Free Math Puzzles - Addition and Subtraction - Free Printable

Let's solve the Tree Adding Puzzle step by step.

---

🔍 Understanding the Rule

- Each number in a hexagon is the sum of the two numbers directly below it.
- We need to fill in the missing numbers so that this rule holds for every hexagon.
- The first tree is already completed as an example.

We'll go through each tree one by one.

---

## 🌲 Tree 1 (Completed Example)
```
13
5 8
2 3 5
```
Check:
- 5 + 8 = 13 ✔
- 2 + 3 = 5 ✔
- 3 + 5 = 8 ✔

This confirms the pattern.

---

## 🌲 Tree 2
Given:
```
?
? ?
5 1 2
```

We work from the bottom up.

Step 1: Middle row

- Left middle: 5 + 1 = 6
- Right middle: 1 + 2 = 3

So now:
```
?
6 3
5 1 2
```

Step 2: Top

- 6 + 3 = 9

Final:
```
9
6 3
5 1 2
```

✔ Solution: 9, 6, 3

---

## 🌲 Tree 3
Given:
```
?
? ?
3 2 4
```

Step 1: Middle row

- Left: 3 + 2 = 5
- Right: 2 + 4 = 6

Now:
```
?
5 6
3 2 4
```

Step 2: Top

- 5 + 6 = 11

Final:
```
11
5 6
3 2 4
```

✔ Solution: 11, 5, 6

---

## 🌲 Tree 4
Given:
```
12
? ?
5 ? 1
```

We know the top is 12, and bottom row has 5 and 1 on the ends. Let’s find the missing middle number.

Let’s denote:
- Bottom row: 5, A, 1
- Middle row: 5+A, A+1
- Top: (5+A) + (A+1) = 12

Solve:
$$
(5 + A) + (A + 1) = 12 \\
5 + A + A + 1 = 12 \\
2A + 6 = 12 \\
2A = 6 \\
A = 3
$$

So middle bottom number is 3

Now compute middle row:
- Left: 5 + 3 = 8
- Right: 3 + 1 = 4

Top: 8 + 4 = 12 ✔

Final:
```
12
8 4
5 3 1
```

✔ Solution: 8, 4, 3

---

## 🌲 Tree 5
Given:
```
15
? ?
? 3 5
```

Let’s denote:
- Bottom: B, 3, 5
- Middle: B+3, 3+5 = 8
- Top: (B+3) + 8 = 15

Solve:
$$
B + 3 + 8 = 15 \\
B + 11 = 15 \\
B = 4
$$

So bottom left = 4

Middle row:
- Left: 4 + 3 = 7
- Right: 3 + 5 = 8

Top: 7 + 8 = 15 ✔

Final:
```
15
7 8
4 3 5
```

✔ Solution: 7, 8, 4

---

## 🌲 Tree 6
Given:
```
20
? ?
5 ? 7
```

Let’s denote:
- Bottom: 5, C, 7
- Middle: 5+C, C+7
- Top: (5+C) + (C+7) = 20

Solve:
$$
5 + C + C + 7 = 20 \\
2C + 12 = 20 \\
2C = 8 \\
C = 4
$$

So middle bottom number is 4

Middle row:
- Left: 5 + 4 = 9
- Right: 4 + 7 = 11

Top: 9 + 11 = 20 ✔

Final:
```
20
9 11
5 4 7
```

✔ Solution: 9, 11, 4

---

✔ Final Answers:

| Tree | Top | Middle Left | Middle Right | Bottom Left | Bottom Middle | Bottom Right |
|------|-----|-------------|---------------|--------------|----------------|----------------|
| 1 | 13 | 5 | 8 | 2 | 3 | 5 |
| 2 | 9 | 6 | 3 | 5 | 1 | 2 |
| 3 | 11 | 5 | 6 | 3 | 2 | 4 |
| 4 | 12 | 8 | 4 | 5 | 3 | 1 |
| 5 | 15 | 7 | 8 | 4 | 3 | 5 |
| 6 | 20 | 9 | 11 | 5 | 4 | 7 |

---

📝 Summary

You can fill in the trees using the rule:
> Each number is the sum of the two numbers directly below it.

Work from bottom to top, adding adjacent pairs.

All puzzles have unique solutions given the constraints — but the problem says "many possibilities", which may be due to multiple ways to assign values if not all numbers were given. However, in these cases, only one solution satisfies the totals.

Let me know if you'd like a printable version or visual diagram!