Answer to Puzzle #25: Bridge crossing in 17 Minutes with Torch

25. Adam, Bob, Clair and Dave are out walking: They come to rickety old wooden bridge. The bridge is weak and only able to carry the weight of two of them at a time. Because they are in a rush and the light is fading they must cross in the minimum time possible and must carry a torch (flashlight,) on each crossing.

They only have one torch and it can't be thrown. Because of their different fitness levels and some minor injuries they can all cross at different speeds. Adam can cross in 1 minute, Bob in 2 minutes, Clair in 5 minutes and Dave in 10 minutes.

Adam, the brains of the group thinks for a moment and declares that the crossing can be completed in 17 minutes. There is no trick. How is this done?

This puzzle was e-mailed to me through this website. The problem is not difficult to solve per se, certainly when you read the answer it seems simple....

picture of a bridge for crossing puzzle Before reading the answer can I interest you in a clue?

Initially most people would tend to assume the the quickest way is to have Adam (1) carry the torch and do all the running. This however, is not the case, the quickest time is achieved by having Clair(5) and Dave(10) cross together.

For simplicity Adam, Bob, Clair and Dave will be know as (1), (2), (5) & (10) respectively

The moves are as follows:

(1) & (2) Cross with Torch2
(1) Returns with Torch1
(5) & (10) Cross with Torch10
(2) Returns with Torch2
(1) & (2) Cross with Torch2

Alternatively the second move can be (2) returning with the torch, the times are the same.

Out Of The Box Thinking

Eric Bowman E-Mailed me with a 10 minute solution. The solution is to have Dave(10) carry the torch and begin to cross with any of the others lets say Adam(1). Each continues at their own pace so in 1 minute Adam has reached the other side and one of the others can begin to cross say Bob(2), when he reaches the other side Clair(5) can begin to cross. Adam, Bob & Clair will be done in 8 minutes and Dave will be done in a further 2.

This solution satisfies the criteria that there are never more than 2 people on the bridge and the torch is always on the bridge whilst someone is crossing. So in that sense it is a neat solution. I personally don't think that this is the solution intended, not least because the question specifically asks you to show it can be done in 17 minutes but also because I believe the torch or flashlight is intended to bind the travelling pairs together. (I have seen a version that specifically says a pair will walk at the speed of the slowest one.) Always with these puzzles it is a matter of extracting the logic of the puzzle from the more verbose real world metaphor and that is my interpretation. However, if you regard these questions as interview preparation then an understanding of the 10 minute argument can do you no harm at all.

Alternate Versions

I've also seen this problem written with A fireman, an athlete, an old woman and a drunk guy escaping a burning house. As they travel down a burning staircase one must carry a fire extinguisher. I'm sure there are other versions too.

First time i asked Bard it refused to answer, second time it gave the right answer.

If you're curious what Bard made of this puzzle...

If you're curious what ChatGPT made of this puzzle...

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