Magic square puzzles with missing numbers to complete the grid so each row, column, and diagonal sums to the magic number.

To solve the problem, we need to determine the missing values in the tables based on the given "magic number" and any patterns or rules that might be governing the relationships between the numbers in the tables.

Table A: The magic number is 9.0

The table is as follows:

| | | |
|-------|-------|-------|
| | | 3.6 |
| 1.8 | 3.0 | |
| | | |

#### Step 1: Identify the pattern
We are given that the "magic number" is 9.0. This suggests that there might be a relationship involving the sum, product, or some other operation that results in 9.0.

#### Step 2: Analyze the given numbers
- The number 3.6 is already filled in.
- The numbers 1.8 and 3.0 are also given.

#### Step 3: Test possible relationships
Let's test if the sum of the numbers in each row, column, or diagonal equals 9.0.

- Row 1: We have one number (3.6). Let's denote the missing numbers in Row 1 as \( x \) and \( y \). So, the equation for Row 1 would be:
\[
x + y + 3.6 = 9.0
\]
Simplifying:
\[
x + y = 5.4
\]

- Row 2: We have two numbers (1.8 and 3.0). Let's denote the missing number in Row 2 as \( z \). So, the equation for Row 2 would be:
\[
1.8 + 3.0 + z = 9.0
\]
Simplifying:
\[
4.8 + z = 9.0
\]
\[
z = 4.2
\]

- Column 1: We have one number (1.8). Let's denote the missing numbers in Column 1 as \( a \) and \( b \). So, the equation for Column 1 would be:
\[
a + 1.8 + b = 9.0
\]
Simplifying:
\[
a + b + 1.8 = 9.0
\]
\[
a + b = 7.2
\]

- Column 2: We have one number (3.0). Let's denote the missing numbers in Column 2 as \( c \) and \( d \). So, the equation for Column 2 would be:
\[
c + 3.0 + d = 9.0
\]
Simplifying:
\[
c + d + 3.0 = 9.0
\]
\[
c + d = 6.0
\]

- Column 3: We have one number (3.6). Let's denote the missing number in Column 3 as \( e \). So, the equation for Column 3 would be:
\[
3.6 + 4.2 + e = 9.0
\]
Simplifying:
\[
7.8 + e = 9.0
\]
\[
e = 1.2
\]

#### Step 4: Solve for the remaining variables
Using the equations:
- From \( x + y = 5.4 \) and the fact that the sum of each row and column must be 9.0, we can fill in the rest of the table.

The completed Table A is:

| | | |
|-------|-------|-------|
| 1.8 | 3.0 | 3.6 |
| 1.8 | 3.0 | 4.2 |
| 5.4 | 3.0 | 0.6 |

Table B: The magic number is 12.6

The table is as follows:

| | | |
|-------|-------|-------|
| | | 4.8 |
| | | |
| 3.6 | 6.6 | |

#### Step 1: Identify the pattern
The "magic number" is 12.6. We will use a similar approach to find the missing numbers.

#### Step 2: Analyze the given numbers
- The number 4.8 is already filled in.
- The numbers 3.6 and 6.6 are also given.

#### Step 3: Test possible relationships
Let's test if the sum of the numbers in each row, column, or diagonal equals 12.6.

- Row 3: We have two numbers (3.6 and 6.6). Let's denote the missing number in Row 3 as \( x \). So, the equation for Row 3 would be:
\[
3.6 + 6.6 + x = 12.6
\]
Simplifying:
\[
10.2 + x = 12.6
\]
\[
x = 2.4
\]

- Column 3: We have two numbers (4.8 and 2.4). Let's denote the missing number in Column 3 as \( y \). So, the equation for Column 3 would be:
\[
4.8 + y + 2.4 = 12.6
\]
Simplifying:
\[
7.2 + y = 12.6
\]
\[
y = 5.4
\]

- Row 1: We have one number (4.8). Let's denote the missing numbers in Row 1 as \( a \) and \( b \). So, the equation for Row 1 would be:
\[
a + b + 4.8 = 12.6
\]
Simplifying:
\[
a + b = 7.8
\]

- Row 2: We have no numbers yet. Let's denote the missing numbers in Row 2 as \( c \), \( d \), and \( e \). So, the equation for Row 2 would be:
\[
c + d + e = 12.6
\]

- Column 1: We have one number (3.6). Let's denote the missing numbers in Column 1 as \( f \) and \( g \). So, the equation for Column 1 would be:
\[
f + g + 3.6 = 12.6
\]
Simplifying:
\[
f + g = 9.0
\]

- Column 2: We have one number (6.6). Let's denote the missing numbers in Column 2 as \( h \) and \( i \). So, the equation for Column 2 would be:
\[
h + i + 6.6 = 12.6
\]
Simplifying:
\[
h + i = 6.0
\]

#### Step 4: Solve for the remaining variables
Using the equations:
- From \( a + b = 7.8 \) and the fact that the sum of each row and column must be 12.6, we can fill in the rest of the table.

The completed Table B is:

| | | |
|-------|-------|-------|
| 3.0 | 4.8 | 4.8 |
| 3.6 | 3.0 | 6.0 |
| 3.6 | 6.6 | 2.4 |

Final Answer

\[
\boxed{
\begin{array}{|c|c|c|}
\hline
1.8 & 3.0 & 3.6 \\
\hline
1.8 & 3.0 & 4.2 \\
\hline
5.4 & 3.0 & 0.6 \\
\hline
\end{array}
\quad
\begin{array}{|c|c|c|}
\hline
3.0 & 4.8 & 4.8 \\
\hline
3.6 & 3.0 & 6.0 \\
\hline
3.6 & 6.6 & 2.4 \\
\hline
\end{array}
}
\]