Magic squares questions with solutions are provided here for practice. A magic square is an arrangement of n2.numbers in an n × n matrix form, where n > 2. These n2 numbers are in an arithmetic progression. This n × n arrangement of numbers is in such a way that the sum of the numbers in each row, column and diagonal is always the same.
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The number which is equal to the sum of each row, column and diagonal is called the magic sum constant M.
If the magic square numbers are from 1 to n2, then
M = n(n2 + 1)/2.
Learn more about magic square puzzles.
The Story of Magic Squares
![](https://cdn1.byjus.com/wp-content/uploads/2021/10/Magic-Square.jpg)
Practice Magic Squares Questions with Solution
Let us practise some magic squares questions.
Question 1:
Solve the magic square problem, whose sum is 30.
Solution:
Given the sum is 30
∴ for the first row 8 + 18 + __ = 30
⇒ 8 + 18 + 4 = 30
Similarly, 2nd column =18 + 10 + __ = 30
⇒ 18 + 10 + 2 = 30
In this way, by completing the missing numbers, we get the magic square
Question 2:
Complete the following magic square:
Solution:
A property of a 3 × 3 magic square is that when the middle number of the grid is multiplied by 9 and then divided by 3, gives the sum of the magic square
∴ (9 × 12)/3 = 108/3 = 36
Thus, each row, column and diagonal sum up to 36.
So, completing the missing numbers, we get the magic square
Question 3:
Solve the following magic square whose sum is 50:
Solution:
Given the sum is 50, then in the 2nd column,
13 + __ + 10 + 16 = 50, solving this we get the missing number 11. Finding all the numbers in this way, we get the magic square
Question 4:
Complete the magic square whose rows, columns and diagonals sum up to 65.
Solution:
Since the sum of each row, column and diagonal is 65. Hence the missing numbers of the magic square are
Question 5:
Complete the given magic square whose sum of each row, column and diagonal is 72.
Solution:
Given the sum of each row, column and diagonal is 72
∴ 21 + 26 + 25 = 72
21 + 28 + 23 = 72 and so on.
The magic square is:
Also, go through:
Question 6:
Solve the following magic square:
Solution:
A property of a 3 × 3 magic square is that when the middle number of the grid is multiplied by 9 and then divided by 3, gives the sum of the magic square
∴ (15 × 9)/3 = 45
Then, 24 + 3 + 18 = 45
And 12 + 15 + 21 = 45 and so on.
The magic square is:
Question 7:
Solve the 4 × 4 magic square, which begins with 1 and ends with 16.
Solution:
Given,
a = 1, l = 16, n = 16
Sum of all the numbers in the magic square = sum of n terms of an AP with last term l = n/2(a + l)
= 16/2 (1 + 16) = 8 × 136
Sum of each row, column and diagonal = 136/4 = 34.
Thus, the magic square is:
Question 8:
Solve the following magic square:
Solution:
In a 3 × 3 magic square,
Sum of each row, column and diagonal = middle element × 3 = 1.5 × 3 = 4.5
Thus, calculating each missing number we get,
Question 9:
Find the value of x and complete the magic square:
Solution:
In a 3 × 3 magic square,
Sum of each row, column and diagonal = middle element × 3 = 6 × 3 = 18
∴ (x – 1) + 6 + (x + 1) = 18
⇒ x = 6
Thus, calculating each missing number we get,
Question 10:
Solve the following 4 × 4 magic square, whose sum is 58.
Solution:
First row: 22 + 8 + 9 + 19 = 58
Third column: 9 + 16 + 12 + 21 = 58 solving so on, we get
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Practice Questions on Magic Squares
1. Solve the following magic squares:
2. Solve the 4 × 4 magic square whose magic sum is 50.
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