Tuesday, 9 October 2012

Bridge Crossing in minimum time

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Problem Statement:

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?

To get everyone across in 17 minutes, we need get the two slowest people across together; otherwise we are 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 |==========================| 


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

 B |==========================| A

   |                          | C

   |==========================| D


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

 A |==========================| C

 B |                          | D



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

   |==========================| A

   |                          | B

   |==========================| C D

Another valid solution is to have A bring the flashlight back in step 2.

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