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

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:

Move	Time
(1) & (2) Cross with Torch	2
(1) Returns with Torch	1
(5) & (10) Cross with Torch	10
(2) Returns with Torch	2
(1) & (2) Cross with Torch	2
	17

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.

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