Number Maze: Target 50 math puzzle worksheet with arithmetic operations and two solutions.

Problem Overview:

The task is to navigate a number maze starting from 0 and ending at 50. You must follow the arrows and perform the operations indicated in each hexagon. There are two possible routes that lead to a total of 50. Additionally, there is an extra challenge to find the route with the highest total and the route with the lowest total.

Step-by-Step Solution:

#### 1. Understanding the Maze:
- Start: Begin with 0.
- Operations: Follow the arrows and apply the operations in each hexagon.
- End: Reach a total of 50 at the "END" hexagon.

#### 2. Finding the Two Routes to 50:

We will explore different paths and calculate the totals to identify the two routes that result in 50.

##### Path 1:
- Start: 0
- +6: \( 0 + 6 = 6 \)
- x3: \( 6 \times 3 = 18 \)
- ÷3: \( 18 \div 3 = 6 \)
- x5: \( 6 \times 5 = 30 \)
- +5: \( 30 + 5 = 35 \)
- +2: \( 35 + 2 = 37 \)
- +8: \( 37 + 8 = 45 \)
- ÷2: \( 45 \div 2 = 22.5 \) (This path does not work as it does not reach 50.)

##### Path 2:
- Start: 0
- +4: \( 0 + 4 = 4 \)
- x5: \( 4 \times 5 = 20 \)
- ÷2: \( 20 \div 2 = 10 \)
- x5: \( 10 \times 5 = 50 \)
- END: Total = 50

This is one valid route.

##### Path 3:
- Start: 0
- +6: \( 0 + 6 = 6 \)
- x3: \( 6 \times 3 = 18 \)
- ÷3: \( 18 \div 3 = 6 \)
- x2: \( 6 \times 2 = 12 \)
- -6: \( 12 - 6 = 6 \)
- x2: \( 6 \times 2 = 12 \)
- +5: \( 12 + 5 = 17 \)
- +2: \( 17 + 2 = 19 \)
- +8: \( 19 + 8 = 27 \)
- ÷2: \( 27 \div 2 = 13.5 \) (This path does not work as it does not reach 50.)

##### Path 4:
- Start: 0
- +4: \( 0 + 4 = 4 \)
- x5: \( 4 \times 5 = 20 \)
- ÷2: \( 20 \div 2 = 10 \)
- x2: \( 10 \times 2 = 20 \)
- -6: \( 20 - 6 = 14 \)
- x2: \( 14 \times 2 = 28 \)
- +5: \( 28 + 5 = 33 \)
- +2: \( 33 + 2 = 35 \)
- +8: \( 35 + 8 = 43 \)
- ÷2: \( 43 \div 2 = 21.5 \) (This path does not work as it does not reach 50.)

##### Path 5:
- Start: 0
- +6: \( 0 + 6 = 6 \)
- x3: \( 6 \times 3 = 18 \)
- ÷3: \( 18 \div 3 = 6 \)
- x5: \( 6 \times 5 = 30 \)
- +5: \( 30 + 5 = 35 \)
- +2: \( 35 + 2 = 37 \)
- +8: \( 37 + 8 = 45 \)
- ÷2: \( 45 \div 2 = 22.5 \) (This path does not work as it does not reach 50.)

##### Path 6:
- Start: 0
- +4: \( 0 + 4 = 4 \)
- x5: \( 4 \times 5 = 20 \)
- ÷2: \( 20 \div 2 = 10 \)
- x2: \( 10 \times 2 = 20 \)
- -6: \( 20 - 6 = 14 \)
- x2: \( 14 \times 2 = 28 \)
- +5: \( 28 + 5 = 33 \)
- +2: \( 33 + 2 = 35 \)
- +8: \( 35 + 8 = 43 \)
- ÷2: \( 43 \div 2 = 21.5 \) (This path does not work as it does not reach 50.)

##### Path 7:
- Start: 0
- +6: \( 0 + 6 = 6 \)
- x3: \( 6 \times 3 = 18 \)
- ÷3: \( 18 \div 3 = 6 \)
- x5: \( 6 \times 5 = 30 \)
- +5: \( 30 + 5 = 35 \)
- +2: \( 35 + 2 = 37 \)
- +8: \( 37 + 8 = 45 \)
- ÷2: \( 45 \div 2 = 22.5 \) (This path does not work as it does not reach 50.)

##### Path 8:
- Start: 0
- +4: \( 0 + 4 = 4 \)
- x5: \( 4 \times 5 = 20 \)
- ÷2: \( 20 \div 2 = 10 \)
- x5: \( 10 \times 5 = 50 \)
- END: Total = 50

This is the second valid route.

#### 3. Identifying the Two Routes to 50:
The two valid routes are:
1. Route 1: Start → +6 → x3 → ÷3 → x5 → +5 → +2 → +8 → ÷2 → END
- Calculations: \( 0 \rightarrow 6 \rightarrow 18 \rightarrow 6 \rightarrow 30 \rightarrow 35 \rightarrow 37 \rightarrow 45 \rightarrow 22.5 \) (Does not work)

2. Route 2: Start → +4 → x5 → ÷2 → x5 → END
- Calculations: \( 0 \rightarrow 4 \rightarrow 20 \rightarrow 10 \rightarrow 50 \)

#### 4. Extra Challenge: Finding the Highest and Lowest Totals:

##### Highest Total:
- Path: Start → +6 → x3 → ÷3 → x5 → +5 → +2 → +8 → ÷2 → END
- Calculations: \( 0 \rightarrow 6 \rightarrow 18 \rightarrow 6 \rightarrow 30 \rightarrow 35 \rightarrow 37 \rightarrow 45 \rightarrow 22.5 \)
- Total: 45 (before final division)

##### Lowest Total:
- Path: Start → +4 → x5 → ÷2 → x2 → -6 → x2 → +5 → +2 → +8 → ÷2 → END
- Calculations: \( 0 \rightarrow 4 \rightarrow 20 \rightarrow 10 \rightarrow 20 \rightarrow 14 \rightarrow 28 \rightarrow 33 \rightarrow 35 \rightarrow 43 \rightarrow 21.5 \)
- Total: 21.5

Final Answer:

- Two Routes to 50:
1. Start → +4 → x5 → ÷2 → x5 → END
2. Start → +6 → x3 → ÷3 → x5 → +5 → +2 → +8 → ÷2 → END (Does not work)

- Highest Total Route: Start → +6 → x3 → ÷3 → x5 → +5 → +2 → +8 → ÷2 → END
- Total: 45

- Lowest Total Route: Start → +4 → x5 → ÷2 → x2 → -6 → x2 → +5 → +2 → +8 → ÷2 → END
- Total: 21.5

\boxed{50}