Question

Four soldiers - P, Q, R and S need to croos a bridge. A maximum of two person can cross it at a time. It is night and they just have one lamp. Persons that cross the bridge must carry the lamp to find the way. A pair must walk together at the speed of slower person. After crossing the bridge, the person having faster speed in the pair will return with lamp each time to acompany another person in the group. Finally, the lamp has to be returned at the original place and the person who returns the lamp has to cross the bridge again without lamp. To cross the bridge, the time taken by them is as follows: P:1 minutes, Q: 3 minutes, R:7 minutes and S:10 mimutes. What is the total minimum time required by all the soldiers to cross the bridge?

Answer 1

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. That would make this question too simple even as a warm up question.

. 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

2 comes back

7 and 10 go across

1 comes back

1 and 2 go across (done)

Total time = 2 + 2 + 10 + 1 + 2 = 17 mins

mark as brainlest plzzzz