the horizontal,vertical,and diagonal columns of a magic 9 square box all add to the same sum. use the digits 1-9 one time each to make a magic square.
Here is one example,
notice that each row, column and diagonal add up to 15
8 1 6
3 5 7
4 9 2
fat face
816
357
492
To create a magic 9 square box where the horizontal, vertical, and diagonal columns all add up to the same sum, we need to follow a specific set of steps. Let's go through the process together:
Step 1: Understand the requirements
In this case, we need to create a 3x3 square using the digits 1-9, such that each digit is used only once and the sum of each row, column, and diagonal is the same.
Step 2: Determine the sum
Since we have a 3x3 square, the sum we need to achieve in each row, column, and diagonal will be equal to the sum of all numbers from 1 to 9, divided by 3.
Sum = (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) / 3
Sum = 45 / 3
Sum = 15
Step 3: Place the numbers in the square
Start filling the square row by row using the digits 1-9, making sure to place each digit only once. Here's an example of one possible arrangement:
8 1 6
3 5 7
4 9 2
Step 4: Verify the sums
Check if the sums of each row, column, and diagonal match the desired sum (15 in this case):
Rows:
8 + 1 + 6 = 15
3 + 5 + 7 = 15
4 + 9 + 2 = 15
Columns:
8 + 3 + 4 = 15
1 + 5 + 9 = 15
6 + 7 + 2 = 15
Diagonals:
8 + 5 + 2 = 15
6 + 5 + 4 = 15
In this example, each row, column, and diagonal adds up to 15, satisfying the requirements of a magic square.
Note: There are multiple valid arrangements for a magic square. The example provided is just one possible solution.