Question

The numbers 1, 2,..., 9 are arranged in a 3 X 3 square grid in such a way that each number occurs once and the entries along each column, each row, and each of the two diagonals add up to the same value.

• A. 2
• B. 1
• C. 3
• D. 5

Answer 1

Answer: (C)

3

Answer 2

In accordance with the given information, the sum of elements in every column, every row, and both diagonals of the 3x3 matrix is constant and equals 15.
To illustrate, let's examine the matrix presented below:

6		2

Next, we will attempt to substitute values from 1 to 9 into the central grid, denoted as 'x'. If x =1 or x =3, the value in the bottom-left grid would exceed 9, which is not a valid possibility. Therefore, x cannot be equal to 2.
If x =4, the value in the bottom-left grid would be 9. However, in this case, the sum of the elements in the first column would exceed 15, making it impossible. Therefore, x cannot be 4. If x =5, the grid would appear as shown below:

6	7	2
1	5	9
8	3	4

Hence, for x = 5 all conditions are satisfied. We see that the bottom middle entry is 3. Hence, 3 is the correct answer.