Puzzle 18 | (Torch and Bridge)

Last Updated : 19 Aug, 2024
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Puzzle: There are 4 persons (A, B, C and D) who want to cross a bridge at night.

  1. A takes 1 minute to cross the bridge.
  2. B takes 2 minutes to cross the bridge.
  3. C takes 5 minutes to cross the bridge.
  4. D takes 8 minutes to cross the bridge.

There is only one torch with them and the bridge cannot be crossed without the torch. There cannot be more than two persons on the bridge at any time, and when two people cross the bridge together, they must move at the slower person’s pace. Can they all cross the bridge in 15 minutes?         Solution: They must cross the bridge in the following way:

  1. Step 1: A and B cross the bridge. A comes back. Time taken 3 minutes. Now B is on the other side.
  2. Step 2: C and D cross the bridge. B comes back. Time taken 8 + 2 = 10 minutes. Now C and D are on the other side.
  3. Step 3: A and B cross the bridge. Time taken is 2 minutes. All are on the other side.

Total time spent: 3 + 10 + 2 = 15 minutes.

To minimize the time:

The trick here is the persons with the fastest speeds only should come back (and that too only if there is a need to come back, as here we need to bring back the torch). A comes back in step-1 and B comes back in step-2. And, finally reduce the number of traveling back, like C, D does not come back.

 


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