Bridge Cross Puzzle

Puzzle Level :- Easy

             This is one of the category of river crossing puzzles.  There are various name for this problem like  Bridge and Torch problem , Dangerous crossing etc....

PUZZLE

       Four people come to a river in the night. There is a narrow bridge, but it can only hold two people at a time. They have one torch and, because it's night, the torch has to be used when crossing the bridge. Each person walks at different speed. Assume 4 persons are A,B,.C,D.
Person A can cross the bridge in 1 minute,
            B in 2 minutes,
            C in 5 minutes,
     and D in 8 minutes.
When two people cross the bridge together, they must move at the slower person's pace.

The question is, What is the minimum time to cross the bridge?

ANSWER

Minimum time to cross the bridge is 15 Minutes.

SOLUTION

This problem can be extended for more than 4 people  with different crossing times.

So to solve this kind of problems we need to keep some points in mind

•  Always  slowest persons should cross together . and same goes for fastest persons
•  Before slowest persons cross the river make sure there are some fast people on other side to  return torch so Fastest persons should cross in first to return torch.
•  While returning the torch to other side always try to use the fastest person

Initial  positions are 

 A(1),B(2),C(5),D(8) (Torch)=====================       (Time :-0 min)

First send fastest persons i.e A,B so it teams 2 mins

                              C(5),D(8)=====================  A(1),B(2) (Torch)    (Time :-2 mins)

Now torch should return so send A back , because he is fastest person available on other side

         A(1),C(5),D(8) (Torch)=====================    B(2)   (Time :-3 mins)

Now let slowest persons cross the river, It takes 8 mins

                                     A(1)=====================   B(2),C(5),D(8) (Torch)   (Time :-11 mins)

Since B is fastest person on other side , let him return the torch

                  B(2),A(1)(Torch)=====================    C(5),D(8)    (Time :-13 mins)

Now A,B crosses bridge

                  B(2),A(1)(Torch)=====================    C(5),D(8)    (Time :-15 mins)

This kind of crossing puzzle can be easily solved if we follow above 3 points even it became complex with more people

-------------------------END----------------------