7 + 12 + 13 + 2 = 34
The sum of elements in first column = 9 + 4 + 14 + 7 = 34
The sum of elements in second column = 6 + 15 + 1 + 12 = 34
The sum of elements in third column = 3 + 10 + 8 + 13 = 34
The sum of elements in fourth column =16 + 5 + 11 + 2 = 34
The sum of elements in one diagonal = 9 + 15 + 8 + 2 = 34
The sum of elements in second diagonal = 7 + 1 + 10 + 16 = 34
Therefore, the given is a magic square 4 x 4.

Question 2:
Find the missing numbers in the given 5 x 5 magic square. Solution:
In the given grid, one diagonal has all the elements. So, find the sum of numbers.
The sum of the numbers of 1st diagonal = 11 + 12 + 13 + 14 + 15 = 65
So, every row, column and diagonal sum should be 65.
The missing number in the 2nd diagonal = 65 – (23 + 13 + 8 + 3)
= 65 – 47 = 18
The missing elements in the 4th row = 65 – (10 + 18 + 1 + 14)
= 65 – 43 = 22
The missing element in 5th column = 65 – (3 + 9 + 22 + 15)
= 65 – 49
The sum of missing elements in the first row = 65 – (11 + 20 + 3)
= 31
Let the missing numbers be 24, 7
The missing number in 2nd column = 65 – (24 + 12 + 18 + 6)
= 5
The missing number in 3rd column = 65 – (7 + 13 + 1 + 19)
= 25
The missing number in 2nd row = 65 – (12 + 25 + 8 + 16) = 4
The missing number in 5th row = 65 – (23 + 6 + 19 + 15) = 2
So, the 5 x 5 magic square puzzle is follows. Question 3:
Write the number of possible similar magic squares for the numbers from 1 to 9.
Solution:
The list of numbers from 1 to 9 is 1, 2, 3, 4, 5, 6, 7, 8, 9
See that the sum of numbers in all rows, columns and diagonals is 15.
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