Question

A magic square is an array of numbers having the same number of rows and columns and the sum of numbers in each row, column or diagonal being the same. Fill in the blank cells of the following magic square:

(i)

	8	13
	12
11

(ii)

22		6	13	20
	10	12	19
9	11	18	25
15	17	24	26
16			7	14

Answer 1

(i) It can be seen that diagonally, 13 + 12 + 11 = 36.
Thus,
Number in the first cell of the first row = 36 − (8 + 13) = 15
Number in the first cell of the second row = 36 − (15 + 11) = 10
Number in the third cell of the second row = 36 − (10 + 12) = 14
Number in the second cell of the third row = 36 − (8 + 12) = 16
Number in the third cell of the third row = 36 − (11 + 16) = 9

15	8	13
10	12	14
11	16	9

(ii) It can be seen that diagonally, 20 + 19 + 18 + 17 + 16 = 90.
Thus,
Number in the second cell of the first row = 90 − (22 + 6 + 13 + 20) = 29
Number in the first cell of the second row = 90 − (22 + 9 + 15 + 16) = 28
Number in the fifth cell of the second row = 90 − (28 + 10 + 12 + 19) = 21
Number in the fifth cell of the third row = 90 − (9 + 11 + 18 + 25) = 27
Number in the fifth cell of the fourth row = 90 − (15 + 17 + 24 + 26) = 8
Number in the second cell of the fifth row = 90 − (29 + 10 + 11 + 17) = 23
Number in the third cell of the fifth row = 90 − (6 + 12 + 18 + 24) = 30

22	29	6	13	20
28	10	12	19	21
9	11	18	25	27
15	17	24	26	8
16	23	30	7	14