## Timed Bridge Problem

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jewish_scientist
Posts: 1006
Joined: Fri Feb 07, 2014 3:15 pm UTC

### Timed Bridge Problem

Nevermind. Apparently I already asked this question, and then forgot I asked it.

Adam, Ben and Carol are on one side of a bridge in the middle of the night. The bridge can support the weight of only two people at a time. They have one lantern. Because there are holes in the bridge, people crossing the bridge need to be able to see; which is why they brought a lantern. Adam can cross the bridge as fast as or faster than Ben; who can cross the bridge as fast as or faster than Carol. The symbol AB represents Adam and Ben crossing the bridge together. What is the fastest way for everyone to cross the bridge. The answer is AB A AC. The total amount of time it took to get everyone across is A+B+C. That was just an easy version so you understand the problem. Now for the real problems:

Adam, Ben, Carol and Dave want to cross the bridge. Carol can cross the bridge as fast as or faster than Dave. What is the fasted way for everyone to cross the bridge?

Spoiler:
The answer is AB A CD B AB and the total amount of time is A+3B+D
The underlined crossings can be switched with equivalent results.

What if Elisabeth want to cross with them?
Spoiler:
I am not sure, but I think the answer is AB B DE A AC A AB, which gives 2A+3B+C+E as the total

Ask this question again and again, each time adding a person.

What if an group of n people want to cross?

Note: I got this problem form a TED talk video on Youtube.[/spoiler]
Last edited by jewish_scientist on Mon Nov 23, 2015 5:57 pm UTC, edited 2 times in total.
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jaap
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### Re: Timed Bridge Problem

Yrgos
Posts: 6
Joined: Fri Nov 06, 2015 10:33 pm UTC

### Re: Timed Bridge Problem

Disagree with solution.
Spoiler:
Without times or factors the solution can't be determined. Take your example. Say of the 4 persons Alice is a sprinter, she can cross in 1 minute. Bob, Charlie and Dave are mere mortals and use say 9, 10 and 11 minutes respectivedly. Then your solution of AB A CD B AB is 39 minutes, but Alice running back and forth with everyone. AB A AC A AD is only 32 minutes.

emlightened
Posts: 42
Joined: Sat Sep 26, 2015 9:35 pm UTC
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### Re: Timed Bridge Problem

If you've already made a thread on this, why not just bump the first one?

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