Hexagon Puzzle (teacher made) - Twinkl - Free Printable

Problem Description:

The task involves solving "Hexagon Puzzles," where the number in each hexagon is the sum of the two numbers directly below it. The goal is to fill in the missing numbers in the empty hexagons.

Solution Approach:

1. Understand the Rule: Each hexagon's value is the sum of the two hexagons directly below it.
2. Work Bottom-Up: Start from the bottom row (where all values are given) and work your way up, calculating the values for each hexagon step by step.
3. Apply the Rule Repeatedly: Use the rule consistently to fill in all missing hexagons.

Step-by-Step Solution:

#### Puzzle 1:
The puzzle is already solved in the image, so we can use it as a reference for understanding the process.

#### Puzzle 2:
We need to solve the following hexagon puzzle:

```
?
/ \
? ?
/ \ / \
7 3 4 2
```

1. Calculate the second row from the bottom:
- The hexagon above `7` and `3`: \( 7 + 3 = 10 \)
- The hexagon above `3` and `4`: \( 3 + 4 = 7 \)
- The hexagon above `4` and `2`: \( 4 + 2 = 6 \)

Updated grid:
```
?
/ \
? ?
/ \ / \
7 3 4 2
\ / \ / \ /
10 7 6
```

2. Calculate the top row:
- The hexagon above `10` and `7`: \( 10 + 7 = 17 \)
- The hexagon above `7` and `6`: \( 7 + 6 = 13 \)

Updated grid:
```
?
/ \
17 13
/ \ / \
7 3 4 2
\ / \ / \ /
10 7 6
```

3. Calculate the topmost hexagon:
- The hexagon above `17` and `13`: \( 17 + 13 = 30 \)

Final grid:
```
30
/ \
17 13
/ \ / \
7 3 4 2
\ / \ / \ /
10 7 6
```

#### Puzzle 3:
We need to solve the following hexagon puzzle:

```
?
/ \
? ?
/ \ / \
12 9 15 7
```

1. Calculate the second row from the bottom:
- The hexagon above `12` and `9`: \( 12 + 9 = 21 \)
- The hexagon above `9` and `15`: \( 9 + 15 = 24 \)
- The hexagon above `15` and `7`: \( 15 + 7 = 22 \)

Updated grid:
```
?
/ \
? ?
/ \ / \
12 9 15 7
\ / \ / \ /
21 24 22
```

2. Calculate the top row:
- The hexagon above `21` and `24`: \( 21 + 24 = 45 \)
- The hexagon above `24` and `22`: \( 24 + 22 = 46 \)

Updated grid:
```
?
/ \
45 46
/ \ / \
12 9 15 7
\ / \ / \ /
21 24 22
```

3. Calculate the topmost hexagon:
- The hexagon above `45` and `46`: \( 45 + 46 = 91 \)

Final grid:
```
91
/ \
45 46
/ \ / \
12 9 15 7
\ / \ / \ /
21 24 22
```

Final Answer:

For Puzzle 2:
\[
\boxed{30}
\]

For Puzzle 3:
\[
\boxed{91}
\]