The Bridge and Torch Riddle: What's the Minimum Crossing Time?
Four people must cross a bridge at night with one torch that holds only two at a time. Their crossing times are 1, 2, 5, and 10 minutes. The torch must be walked back each time. What is the minimum total time?
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What is the answer to the bridge and torch riddle?
The minimum time is 17 minutes. Send the 1 and 2 across (2 min), 1 returns (1 min), send the 5 and 10 across (10 min), 2 returns (2 min), then 1 and 2 cross again (2 min): 2 + 1 + 10 + 2 + 2 = 17 minutes.
Why isn't the answer 19 minutes?
The intuitive plan sends the fastest person on every trip, giving 10 + 1 + 5 + 1 + 2 = 19 minutes. The trick is to pair the two slowest people (5 and 10) so their times overlap on one crossing, which saves 2 minutes and gets you to 17.
How do you solve the bridge and torch riddle?
Get the two fastest across first and send one back with the torch, then send the two slowest together so their long times count only once, and finally bring the remaining fast pair over. This overlap of the slow walkers is the key insight.