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

The Correct Option is C

To solve this problem, understand that you are tasked with arranging the numbers 1 through 9 in a 3x3 grid such that the sums of each row, each column, and both diagonals are equal. This is effectively creating a magic square.

Step 1: Calculate the Magic Constant

The sum of numbers 1 to 9 is:

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45

Since the square is 3x3, each row, column and diagonal must have a sum of:

Sum = Total Sum / 3 = 45 / 3 = 15

Step 2: Arranging Numbers Properly

The arrangement can be achieved as follows:

2	9	4
7	5	3
6	1	8

Step 3: Verify the Arrangement

• Rows: 2+9+4=15, 7+5+3=15, 6+1+8=15
• Columns: 2+7+6=15, 9+5+1=15, 4+3+8=15
• Diagonals: 2+5+8=15, 4+5+6=15

With this arrangement, both diagonals, all rows, and all columns sum to 15, confirming that it is a magic square.

The correct answer is 3 for the common sum of the numbers in each row, column, and diagonal.