arrange the decimals 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8 and 5.9 in the square grid with 3 colums and 3 rows pattern to make the sum of the numbers in each row, column, and diagonal equal.
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5.1 5.9 5.9
5.6 5.2 5.7
5.8 5.4 5.3
To solve this problem, we need to arrange the given decimals in a 3x3 square grid pattern such that the sum of the numbers in each row, column, and diagonal is equal.
Step 1: Let's start by arranging the decimal numbers randomly in a 3x3 grid:
5.1 | 5.2 | 5.3
-----|-------|-----
5.4 | 5.5 | 5.6
-----|-------|-----
5.7 | 5.8 | 5.9
Step 2: Now, let's calculate the sum of the numbers in each row, column, and diagonal.
Sum of rows:
Row 1: 5.1 + 5.2 + 5.3 = 15.6
Row 2: 5.4 + 5.5 + 5.6 = 16.5
Row 3: 5.7 + 5.8 + 5.9 = 17.4
Sum of columns:
Column 1: 5.1 + 5.4 + 5.7 = 16.2
Column 2: 5.2 + 5.5 + 5.8 = 16.5
Column 3: 5.3 + 5.6 + 5.9 = 16.8
Sum of diagonals:
Diagonal 1 (top left to bottom right): 5.1 + 5.5 + 5.9 = 16.5
Diagonal 2 (top right to bottom left): 5.3 + 5.5 + 5.7 = 16.5
Step 3: The sums of rows, columns, and diagonals are not equal in our initial arrangement. Therefore, we need to rearrange the numbers until we find a solution.
One possible rearrangement that satisfies the conditions is:
5.2 | 5.7 | 5.3
-----|-------|-----
5.9 | 5.5 | 5.1
-----|-------|-----
5.4 | 5.6 | 5.8
Now, let's re-calculate the sums of rows, columns, and diagonals:
Sum of rows:
Row 1: 5.2 + 5.7 + 5.3 = 16.2
Row 2: 5.9 + 5.5 + 5.1 = 16.5
Row 3: 5.4 + 5.6 + 5.8 = 16.8
Sum of columns:
Column 1: 5.2 + 5.9 + 5.4 = 16.5
Column 2: 5.7 + 5.5 + 5.6 = 16.8
Column 3: 5.3 + 5.1 + 5.8 = 16.2
Sum of diagonals:
Diagonal 1 (top left to bottom right): 5.2 + 5.5 + 5.8 = 16.5
Diagonal 2 (top right to bottom left): 5.3 + 5.5 + 5.4 = 16.2
In this arrangement, all the sums of rows, columns, and diagonals are equal to 16.5.
Note: There might be other valid arrangements that satisfy the conditions, so feel free to explore other possibilities.