9 squares and the 5 is in the middle, fill in the other squares using 1-9 to make all columns, rows, and diagonals equal.
ah yes, the classic odd-order magic square.
Place 1 in the middle of the top row. Move upward diagonally, counting as you go. Wrap across at boundaries. Move down when you can't move due to a full square or a corner boundary:
8 1 6
3 5 7
4 9 2
To solve this puzzle, you need to manipulate the numbers 1-9 to fill in the other squares around the 5, ensuring that all columns, rows, and diagonals have the same sum. Here's how you can approach:
1. Start by placing the number 5 in the center square. Since the sum of each row, column, and diagonal should be equal, this will be the target sum for each line.
2. Now, let's focus on placing the remaining numbers. Begin by considering the diagonals first, as they are the easiest to determine. Both diagonals pass through the center square, so we can assign two numbers to each diagonal. Place the numbers with the same parity (even or odd) along one diagonal, and the remaining numbers along the other.
3. Next, consider the rows and columns. Start by placing the missing numbers in the top row and the leftmost column. Ensure that these numbers are different from the ones already placed in the diagonals.
4. After filling in the first row and left column, move to the next row and place the remaining numbers, excluding the first number you used in the row above. Repeat this process until all rows are filled.
5. Similarly, move to the next column and fill in the numbers, excluding the first number used in the column to the left. Repeat until all columns are filled.
6. Finally, check if the sum of each row, column, and diagonal is equal to the target sum (in this case, 15, as the center is 5). If any sum is not equal, adjust the numbers until all sums are equal.
By following these steps, you should be able to fill in the remaining squares with numbers 1-9 in a way that satisfies the condition of having equal sums in all columns, rows, and diagonals.