Problem Analysis
We are tasked with determining which of the starting numbers (10, 4, 6, and 3) can navigate through the maze and transform into one of the target exit numbers (9, 3.5, 12, 20, 8, and 14). The maze consists of operations that modify the numbers as they move through it.
#### Key Points:
1.
Starting Numbers: 10, 4, 6, and 3.
2.
Exit Numbers: 9, 3.5, 12, 20, 8, and 14.
3.
Operations in the Maze:
- `+3`: Add 3 to the number.
- `×2`: Multiply the number by 2.
- `+5`: Add 5 to the number.
- `-2`: Subtract 2 from the number.
- `×3`: Multiply the number by 3.
- `÷2`: Divide the number by 2.
- `+1`: Add 1 to the number.
- `-3`: Subtract 3 from the number.
#### Objective:
Find a path for each starting number such that it transforms into one of the exit numbers.
---
Step-by-Step Solution
#### 1. Starting Number:
10
We need to find a sequence of operations that transforms 10 into one of the exit numbers.
-
Path 1:
- Start: 10
- `+3`: 10 + 3 = 13
- `×2`: 13 × 2 = 26
- `÷2`: 26 ÷ 2 = 13
- `+1`: 13 + 1 = 14
Result: 14 (which is an exit number).
Thus,
10 can survive the maze and transform into
14.
---
#### 2. Starting Number:
4
We need to find a sequence of operations that transforms 4 into one of the exit numbers.
-
Path 1:
- Start: 4
- `×2`: 4 × 2 = 8
- `+1`: 8 + 1 = 9
Result: 9 (which is an exit number).
Thus,
4 can survive the maze and transform into
9.
---
#### 3. Starting Number:
6
We need to find a sequence of operations that transforms 6 into one of the exit numbers.
-
Path 1:
- Start: 6
- `+5`: 6 + 5 = 11
- `-2`: 11 - 2 = 9
Result: 9 (which is an exit number).
Thus,
6 can survive the maze and transform into
9.
---
#### 4. Starting Number:
3
We need to find a sequence of operations that transforms 3 into one of the exit numbers.
-
Path 1:
- Start: 3
- `×2`: 3 × 2 = 6
- `+5`: 6 + 5 = 11
- `-2`: 11 - 2 = 9
Result: 9 (which is an exit number).
Thus,
3 can survive the maze and transform into
9.
---
Summary of Results
-
10 →
14
-
4 →
9
-
6 →
9
-
3 →
9
All starting numbers can survive the maze and transform into one of the exit numbers.
---
Final Answer
$$
\boxed{10, 4, 6, 3}
$$
Parent Tip: Review the logic above to help your child master the concept of fun math pages.
