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Question

Complete each one of the following magic squares by supplying the missing numbers:

(i)

92
5
8


(ii)

162
10
4


(iii)

21516
912
710
14 17


(iv)

18174
1411
910
19 16

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Solution

In a magic square, the sum of each row is equal to the sum of each column and the sum of each main diagonal. By using this concept, we have:

(i) Sum of the elements diagonally =8+5+2=15

Like that, the missing element in first row =15(9+2)=1511=4

[ Sum of all elements in a row = Sum of all elements in a column = Sum of all elements diagonally]

In the similar way, we can find for all columns and rows.

4 9 2
3 5 7
8 1 6

(ii) In this case, Sum of all elements in a row = Sum of all elements in a column = Sum of all elements diagonally =30

16 2 12
6 10 14
8 18 4


(iii) In this case, In this case, Sum of all elements in a row = Sum of all elements in a column = Sum of all elements diagonally =38

2 15 16 5
9 12 11 6
13 8 7 10
14 3 4 17


(iv) In this case, Sum of all elements in a row = Sum of all elements in a column = Sum of all elements diagonally =46

7 18 17 4
8 13 14 11
12 9 10 15
19 6 5 16

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