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Crossing the bridge


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Question

A group of four people has to cross a bridge. It is dark, and they have to light the path with a flashlight. No more than two people can cross the bridge simultaneously, and the group has only one flashlight. It takes different time for the people in the group to cross the bridge:

Annie crosses the bridge in 1 minute,
Bob crosses the bridge in 2 minutes,
Caren crosses the bridge in 5 minutes,
Dorothy crosses the bridge in 10 minutes.

How can the group cross the bridge in 17 minutes?

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  • Solution

First, A and B cross, taking 2 minutes. Then A returns with the flashlight in an additional 1 minute. Then C and D cross, taking an additional 10 minutes. Then B runs back with the flashlight in 2 additional minutes. Finally, A and B cross in 2 additional minutes. 2 + 1 + 10 + 2 + 2 = 17.

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Send A and B together (2 min), bring B back (+2 min) with the flashlight. Send C and D together (+10 min), bring A back with the flashlight (+1 min). Send A and B together (+2 min). All have crossed the bridge with total time=2+2+10+1+2=17 min.

Edited by sabjiwala
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