Fill in the missing numbers to complete the magic squares with specified sums.

Here are the solutions for the magic squares. In a magic square, every row, column, and diagonal must add up to the same "Magic Sum."

Part 1

1) The sum is 15.
* Row 1: We have `_ + 9 + 4 = 15`. Since $9 + 4 = 13$, the missing number is $15 - 13 = \mathbf{2}$.
* Column 1: We now have `2`, `7`, and `_`. $2 + 7 = 9$. The missing number is $15 - 9 = \mathbf{6}$.
* Row 2: We have `7`, `_`, `_`. Let's look at Column 2 first: `9`, `_`, `1`. $9 + 1 = 10$. The middle number is $15 - 10 = \mathbf{5}$.
* Row 2 (finish): Now we have `7`, `5`, `_`. $7 + 5 = 12$. The last number is $15 - 12 = \mathbf{3}$.
* Row 3: We have `6`, `1`, `_`. $6 + 1 = 7$. The last number is $15 - 7 = \mathbf{8}$.

Completed Grid:
| 2 | 9 | 4 |
|---|---|---|
| 7 | 5 | 3 |
| 6 | 1 | 8 |

***

2) The sum is 33.
* Row 2: `15 + 11 + _ = 33`. $15 + 11 = 26$. Missing number is $33 - 26 = \mathbf{7}$.
* Column 2: `_ + 11 + 19 = 33`. $11 + 19 = 30$. Missing number is $33 - 30 = \mathbf{3}$.
* Row 1: `13 + 3 + _ = 33`. $13 + 3 = 16$. Missing number is $33 - 16 = \mathbf{17}$.
* Diagonal (top-left to bottom-right): `13 + 11 + _ = 33`. $13 + 11 = 24$. Missing number is $33 - 24 = \mathbf{9}$.
* Row 3: `_ + 19 + 9 = 33`. $19 + 9 = 28$. Missing number is $33 - 28 = \mathbf{5}$.

Completed Grid:
| 13 | 3 | 17 |
|----|---|----|
| 15 | 11| 7 |
| 5 | 19| 9 |

***

3) The sum is 45.
* Row 2: `_ + 15 + 27 = 45`. $15 + 27 = 42$. Missing number is $45 - 42 = \mathbf{3}$.
* Column 2: `9 + 15 + _ = 45`. $9 + 15 = 24$. Missing number is $45 - 24 = \mathbf{21}$.
* Row 1: `_ + 9 + 12 = 45`. $9 + 12 = 21$. Missing number is $45 - 21 = \mathbf{24}$.
* Diagonal (top-left to bottom-right): `24 + 15 + _ = 45`. $24 + 15 = 39$. Missing number is $45 - 39 = \mathbf{6}$.
* Row 3: `_ + 21 + 6 = 45`. $21 + 6 = 27$. Missing number is $45 - 27 = \mathbf{18}$.

Completed Grid:
| 24 | 9 | 12 |
|----|---|----|
| 3 | 15| 27 |
| 18 | 21| 6 |

***

4) The sum is 60.
* Row 1: `21 + _ + 23 = 60`. $21 + 23 = 44$. Missing number is $60 - 44 = \mathbf{16}$.
* Diagonal (top-left to bottom-right): `21 + _ + 19 = 60`. $21 + 19 = 40$. Middle number is $60 - 40 = \mathbf{20}$.
* Column 2: `16 + 20 + _ = 60`. $16 + 20 = 36$. Missing number is $60 - 36 = \mathbf{24}$.
* Row 3: `17 + 24 + 19 = 60`. Check: $17+24=41$, $41+19=60$. Correct.
* Column 1: `21 + _ + 17 = 60`. $21 + 17 = 38$. Missing number is $60 - 38 = \mathbf{22}$.
* Column 3: `23 + _ + 19 = 60`. $23 + 19 = 42$. Missing number is $60 - 42 = \mathbf{18}$.

Completed Grid:
| 21 | 16 | 23 |
|----|----|----|
| 22 | 20 | 18 |
| 17 | 24 | 19 |

---

Part 2

1) The sum is 75.
* Row 2: `_ + 25 + 15 = 75`. $25 + 15 = 40$. Missing number is $75 - 40 = \mathbf{35}$.
* Column 2: `_ + 25 + 45 = 75`. $25 + 45 = 70$. Top middle number is $75 - 70 = \mathbf{5}$.
* Row 3: `10 + 45 + _ = 75`. $10 + 45 = 55$. Missing number is $75 - 55 = \mathbf{20}$.
* Column 3: `_ + 15 + 20 = 75`. $15 + 20 = 35$. Top right number is $75 - 35 = \mathbf{40}$.
* Row 1: `_ + 5 + 40 = 75`. $5 + 40 = 45$. Top left number is $75 - 45 = \mathbf{30}$.

Completed Grid:
| 30 | 5 | 40 |
|----|---|----|
| 35 | 25| 15 |
| 10 | 45| 20 |

***

2) The sum is 42.
* Column 3: `_ + 8 + _ = 42`. Let's find the middle number using the diagonal or other rows.
* Diagonal (top-right to bottom-left): `11 + Middle + Bottom-Left = 42`. This has two unknowns.
* Let's find the center first. In a 3x3 magic square, the Center Number $\times$ 3 = Magic Sum. $42 / 3 = \mathbf{14}$. So the center is 14.
* Column 3: `_ + 8 + _ = 42`? No, let's use Row 2: `_ + 14 + 8 = 42`. $14 + 8 = 22$. Left middle is $42 - 22 = \mathbf{20}$.
* Column 2: `_ + 14 + 2 = 42`. $14 + 2 = 16$. Top middle is $42 - 16 = \mathbf{26}$.
* Row 1: `_ + 26 + 11 = 42`. $26 + 11 = 37$. Top left is $42 - 37 = \mathbf{5}$.
* Column 1: `5 + 20 + _ = 42`. $5 + 20 = 25$. Bottom left is $42 - 25 = \mathbf{17}$.
* Row 3: `17 + 2 + _ = 42`. $17 + 2 = 19$. Bottom right is $42 - 19 = \mathbf{23}$.

Completed Grid:
| 5 | 26 | 11 |
|---|----|----|
| 20| 14 | 8 |
| 17| 2 | 23 |

***

3) The sum is 36.
* Column 3: `_ + 10 + 15 = 36`. $10 + 15 = 25$. Top right is $36 - 25 = \mathbf{11}$.
* Row 1: `9 + _ + 11 = 36`. $9 + 11 = 20$. Top middle is $36 - 20 = \mathbf{16}$.
* Column 2: `16 + _ + _ = 36`. We need more info.
* Diagonal (top-left to bottom-right): `9 + Center + 15 = 36`. $9 + 15 = 24$. Center is $36 - 24 = \mathbf{12}$.
* Column 2 (finish): `16 + 12 + _ = 36`. $16 + 12 = 28$. Bottom middle is $36 - 28 = \mathbf{8}$.
* Row 3: `_ + 8 + 15 = 36`. $8 + 15 = 23$. Bottom left is $36 - 23 = \mathbf{13}$.
* Row 2: `_ + 12 + 10 = 36`. $12 + 10 = 22`. Left middle is $36 - 22 = \mathbf{14}$.

Completed Grid:
| 9 | 16 | 11 |
|---|----|----|
| 14| 12 | 10 |
| 13| 8 | 15 |

***

4) The sum is 150.
* Row 1: `20 + 70 + _ = 150`. $20 + 70 = 90$. Top right is $150 - 90 = \mathbf{60}$.
* Center Number: $150 / 3 = \mathbf{50}$. The center is 50.
* Diagonal (top-left to bottom-right): `20 + 50 + _ = 150`. $20 + 50 = 70$. Bottom right is $150 - 70 = \mathbf{80}$.
* Column 3: `60 + _ + 80 = 150`. $60 + 80 = 140`. Right middle is $150 - 140 = \mathbf{10}$.
* Row 2: `_ + 50 + 10 = 150`. $50 + 10 = 60`. Left middle is $150 - 60 = \mathbf{90}$.
* Column 1: `20 + 90 + _ = 150`. $20 + 90 = 110`. Bottom left is $150 - 110 = \mathbf{40}$.
* Check Row 3: `40 + 30 + 80 = 150`. Correct.

Completed Grid:
| 20 | 70 | 60 |
|----|----|----|
| 90 | 50 | 10 |
| 40 | 30 | 80 |

──────────────────────────────────────

Final Answer:

Part 1 Solutions:
1)
| 2 | 9 | 4 |
| 7 | 5 | 3 |
| 6 | 1 | 8 |

2)
| 13 | 3 | 17 |
| 15 | 11 | 7 |
| 5 | 19 | 9 |

3)
| 24 | 9 | 12 |
| 3 | 15 | 27 |
| 18 | 21 | 6 |

4)
| 21 | 16 | 23 |
| 22 | 20 | 18 |
| 17 | 24 | 19 |

Part 2 Solutions:
1)
| 30 | 5 | 40 |
| 35 | 25 | 15 |
| 10 | 45 | 20 |

2)
| 5 | 26 | 11 |
| 20 | 14 | 8 |
| 17 | 2 | 23 |

3)
| 9 | 16 | 11 |
| 14 | 12 | 10 |
| 13 | 8 | 15 |

4)
| 20 | 70 | 60 |
| 90 | 50 | 10 |
| 40 | 30 | 80 |