Bridge and Torch Riddle: The Minimum Crossing Time
Classic consulting and tech interview puzzle
The riddle
Four people must cross a bridge at night with only one torch. The bridge holds at most two people at a time, and the torch must accompany every crossing, so it has to be carried back when needed. They take 1, 2, 5 and 10 minutes to cross alone respectively, and a pair moves at the speed of the slower person. What is the minimum time for all four to reach the other side?
Need a hint?
Think about who should cross together with the slowest person, and who can bring the torch back without costing the slow ones extra time.
Show the answer and the solution
Answer: 17 minutes: the 1-minute and 2-minute people cross, the 1-minute person comes back, the 5-minute and 10-minute people cross, the 2-minute person comes back, then the 1-minute and 2-minute people cross again.
The reasoning
The trap is to have each slow person escorted back by the fastest one, which costs 19 minutes. The best strategy makes the two slowest people cross together, so that they do not have to come back. First, the 1-minute and 2-minute people cross together, taking 2 minutes. Then the 1-minute person brings the torch back, taking 1 minute. Next, the 5-minute and 10-minute people cross together, taking 10 minutes. The 2-minute person returns, taking 2 minutes. Finally, the 1-minute and 2-minute people cross together again, taking 2 minutes. The total is 2 + 1 + 10 + 2 + 2 = 17 minutes.
What next?
Reasoning improves like memory: by practising often. Next, test yourself on our general knowledge quizzes.