Puzzle | Torch and Bridge

There are 4 people (A, B, C, and D) who want to cross a bridge at night.

• A, B, C, and D take 1, 2, 5, and 8 minutes, respectively, 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 people 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?

Check if you were right - full answer with solution below.

Solution: They must cross the bridge in the following way:

Step 1:

A and B cross the bridge together at B's pace, taking 2 minutes. Then A comes back with the torch, taking 1 more minute.

Total time so far: 2 + 1 = 3 minutes.

👁 man_2

Step 2:

C and D cross the bridge together at D's pace, taking 8 minutes. Then B comes back with the torch, taking 2 more minutes.

Total time so far: 3 + 8 + 2 = 13 minutes.

👁 man_3

Step 3:

A and B cross the bridge together again at B's pace, taking 2 minutes.

All four - A, B, C, and D are now on the other side.

👁 man_4

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

To minimize the time:

The trick here is that 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.