Complete the adjoining magic square. (Hint: in a 3 × 3 magic square, the magic sum is three times the central number.)

First, let us understand what magic square is.

A magic square is an arrangement of numbers in a square in such a way that the sum of each row, column, and diagonal is one constant number, the so-called “magic sum” or sometimes “magic constant”.

The magic number is given as,

Magic number = 3 × (central number)

⇒ Magic number = 3 × 7

⇒ Magic number = 21

This means, sum of rows = 21.

Take row 2,

Sum of row 2 = 3 + 7 + ?

⇒ 21 = 3 + 7 + ?

⇒ ? = 21 – 10

⇒ ? = 11

Also, in column 1,

Sum of column 1 = 8 + 3 + ?

⇒ 21 = 8 + 3 + ? [∵ Magic sum = 21]

⇒ 21 = 11 + ?

⇒ ? = 21 – 11

⇒ ? = 10

We get,

Also, along the diagonal, we can say that

Sum of diagonal = 8 + 7 + ?

⇒ 21 = 15 + ?

⇒ ? = 21 – 15

⇒ ? = 6

We get,

Here, Sum of third column is the magic number.

⇒ Sum of third column = ? + 11 + 6

⇒ 21 = ? + 17

⇒ ? = 21 – 17

⇒ ? = 4

We get,

For X and Y,

We can say that,

Sum of first row = 21

⇒ 8 + X + 4 = 21

⇒ 12 + X = 21

⇒ X = 21 – 12

⇒ X = 9

Sum of third row = 21

⇒ 10 + Y + 6 = 21

⇒ 16 + Y = 21

⇒ Y = 21 – 16

⇒ Y = 5

We get,

Thus, this is the magic square.