Puzzle 3| The Bridge & The Torch
- Four people need to cross a narrow bridge at night. They have just one torch, and at most two people can cross at a time.
Their crossing times (alone) are: 1 minute, 2 minutes, 7 minutes, and 10 minutes.
When two people cross together, they move at the slower person’s pace. The torch must be carried whenever someone crosses.
What is the **minimum total time** needed for all four to cross the bridge?
Show Answer
Answer:
17 minutes
Explanation
Label the people A=1, B=2, C=7, D=10.
Optimal sequence:
1. A and B cross → time = 2 (torch on far side: A,B)
2. A returns → time = 1 (total 3)
3. C and D cross → time = 10 (total 13)
4. B returns → time = 2 (total 15)
5. A and B cross again → time = 2 (total 17)
Why this works best:
– Pairing the two slowest (C & D) to cross together saves time because sending them separately would cost 7+10 = 17 just for them, whereas together is only 10.
– Using the two fastest (A & B) as shuttleers minimizes return overhead (returns cost 1 or 2 minutes).
This yields the minimum total of **17 minutes**.
