Question

Find the value of magic square.

Answer 1

Hint: First, we will assume the empty spaces in the magic square to be some random variable say x, y, z, a, b, c. So, we will get the square something like this.

Then, we should know that in a magic square the sum of all numbers in each row, column and diagonal are equal to 15. So, making equations and solving, we will get each value of variables.

Complete step-by-step answer:
Here, we should know that the concept of solving a magic square is that the sum of all numbers in each row, column and diagonal are equal to 15.
So, we will assume some variables in empty spaces in the square. We get as

As we know the sum of every row column and diagonal should be equal to 15. So, taking first row, we get equation as
$7+x+17=15$
On solving we get x as,
$x=15-24=-9$ ……………………..(1)
Now, taking second column we get as
$x+5+b=15$
On putting value of x, we get value of b as
$-9+5+b=15$
On further solving, we get
$b=15+4=19$ ………………………..(2)
Now, taking the first diagonal. We get as
 $7+5+c=15$
On solving, we get value of c as
$c=15-12=3$ ………………………….(3)
Now, taking second diagonal, we get as
$17+5+a=15$
So, value of ‘a’ will be
$a=15-22=-7$ …………………………(4)
Now, considering first column, we get y as
$7+y+a=15$
On putting value of a, we get y as
$7+y-7=15$
$y=15$ …………………………(5)
We will take middle row to find z, we get as
$y+5+z=15$
$15+5+z=15$
On solving, we get as
$z=15-20=-5$ ………………………..(6)
So, magic square looks like:

Thus, we got all the values of magic square.

Note: Students should know the concept of magic square otherwise they will assume the sum to be different from 15 i.e. let’s say if the assumed sum is to be equal to 10 then the answer of magic square will be different. So, it is important that concepts should be known properly before solving this type of problem.