The number of possible combinations of three distinct numbers from 1 to 9 that have a sum of 9 or 18 is

Question

Let A = [aij] 3 be a square matrix of order 3 whose elements are distinct integers from 1, 2, …, 9. The matrix is formed so that the sum of numbers in every row, column and diagonal is a multiple of 9.

The number of possible combinations of three distinct numbers from 1 to 9 that have a sum of 9 or 18 is

(A) 10

(B) 7

(C) 8

(D) 9

Answer 1

Answer is (A) 10

In a matrix

a₂₂ must be a multiple of 3(3, 6 or 9) because from the above possible combinations only 3, 6 and 9 are repeated four times in a row or column or diagonal.