Magic Square Worksheets Are Fun And Help Kids Buld Math Skills. - Free Printable

To solve the magic square problems, we need to ensure that the sum of each row, column, and diagonal equals the given "Magic Number." Let's go through each magic square step by step.

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Magic Square 1: Magic Number = 27

The numbers provided are: 5, 6, 7, 8, 9, 10, 11, 12, 13.

#### Step 1: Verify the Magic Number
The sum of all numbers is:
\[ 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 = 81 \]

Since there are 3 rows (or columns), the sum of each row (or column) should be:
\[ \text{Magic Number} = \frac{\text{Total Sum}}{3} = \frac{81}{3} = 27 \]

#### Step 2: Fill in the Known Numbers
The partially filled magic square is:
\[
\begin{array}{|c|c|c|}
\hline
5 & 12 & ? \\
\hline
? & ? & ? \\
\hline
9 & 8 & ? \\
\hline
\end{array}
\]

#### Step 3: Solve Row by Row, Column by Column, and Diagonal
- First Row: \( 5 + 12 + ? = 27 \)
\[ ? = 27 - 5 - 12 = 10 \]

- Third Row: \( 9 + 8 + ? = 27 \)
\[ ? = 27 - 9 - 8 = 10 \]

- Second Column: \( 12 + ? + 8 = 27 \)
\[ ? = 27 - 12 - 8 = 7 \]

- First Column: \( 5 + ? + 9 = 27 \)
\[ ? = 27 - 5 - 9 = 13 \]

- Third Column: \( 10 + ? + 10 = 27 \)
\[ ? = 27 - 10 - 10 = 7 \]

- Diagonal (Top-left to Bottom-right): \( 5 + ? + 10 = 27 \)
\[ ? = 27 - 5 - 10 = 12 \] (Already filled)

- Diagonal (Top-right to Bottom-left): \( 12 + ? + 9 = 27 \)
\[ ? = 27 - 12 - 9 = 6 \]

#### Final Magic Square:
\[
\begin{array}{|c|c|c|}
\hline
5 & 12 & 10 \\
\hline
13 & 9 & 5 \\
\hline
9 & 8 & 10 \\
\hline
\end{array}
\]

---

Magic Square 2: Magic Number = 165

The numbers provided are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100.

#### Step 1: Verify the Magic Number
The sum of all numbers is:
\[ 1 + 2 + 3 + \ldots + 100 = \frac{100 \times 101}{2} = 5050 \]

Since there are 3 rows (or columns), the sum of each row (or column) should be:
\[ \text{Magic Number} = \frac{\text{Total Sum}}{3} = \frac{5050}{3} = 165 \]

#### Step 2: Fill in the Known Numbers
The partially filled magic square is:
\[
\begin{array}{|c|c|c|}
\hline
? & ? & ? \\
\hline
? & 55 & ? \\
\hline
25 & 95 & ? \\
\hline
\end{array}
\]

#### Step 3: Solve Row by Row, Column by Column, and Diagonal
- Third Row: \( 25 + 95 + ? = 165 \)
\[ ? = 165 - 25 - 95 = 45 \]

- Second Column: \( ? + 55 + 95 = 165 \)
\[ ? = 165 - 55 - 95 = 15 \]

- Third Column: \( ? + ? + 45 = 165 \)
Let the top number in the third column be \( x \):
\[ x + ? + 45 = 165 \]
\[ x + ? = 120 \]

- First Row: \( ? + ? + x = 165 \)
Let the first number in the first row be \( a \) and the second number be \( b \):
\[ a + b + x = 165 \]

- Diagonal (Top-left to Bottom-right): \( a + 55 + 45 = 165 \)
\[ a + 100 = 165 \]
\[ a = 65 \]

- Diagonal (Top-right to Bottom-left): \( x + 55 + 25 = 165 \)
\[ x + 80 = 165 \]
\[ x = 85 \]

- First Row: \( 65 + b + 85 = 165 \)
\[ b = 165 - 65 - 85 = 15 \]

- Second Row: \( ? + 55 + ? = 165 \)
Let the first number in the second row be \( y \):
\[ y + 55 + 45 = 165 \]
\[ y = 165 - 55 - 45 = 65 \]

#### Final Magic Square:
\[
\begin{array}{|c|c|c|}
\hline
65 & 15 & 85 \\
\hline
65 & 55 & 45 \\
\hline
25 & 95 & 45 \\
\hline
\end{array}
\]

---

Magic Square 3: Magic Number = 42

The numbers provided are: 10, 11, 12, 13, 14, 15, 16, 17, 18.

#### Step 1: Verify the Magic Number
The sum of all numbers is:
\[ 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 = 135 \]

Since there are 3 rows (or columns), the sum of each row (or column) should be:
\[ \text{Magic Number} = \frac{\text{Total Sum}}{3} = \frac{135}{3} = 45 \]

#### Step 2: Fill in the Known Numbers
The partially filled magic square is:
\[
\begin{array}{|c|c|c|}
\hline
? & ? & ? \\
\hline
? & 17 & ? \\
\hline
16 & 12 & ? \\
\hline
\end{array}
\]

#### Step 3: Solve Row by Row, Column by Column, and Diagonal
- Third Row: \( 16 + 12 + ? = 45 \)
\[ ? = 45 - 16 - 12 = 17 \]

- Second Column: \( ? + 17 + 12 = 45 \)
\[ ? = 45 - 17 - 12 = 16 \]

- First Column: \( ? + ? + 16 = 45 \)
Let the top number in the first column be \( x \):
\[ x + ? + 16 = 45 \]
\[ x + ? = 29 \]

- First Row: \( x + ? + ? = 45 \)
Let the second number in the first row be \( y \):
\[ x + y + ? = 45 \]

- Diagonal (Top-left to Bottom-right): \( x + 17 + 17 = 45 \)
\[ x + 34 = 45 \]
\[ x = 11 \]

- Diagonal (Top-right to Bottom-left): \( ? + 17 + 16 = 45 \)
\[ ? = 45 - 17 - 16 = 12 \]

- First Row: \( 11 + y + 16 = 45 \)
\[ y = 45 - 11 - 16 = 18 \]

#### Final Magic Square:
\[
\begin{array}{|c|c|c|}
\hline
11 & 18 & 16 \\
\hline
13 & 17 & 15 \\
\hline
16 & 12 & 17 \\
\hline
\end{array}
\]

---

Magic Square 4: Magic Number = 10

The numbers provided are: 2, 4, 6, 8, 10, 12, 14, 16, 18.

#### Step 1: Verify the Magic Number
The sum of all numbers is:
\[ 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 = 90 \]

Since there are 3 rows (or columns), the sum of each row (or column) should be:
\[ \text{Magic Number} = \frac{\text{Total Sum}}{3} = \frac{90}{3} = 30 \]

#### Step 2: Fill in the Known Numbers
The partially filled magic square is:
\[
\begin{array}{|c|c|c|}
\hline
? & ? & ? \\
\hline
? & 10 & ? \\
\hline
4 & 18 & ? \\
\hline
\end{array}
\]

#### Step 3: Solve Row by Row, Column by Column, and Diagonal
- Third Row: \( 4 + 18 + ? = 30 \)
\[ ? = 30 - 4 - 18 = 8 \]

- Second Column: \( ? + 10 + 18 = 30 \)
\[ ? = 30 - 10 - 18 = 2 \]

- First Column: \( ? + ? + 4 = 30 \)
Let the top number in the first column be \( x \):
\[ x + ? + 4 = 30 \]
\[ x + ? = 26 \]

- First Row: \( x + ? + ? = 30 \)
Let the second number in the first row be \( y \):
\[ x + y + ? = 30 \]

- Diagonal (Top-left to Bottom-right): \( x + 10 + 8 = 30 \)
\[ x + 18 = 30 \]
\[ x = 12 \]

- Diagonal (Top-right to Bottom-left): \( ? + 10 + 4 = 30 \)
\[ ? = 30 - 10 - 4 = 16 \]

- First Row: \( 12 + y + 6 = 30 \)
\[ y = 30 - 12 - 6 = 12 \]

#### Final Magic Square:
\[
\begin{array}{|c|c|c|}
\hline
12 & 6 & 12 \\
\hline
14 & 10 & 6 \\
\hline
4 & 18 & 8 \\
\hline
\end{array}
\]

---

Final Answers

\[
\boxed{
\begin{array}{|c|c|c|}
\hline
5 & 12 & 10 \\
\hline
13 & 9 & 5 \\
\hline
9 & 8 & 10 \\
\hline
\end{array}
\quad
\begin{array}{|c|c|c|}
\hline
65 & 15 & 85 \\
\hline
65 & 55 & 45 \\
\hline
25 & 95 & 45 \\
\hline
\end{array}
\quad
\begin{array}{|c|c|c|}
\hline
11 & 18 & 16 \\
\hline
13 & 17 & 15 \\
\hline
16 & 12 & 17 \\
\hline
\end{array}
\quad
\begin{array}{|c|c|c|}
\hline
12 & 6 & 12 \\
\hline
14 & 10 & 6 \\
\hline
4 & 18 & 8 \\
\hline
\end{array}
}
\]