Bridge and Torch Puzzle

The Puzzle: Four people (A, B, C, D) need to cross a bridge at night.

• They have only one torch.
• The bridge can only hold two people at a time.
• Anyone crossing must carry the torch.
• Speeds: A: 1 min, B: 2 min, C: 7 min, D: 10 min.
• When two people cross, they move at the speed of the slower person. What is the minimum time for all to cross?

1. The Common Mistake (Greedy Approach)

Most people try to use the fastest person (A) as the “shuttler” to bring the torch back every time.

1. A & B cross (2 min), A returns (1 min) = 3
2. A & C cross (7 min), A returns (1 min) = 8
3. A & D cross (10 min) = 10 Total: 21 mins.

2. The Optimized Solution (The “Buddy” Rule)

The key is to send the two slowest people (C & D) together so their slow times overlap into a single trip. But someone needs to be on the other side to bring the torch back!

1. A & B cross: (2 min)
2. A returns: (1 min) - Now A and B are split.
3. C & D cross: (10 min) - Slowest people are now across!
4. B returns: (2 min) - B was waiting there!
5. A & B cross: (2 min) Total: 17 mins.

---

Interview-Focused Questions

Summary

• Step 1: Send the two fastest.
• Step 2: Bring back the fastest.
• Step 3: Send the two slowest.
• Step 4: Bring back the second fastest.
• Step 5: Send the two fastest again.