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.

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