Free Printable Magic Square Worksheets - Worksheet Zone - Free Printable

Here are the solutions for the four magic square puzzles. Remember, in a magic square, every row (across), column (down), and diagonal must add up to the same "Magic Sum."

Puzzle 1: Magic Sum = 15

Step-by-step Solution:
1. Top Row: We have `8` and `1`. The sum needs to be 15.
* $8 + 1 = 9$.
* $15 - 9 = 6$. So, the top-right number is 6.
2. Middle Row: We have `3` and `7`.
* $3 + 7 = 10$.
* $15 - 10 = 5$. So, the center number is 5.
3. Left Column: We have `8` and `3`.
* $8 + 3 = 11$.
* $15 - 11 = 4$. So, the bottom-left number is 4.
4. Right Column: We now have `6` (from step 1) and `7`.
* $6 + 7 = 13$.
* $15 - 13 = 2$. So, the bottom-right number is 2.
5. Check Bottom Row: We have `4`, `9`, and `2`.
* $4 + 9 + 2 = 15$. This is correct.

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

***

Puzzle 2: Magic Sum = 18

Step-by-step Solution:
1. Top Row: We have `2` and `7`.
* $2 + 7 = 9$.
* $18 - 9 = 9$. So, the top-left number is 9.
2. Middle Row: We have `4` and `6`.
* $4 + 6 = 10$.
* $18 - 10 = 8$. So, the middle-right number is 8.
3. Right Column: We have `7` (top) and `8` (middle).
* $7 + 8 = 15$.
* $18 - 15 = 3$. This matches the given bottom-right number, so our math is good so far.
4. Left Column: We have `9` (top) and `4` (middle).
* $9 + 4 = 13$.
* $18 - 13 = 5$. So, the bottom-left number is 5.
5. Bottom Row: We have `5` (left) and `3` (right).
* $5 + 3 = 8$.
* $18 - 8 = 10$. So, the bottom-middle number is 10.
6. Check Middle Column: `2` + `6` + `10` = 18. Correct.

Completed Grid:
| 9 | 2 | 7 |
|---|---|---|
| 4 | 6 | 8 |
| 5 | 10 | 3 |

***

Puzzle 3: Magic Sum = 30

Step-by-step Solution:
1. Top Row: We have `13` and `6`.
* $13 + 6 = 19$.
* $30 - 19 = 11$. So, the top-right number is 11.
2. Middle Row: We have `10` and `12`.
* $10 + 12 = 22$.
* $30 - 22 = 8$. So, the middle-left number is 8.
3. Right Column: We have `11` (top) and `7` (bottom).
* $11 + 7 = 18$.
* $30 - 18 = 12$. Wait, the middle right is already 12. Let's re-read the grid. Ah, the bottom right is 7. The middle right is 12. The top right is blank.
* Let's restart the Right Column calculation properly. We have Middle-Right `12` and Bottom-Right `7`.
* $12 + 7 = 19$.
* $30 - 19 = 11$. So, the top-right number is 11. (This matches Step 1).
4. Left Column: We have `13` (top) and `8` (middle, found in step 2).
* $13 + 8 = 21$.
* $30 - 21 = 9$. So, the bottom-left number is 9.
5. Bottom Row: We have `9` (left) and `7` (right).
* $9 + 7 = 16$.
* $30 - 16 = 14$. So, the bottom-middle number is 14.
6. Check Middle Column: `6` + `10` + `14` = 30. Correct.

Completed Grid:
| 13 | 6 | 11 |
|---|---|---|
| 8 | 10 | 12 |
| 9 | 14 | 7 |

***

Puzzle 4: Magic Sum = 24

Step-by-step Solution:
1. Bottom Row: We have `7` and `12`.
* $7 + 12 = 19$.
* $24 - 19 = 5$. So, the bottom-right number is 5.
2. Right Column: We have `9` (top) and `5` (bottom).
* $9 + 5 = 14$.
* $24 - 14 = 10$. So, the middle-right number is 10.
3. Middle Row: We have `8` (center) and `10` (right).
* $8 + 10 = 18$.
* $24 - 18 = 6$. So, the middle-left number is 6.
4. Left Column: We have `11` (top) and `6` (middle).
* $11 + 6 = 17$.
* $24 - 17 = 7$. This matches the given bottom-left number. Good.
5. Top Row: We have `11` and `9`.
* $11 + 9 = 20$.
* $24 - 20 = 4$. So, the top-middle number is 4.
6. Check Middle Column: `4` + `8` + `12` = 24. Correct.

Completed Grid:
| 11 | 4 | 9 |
|---|---|---|
| 6 | 8 | 10 |
| 7 | 12 | 5 |

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Final Answer:

Puzzle 1 (Sum 15):
Row 1: 8, 1, 6
Row 2: 3, 5, 7
Row 3: 4, 9, 2

Puzzle 2 (Sum 18):
Row 1: 9, 2, 7
Row 2: 4, 6, 8
Row 3: 5, 10, 3

Puzzle 3 (Sum 30):
Row 1: 13, 6, 11
Row 2: 8, 10, 12
Row 3: 9, 14, 7

Puzzle 4 (Sum 24):
Row 1: 11, 4, 9
Row 2: 6, 8, 10
Row 3: 7, 12, 5