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100 adults and 2 children need to cross a river on a boat which can carry a maximum of 1 adult or 2 children at a time. If, initially, all of them are present on the same side of the river, how many times will the boat travel across the river to move all of them to the other side? 1) 397 2) 399 3) 400 4) 401?
Most Upvoted Answer
100 adults and 2 children need to cross a river on a boat which can ca...
Problem Analysis:
To solve this problem, we need to devise a strategy to move all 100 adults and 2 children across the river using a boat that can carry a maximum of 1 adult or 2 children at a time. We will consider the following points while devising our strategy:

1. The boat can carry a maximum of 1 adult or 2 children at a time.
2. The boat must carry at least one person on each trip.
3. The goal is to move all 100 adults and 2 children across the river.

Solution:
We can solve this problem by dividing it into smaller steps and finding a pattern. Let's devise a strategy to move the people across the river:

Step 1: Move 2 children across the river.
- Take the boat with 2 children to the other side of the river.
- This will take 1 trip.

Step 2: Move 1 child back to the starting side.
- Leave 1 child on the other side of the river and take the boat back to the starting side.
- This will take 1 trip.

Step 3: Move 2 adults across the river.
- Take the boat with 2 adults to the other side of the river.
- This will take 1 trip.

Step 4: Move 1 adult back to the starting side.
- Leave 1 adult on the other side of the river and take the boat back to the starting side.
- This will take 1 trip.

Now, we have successfully moved 2 children and 2 adults to the other side of the river. We can repeat these steps until all the people are moved across the river.

Pattern:
Let's analyze the pattern to find out how many trips will be required to move all the people across the river:

- In each set of 4 trips (Step 1, Step 2, Step 3, Step 4), 3 people are moved across the river (2 adults and 1 child).
- After each set of 4 trips, 3 people are successfully moved to the other side.
- Therefore, to move all 100 adults and 2 children, we will need (100 + 2) / 3 sets of 4 trips.

Calculations:
Number of sets of 4 trips = (100 + 2) / 3 = 34

Total number of trips = (Number of sets of 4 trips) * 4 = 34 * 4 = 136

Therefore, the boat will travel across the river 136 times to move all 100 adults and 2 children to the other side.

Conclusion:
The correct answer is 136 trips.
Community Answer
100 adults and 2 children need to cross a river on a boat which can ca...
Answer 401
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100 adults and 2 children need to cross a river on a boat which can carry a maximum of 1 adult or 2 children at a time. If, initially, all of them are present on the same side of the river, how many times will the boat travel across the river to move all of them to the other side? 1) 397 2) 399 3) 400 4) 401?
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