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Problem 8 (Bridge Problem)

Four people come upon a bridge in the middle of the night. It is dark and they must use a flashlight to get across the bridge but they only have one flashlight, and the bridge is so rickety that no more than two people an be on the bridge at the same time. One person (person A) can cross the bridge in 1 minute, the second person (person B) can cross the bridge in 2 minutes, the third person (person C) can cross the bridge in 4 minutes, and the last person (person D) can cross the bridge in 10 minutes. Can the four people cross the bridge to the other side in 18 minutes or less ? If so, how ?

Solution

The four people can cross the bridge in 18 minutes by using the following strategy:

• person A crosses the bridge with person B (takes 2 minutes)
• then A returns (1 minute)
• then A crosses with C (4 minutes)
• then A returns (1 minute)
• finally A crosses with D (10 minutes)
• Total: 18 minutes

Of course, just because you can't find a faster way for the people to cross the bridge, have we really proven this is the best way ? Is possible to enumerate all the different ways the people can cross the bridge ?

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Last modified on Tuesday, January 12, 1999