Ashok, Balu, Chiru, and Dareesh are crossing a bridge at night which requires a torch light. With a given torch maximum only 2 people can walk together. If third person tries to walk with them, then one of them may fall into the water. Each of them crosses the bridge with different speeds. Ashok takes one minute, Balu takes 2 minutes, Chiru takes seven minutes, and Dareesh takes ten minutes to cross.
Find out what is the shortest time for all of them to cross that bridge?
Note: If two persons are walking together, then faster person has to slow down to accompany the slower rate person.
The initial solution most people will think of is to use the fastest person as an usher to guide everyone across. How long would that take? 10 + 1 + 7 + 1 + 2 = 21 mins. Is that it? No. To reduce the amount of time, we should find a way for 10 and 7 to go together. If they cross together, then we need one of them to come back to get the others. That would not be ideal. How do we get around that? Maybe we can have 1 waiting on the other side to bring the torch back. The fastest way to get 1 across and be back is to use 2 to usher 1 across. So let's put all this together.
1 and 2 go cross (Ashok and Balu goes first)
2 comes back (Balu comes back)
7 and 10 go across (Chiru and Dareesh goes next)
1 comes back (Ashok comes back)
1 and 2 go across (Ashok and Balue goes) (done)
Total time = 2 + 2 + 10 + 1 + 2 = 17 mins
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