Torch and Bridge | Puzzle

Puzzle: There are 4 persons (A, B, C, and D) They 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.

Is it possible to cross the bridge in 15 minutes?

Solution:
Let's see how they cross the bridge in 15 minutes.

Step 1: A and B cross the bridge. A comes back. 

A+B = 1+2 = 3 minutes. 

Now B is on the other side.

A, C, D   ————————  B

Step 2: C and D cross the bridge. B comes back. 

C+ D = 8 + 2 = 10 minutes. 

Now C and D are on the other side.

A, B     ————————  C, D

Step 3: A and B cross the bridge. Noone comes back. 

A+B = 2 minutes. 

All are on the other side.

            ————————  A, B, C, D

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

Trick to apply:

Trick is persons with the fastest speed only should come back (only if there is a need to come back as here we need to bring back the torch).

Let me know in comment if you have any questions.