Four Persons Bridge and Torch River Crossing in 15 minutes Puzzle

Four persons to cross a bridge in a dark night with one torch in 15 minutes. Two persons max can cross at a time. One crosses in 1 min, second in 2 mins...

The riddle

Apu, Bishnu, Camelia and Debu have to cross a frail bridge on a dark night with only one torch between them. The bridge can take the weight of only two persons. Apu takes 1 minute to cross, Bishnu takes 2 minutes, Camelia 5 minutes and Debu is the slowest. He takes 8 minutes to cross. How can all of them cross safely in 15 minutes?

Can you find out the way out? Your time is also 15 minutes.

Remember, in each crossing they need the torch. Question: what is the most difficult part of the problem they must solve?

Solution to the Bridge and Torch River Crossing in 15 minutes Puzzle

Let us first concentrate on the biggest hurdle of the crossing, knowing full well when two persons cross, total time taken will be the time taken by the slowest person. For example, if Apu and Debu cross together, they will cross in 8 minutes, not 9 minutes.

Analyze the time of crossing of the four, taken two at a time.

Crucial clue: If the two slowest persons cross in separate trips, total time of the two trips will be 13 minutes. Even if they had two torches, they cannot cross the bridge in 15 minutes.

So, the two slowest persons, Camelia and Debu, must cross together in one trip taking 8 minutes. 5 minutes crossing time of Camelia will be saved.

But they cannot be the first or last pair to cross (how can they get the torch). They must take a midway trip when in an earlier trip the two faster persons cross together, one stays back and the other returns with the torch.

That clears up the solution:

1. First forward and return trip: Fastest two, Apu and Bishnu, cross together in 2 minutes. Bishnu stays back, Apu returns with the torch in 1 more minute. Total 3 minutes gone.
2. Second crucial trip (forward and return): Camelia and Debu cross with the torch in 8 minutes. Bishnu was waiting. He returns with the torch in 2 more minutes. Total 10 minutes, cumulative 13 minutes gone.
3. Third and final trip: Apu and Bishnu cross together with the torch taking 2 more minutes and all four cross in within 15 minutes.

Know the biggest hurdle in a problem, a possibility that must be avoided. Find out by analysis and logic, how to get over the biggest hurdle. That will give you the solution.

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