Arrange the digits 1-9 in 3 rows and 3 colums, in such a way that each row across and down has the same total. Hint: each row will total 15
8 1 6
3 5 7
4 9 2
notice even my diagonals add up to 15
To solve this puzzle, we need to arrange the digits 1-9 in a 3x3 grid such that each row across and down has the same total of 15.
Let's start by placing the number 5 in the middle of the grid as it is the only way to achieve the total of 15 in all possible combinations. We can place any number next to it in any row or column.
Now, we can look at the possibilities for the remaining numbers:
1. Placing 9 in any corner:
If we place 9 in a corner, such as the top left corner, we need to find two other numbers that sum up to 6 (15 - 9 = 6). The only possible pair is 1 and 5. We can place them in the top row, one on the left and the other on the right of the corner, forming a row that sums up to 15. Now, we can complete the grid by placing the remaining numbers in the middle and bottom rows.
2. Placing 9 in a non-corner position:
If we place 9 in a non-corner position, such as the top middle or center left, we need to find two other numbers that sum up to 6 (15 - 9 = 6). The only possible pair is 2 and 4. We can place them in the same row or column as the 9, forming a row or column that sums up to 15. Now, we can complete the grid by placing the remaining numbers in the other rows and columns.
To summarize, here are two possible arrangements that satisfy the given conditions:
Arrangement 1:
9 1 5
2 5 8
4 3 6
Arrangement 2:
2 9 4
7 5 3
6 1 8
In both arrangements, each row across and down has the same total of 15.