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The Rope Bridge

 

Four people need to cross a rickety rope bridge to get back to their camp at night. Unfortunately, they only have one flashlight and it only has enough light left for seventeen minutes. The bridge is too dangerous to cross without a flashlight, and it’s only strong enough to support two people at any given time.

Each of the campers walks at a different speed. One can cross the bridge in 1 minute, another in 2 minutes, the third in 5 minutes, and the slow poke takes 10 minutes to cross. How do the campers make it across in 17 minutes?

 

 

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Solution

To get everyone across in 17 minutes, we need the two slowest people to travel across together; otherwise we're wasting too much time. Once we
get them across, how do we not make one of them walk back with the flashlight? Just have one of the faster people already there waiting to


sprint the flashlight back across.
person A: 1 minute
person B: 2 minutes
person C: 5 minutes
person D:10 minutes

1. A & B cross. total time: 2 minutes.

C |--------------------------| A
D |                                       | B
   |--------------------------| flashlight

2. B comes back. total time: 4 minutes.

C |--------------------------| A
D |                                       |
B |--------------------------|
flashlight

3. C & D cross. total time: 14 minutes.

B |--------------------------| A
   |                                        | C
   |--------------------------| D
                                             flashlight

4. A comes back. total time: 15 minutes.

A |--------------------------| C
B |                                          | D
   |--------------------------|
flashlight

5. A & B cross. total time: 17 minutes.

|--------------------------| A
|                                             | B
|--------------------------| C D
                                               flashlight
 
Another valid solution is to have A bring the flashlight back in step 2.


Difficulty
    • Moderate
      		Type
        • Logic


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            Comments

            this solution is wrong. if B and A cross it will be a total time of 3mins not 2mins. then if B comes back then it will be a total time of 5 mins. then if C and D cross then just them two will be 15mins, add that onto the 5 mins and it will become 20mins. then if A crosses then it will be a total time of 21mins. and then if B and A cross it will be a total time of 24mins NOT 17MINS!!
            - kitty (25 May 2009)

            No you are wrong, they are walking together, remember they need to have the flashlight. The faster person will walk at the pace of the slower person. this solution is correct
            - Tyler (18 Jun 2009)

            Kitty you're not the smartest.
            - jimbo (10 Oct 2009)

            If you piggy back some one you can cut your time down tremendously, have the one minute guy(A) piggy back B, go back for C, then go back for D, total 5 minutes.
            - chris (31 Jan 2010)

            PS I understand that you were looking to do it 17 mins., but why not 5 mins. as a teaser.
            - chris (31 Jan 2010)

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