two men and two boys want to cross a river, using a small canoe. the canoe can carry two boys or one man. what is the least number of times the canoe must cross the river to get everyone to the other side.
The solution to this problem involves considering the constraints and optimizing the number of crossings.
First, let's establish the facts:
- Two men and two boys need to cross a river.
- The canoe can carry either two boys or one man.
Given these constraints, we need to find the least number of times the canoe must cross the river to get everyone to the other side.
Let's consider the possible combinations of people that can be transported in each crossing:
1. Two boys cross the river.
2. One boy returns with the canoe.
3. Two men cross the river.
4. One man returns with the canoe.
5. Two boys cross the river again.
Now, we have transported both boys to the other side. We need to bring back the canoe to pick up the other two people. The breakdown of the remaining steps can be as follows:
6. One man and one boy cross the river.
7. The man returns with the canoe.
8. Two men cross the river.
9. One boy returns with the canoe.
10. Two boys cross the river.
Now, everyone has crossed the river, and they have reached the other side. We can see that this sequence of steps requires a total of 10 crossings.
To summarize, the least number of times the canoe must cross the river to get everyone to the other side is 10.
To find the least number of times the canoe must cross the river to get everyone to the other side, we need to consider the restrictions:
1. The canoe can carry two boys or one man.
2. There are two men and two boys.
Let's break down the steps:
Step 1: Both boys cross the river together.
- Cross the river once (2 boys).
Step 2: One boy returns with the canoe.
- Cross the river once (1 boy).
Step 3: Two men cross the river together.
- Cross the river once (2 men).
Step 4: One boy returns with the canoe.
- Cross the river once (1 boy).
Step 5: Both boys cross the river together.
- Cross the river once (2 boys).
In total, the canoe must cross the river 5 times to get everyone to the other side.