Addition Squares - Logic Puzzle Worksheets - Free Printable

Let’s solve each square one by one.

---

First Square (Already Done — for reference):

We have:

```
2 0 8 → sum = 10
5 9 4 → sum = 18
6 6 1 → sum = 13
↓ ↓ ↓
13 15 13
```

Check columns:
2+5+6=13 ✔️
0+9+6=15 ✔️
8+4+1=13 ✔️

Good! Now let’s solve the others.

---

Second Square:

Given:

```
_ _ 2 → row sum = 4
1 _ _ → row sum = 14
3 _ 9 → row sum = 16
↓ ↓ ↓
4 14 16
```

Let’s label unknowns as variables to make it easier.

Call the grid:

A B 2
1 C D
3 E 9

Row sums:
A + B + 2 = 4 → A + B = 2
1 + C + D = 14 → C + D = 13
3 + E + 9 = 16 → E = 4 ✔

Column sums:
A + 1 + 3 = 4 → A = 0
B + C + E = 14 → B + C + 4 = 14 → B + C = 10
2 + D + 9 = 16 → D = 5

Now plug back:

From A = 0, and A + B = 2 → B = 2
From D = 5, and C + D = 13 → C = 8
Check B + C = 2 + 8 = 10 ✔️

So filled grid:

0 2 2
1 8 5
3 4 9

Wait — first row: 0 + 2 + 2 = 4 ✔️
Second row: 1 + 8 + 5 = 14 ✔️
Third row: 3 + 4 + 9 = 16 ✔️
Columns:
0+1+3=4 ✔️
2+8+4=14 ✔️
2+5+9=16 ✔️

Perfect!

---

Third Square:

Given:

```
9 1 _ → sum = 11
_ 5 1 → sum = 12
_ _ _ → sum = 15
↓ ↓ ↓
17 12 9
```

Label:

9 1 A
B 5 1
C D E

Row sums:
9 + 1 + A = 11 → A = 1
B + 5 + 1 = 12 → B = 6
C + D + E = 15

Column sums:
9 + B + C = 17 → 9 + 6 + C = 17 → C = 2
1 + 5 + D = 12 → D = 6
A + 1 + E = 9 → 1 + 1 + E = 9 → E = 7

Check third row: C + D + E = 2 + 6 + 7 = 15 ✔️

Filled grid:

9 1 1
6 5 1
2 6 7

Check all:

Rows:
9+1+1=11 ✔️
6+5+1=12 ✔️
2+6+7=15 ✔️
Cols:
9+6+2=17 ✔️
1+5+6=12 ✔️
1+1+7=9 ✔️

Great!

---

Fourth Square:

Given:

```
3 _ 6 → sum = 11
_ _ _ → sum = 19
_ 6 _ → sum = 9
↓ ↓ ↓
9 17 13
```

Label:

3 A 6
B C D
E 6 F

Row sums:
3 + A + 6 = 11 → A = 2
B + C + D = 19
E + 6 + F = 9 → E + F = 3

Column sums:
3 + B + E = 9 → B + E = 6
A + C + 6 = 17 → 2 + C + 6 = 17 → C = 9
6 + D + F = 13 → D + F = 7

Now we have:

A = 2
C = 9
B + E = 6
E + F = 3
D + F = 7
B + C + D = 19 → B + 9 + D = 19 → B + D = 10

Let’s solve system:

From B + E = 6 → E = 6 - B
From E + F = 3 → (6 - B) + F = 3 → F = B - 3
From D + F = 7 → D + (B - 3) = 7 → D = 10 - B

But from earlier: B + D = 10 → B + (10 - B) = 10 → 10 = 10 ✔️ Always true.

So we need integer values that fit. Try small integers.

Try B = 4 → then E = 2, F = 1, D = 6
Check D + F = 6 + 1 = 7 ✔️
E + F = 2 + 1 = 3 ✔️
B + D = 4 + 6 = 10 ✔️

All good.

So:

A = 2
B = 4
C = 9
D = 6
E = 2
F = 1

Grid:

3 2 6
4 9 6
2 6 1

Check rows:
3+2+6=11 ✔️
4+9+6=19 ✔️
2+6+1=9 ✔️
Cols:
3+4+2=9 ✔️
2+9+6=17 ✔️
6+6+1=13 ✔️

Perfect!

---

Final Answers:

Second Square:
0 2 2
1 8 5
3 4 9

Third Square:
9 1 1
6 5 1
2 6 7

Fourth Square:
3 2 6
4 9 6
2 6 1

Final Answer:
Second Square:
0 2 2
1 8 5
3 4 9

Third Square:
9 1 1
6 5 1
2 6 7

Fourth Square:
3 2 6
4 9 6
2 6 1