Answer :

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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