The problem you've described involves a classic mathematical puzzle known as the
"River Crossing Problem". Let's break it down step by step and solve it systematically.
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Problem Statement
Jehovah sent Noah to build an ark for a great flood that would wipe out all life on Earth except those aboard the ark. The task is to transport a fox, a goose, and a bag of beans across a river using a small boat. However:
1. The fox cannot be left alone with the goose (the fox will eat the goose).
2. The goose cannot be left alone with the bag of beans (the goose will eat the beans).
Noah can only take one item at a time in the boat. The goal is to get all three items safely across the river without any of them being eaten.
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Solution Approach
We need to carefully plan each trip across the river to ensure that no two conflicting items are left alone together. Here’s how we can solve this:
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Step-by-Step Solution:
1.
Initial State:
- Left bank: Fox, Goose, Beans
- Right bank: None
- Boat: Empty
2.
First Trip:
- Noah takes the
Goose across the river.
- Left bank: Fox, Beans
- Right bank: Goose
- Boat: Empty
3.
Second Trip:
- Noah returns to the left bank alone.
- Left bank: Fox, Beans
- Right bank: Goose
- Boat: Empty
4.
Third Trip:
- Noah takes the
Fox across the river.
- Left bank: Beans
- Right bank: Fox, Goose
- Boat: Empty
5.
Fourth Trip:
- Noah brings the
Goose back to the left bank (since leaving the Fox and Goose alone on the right bank would result in the Fox eating the Goose).
- Left bank: Goose, Beans
- Right bank: Fox
- Boat: Empty
6.
Fifth Trip:
- Noah takes the
Beans across the river.
- Left bank: Goose
- Right bank: Fox, Beans
- Boat: Empty
7.
Sixth Trip:
- Noah returns to the left bank alone.
- Left bank: Goose
- Right bank: Fox, Beans
- Boat: Empty
8.
Seventh Trip:
- Noah takes the
Goose across the river.
- Left bank: None
- Right bank: Fox, Goose, Beans
- Boat: Empty
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Final State:
All three items (Fox, Goose, and Beans) are safely on the right bank without any of them being eaten.
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Explanation of the Solution
The key to solving this problem is to carefully manage the constraints:
- The Fox cannot be left alone with the Goose.
- The Goose cannot be left alone with the Beans.
By planning each trip strategically, we ensure that no two conflicting items are ever left alone together. The solution involves multiple trips back and forth, with Noah bringing items back when necessary to avoid conflicts.
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Answer:
The sequence of trips required to safely transport the Fox, Goose, and Beans across the river is as follows:
1. Take the Goose to the right bank.
2. Return alone.
3. Take the Fox to the right bank.
4. Bring the Goose back to the left bank.
5. Take the Beans to the right bank.
6. Return alone.
7. Take the Goose to the right bank.
Thus, the final answer is:
\[
\boxed{7}
\]
This indicates that it takes
7 trips to complete the task.
Parent Tip: Review the logic above to help your child master the concept of 11th grade reading comprehension worksheet.