Question

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

(i)

	9	2
	5
8

(ii)

16	2
	10
		4

(iii)

2	15	16
9	12
		7	10
14			17

(iv)

	18	17	4
		14	11
	9	10
19			16

Answer 1

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 $=15-(9+2)=15-11=4$

[$\because$ 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