Four friends A, B, C and D need to cross a bridge in the night. A maximum of 2 people can cross at a time. They have only one lamp. A takes one minute to cross the bridge. B takes 2 minutes, C takes 8 minutes and D takes 11 minutes to cross the bridge respectively. A pair must walk together at the speed of the person who walks slowly. What is the minimum time required to cross the bridge by all four people?
Given:
- Friends and their time to cross the bridge:
- A: 1 minute
- B: 2 minutes
- C: 8 minutes
- D: 11 minutes
Rules:
1. Two people can cross the bridge at a time.
2. They must move at the slower person’s pace.
3. One person must return with the flashlight (if needed for subsequent crossings).
Strategy:
- Since A is the fastest, A will accompany each friend to minimize total time.
Steps:
1. A and B cross together:
- Time taken: 2 minutes (slowest of A and B).
- A returns: 1 minute.
- Total time so far: \(2 + 1 = 3\) minutes.
2. A and C cross together:
- Time taken: 8 minutes.
- A returns: 1 minute.
- Total time so far: \(3 + 8 + 1 = 12\) minutes.
3. A and D cross together:
- Time taken: 11 minutes.
- No return needed (all have crossed).
- Total time: \(12 + 11 = 23\) minutes.
Final Answer:
The minimum time required for all four friends to cross the bridge is \(23 \text{ minutes}\).
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