Let’s solve each magic square one by one. Remember: in a magic square, every row, every column, and both diagonals must add up to the “Magic Sum” given above each square.
---
First Magic Square (Top Left) — Magic Sum = 15
Grid:
```
8 1 ?
3 ? 7
? 9 ?
```
Step 1: Top row → 8 + 1 + ? = 15 → ? = 6
So top right is
6
Now grid:
```
8 1 6
3 ? 7
? 9 ?
```
Step 2: Middle row → 3 + ? + 7 = 15 → ? = 5
Center is
5
Now:
```
8 1 6
3 5 7
? 9 ?
```
Step 3: Bottom row → ? + 9 + ? = 15 → We need two numbers that with 9 make 15 → sum of missing two = 6
Also, left column: 8 + 3 + ? = 15 → ? = 4 → bottom left is
4
Then bottom row: 4 + 9 + ? = 15 → ? = 2 → bottom right is
2
Check last column: 6 + 7 + 2 = 15
✔
Check diagonal: 8 + 5 + 2 = 15
✔
Other diagonal: 6 + 5 + 4 = 15
✔
✔ First square done!
Final for first square:
```
8 1 6
3 5 7
4 9 2
```
---
Second Magic Square (Top Right) — Magic Sum = 18
Grid:
```
? 2 7
4 6 ?
? ? 3
```
Step 1: Top row → ? + 2 + 7 = 18 → ? = 9 → top left is
9
Now:
```
9 2 7
4 6 ?
? ? 3
```
Step 2: Middle row → 4 + 6 + ? = 18 → ? = 8 → middle right is
8
Now:
```
9 2 7
4 6 8
? ? 3
```
Step 3: Right column → 7 + 8 + 3 = 18
✔ Good.
Left column: 9 + 4 + ? = 18 → ? = 5 → bottom left is
5
Bottom row: 5 + ? + 3 = 18 → ? = 10 → bottom middle is
10
Check middle column: 2 + 6 + 10 = 18
✔
Check diagonal: 9 + 6 + 3 = 18
✔
Other diagonal: 7 + 6 + 5 = 18
✔
✔ Second square done!
Final for second square:
```
9 2 7
4 6 8
5 10 3
```
---
Third Magic Square (Bottom Left) — Magic Sum = 30
Grid:
```
13 6 ?
? 10 12
? ? 7
```
Step 1: Top row → 13 + 6 + ? = 30 → ? = 11 → top right is
11
Now:
```
13 6 11
? 10 12
? ? 7
```
Step 2: Middle row → ? + 10 + 12 = 30 → ? = 8 → middle left is
8
Now:
```
13 6 11
8 10 12
? ? 7
```
Step 3: Left column → 13 + 8 + ? = 30 → ? = 9 → bottom left is
9
Bottom row → 9 + ? + 7 = 30 → ? = 14 → bottom middle is
14
Check middle column: 6 + 10 + 14 = 30
✔
Right column: 11 + 12 + 7 = 30
✔
Diagonal: 13 + 10 + 7 = 30
✔
Other diagonal: 11 + 10 + 9 = 30
✔
✔ Third square done!
Final for third square:
```
13 6 11
8 10 12
9 14 7
```
---
Fourth Magic Square (Bottom Right) — Magic Sum = 24
Grid:
```
11 ? 9
? 8 ?
7 12 ?
```
Step 1: Top row → 11 + ? + 9 = 24 → ? = 4 → top middle is
4
Now:
```
11 4 9
? 8 ?
7 12 ?
```
Step 2: Middle column → 4 + 8 + 12 = 24
✔ Good.
Left column → 11 + ? + 7 = 24 → ? = 6 → middle left is
6
Middle row → 6 + 8 + ? = 24 → ? = 10 → middle right is
10
Bottom row → 7 + 12 + ? = 24 → ? = 5 → bottom right is
5
Check right column: 9 + 10 + 5 = 24
✔
Check diagonal: 11 + 8 + 5 = 24
✔
Other diagonal: 9 + 8 + 7 = 24
✔
✔ Fourth square done!
Final for fourth square:
```
11 4 9
6 8 10
7 12 5
```
---
Final Answer:
Top Left (Sum=15):
8 1 6
3 5 7
4 9 2
Top Right (Sum=18):
9 2 7
4 6 8
5 10 3
Bottom Left (Sum=30):
13 6 11
8 10 12
9 14 7
Bottom Right (Sum=24):
11 4 9
6 8 10
7 12 5
Parent Tip: Review the logic above to help your child master the concept of magic squares worksheet.