Four people need to cross a rickety bridge at night. Unfortunately, they have…
2025
Four people need to cross a rickety bridge at night. Unfortunately, they have only one torch and the bridge is too dangerous to cross without one. The bridge is only strong enough to support two people at a time. Not all people take the same time to cross the bridge. Times for each person: 1 min, 2 mins, 7 mins and 10 mins. What is the shortest time needed for all four of them to cross the bridge?
- A.
10 mins
- B.
15 mins
- C.
17 mins
- D.
20 mins
Show answer & explanation
Correct answer: C
Concept: This is the classic “two at a time, one torch” bridge-crossing puzzle. Because a joint crossing takes as long as its slower member, the total time is minimized only by (1) always sending back the fastest person(s) available with the torch, and (2) sending the two slowest people across together in a single trip, so their large individual times are paid once instead of twice.
Step-by-step application:
The 1-minute and 2-minute person cross together — this trip takes 2 minutes (bounded by the slower of the two).
The 1-minute person returns alone with the torch — this trip takes 1 minute.
The 7-minute and 10-minute person cross together — this trip takes 10 minutes. Pairing the two slowest people into one crossing means their large times are paid only once.
The 2-minute person, who was left on the far side after the first crossing, returns alone with the torch — this trip takes 2 minutes.
The 1-minute and 2-minute person cross together one final time — this trip takes 2 minutes.
Cross-check: Total time = 2 + 1 + 10 + 2 + 2 = 17 minutes. Compare this with the strategy of using only the fastest person to ferry the torch back and forth for every single crossing: 2 + 1 + 7 + 1 + 10 = 21 minutes — 4 minutes worse, because that strategy pays the 7-minute crossing on its own instead of pairing it with the 10-minute crossing. This confirms that pairing the two slowest travellers into one joint crossing gives the minimum total.
Answer: The shortest total time for all four people to cross is 17 minutes.