Torch Bridge Crossing Puzzle

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

A takes 1 minute to cross the bridge.

B takes 2 minutes to cross the bridge.

C takes 5 minutes to cross the bridge.

D takes 10 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 this bridge in no more than 17 minutes?

Answer

Yes, they can all cross in 17 minutes.

Solution

Let’s denote the crossing times again:

  • A = 1 minute
  • B = 2 minutes
  • C = 5 minutes
  • D = 10 minutes

They must share a torch, so someone needs to return with it each time.

  1. A and B cross → 2 minutes
    (Fastest two cross first)
    ⏱ Total = 2
  2. A returns → 1 minute
    (Fastest person brings torch back)
    ⏱ Total = 3
  3. C and D cross → 10 minutes
    (Slowest two cross together)
    ⏱ Total = 13
  4. B returns → 2 minutes
    (Faster of the initial two returns)
    ⏱ Total = 15
  5. A and B cross again → 2 minutes
    (Fastest two cross again)
    ⏱ Total = 17

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