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The Magic Cafe Forum Index » » Puzzle me this... » » Cross the river (0 Likes) Printer Friendly Version

Steve Martin
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Here is a nice puzzle, which foxed me for ages:

Adam, Bill, Chris and Dave are on one side of a bridge over a river at night.

Each of them is able to walk at different speeds.

Adam is the fastest - it takes him 1 minute to cross the bridge.
Bill is the next-fastest - it takes him 2 minutes to cross the bridge.
Chris is the next-fastest - it takes him 5 minutes to cross the bridge.
Dave is the slowest - it takes him 10 minutes to cross the bridge.

They have one torch between them, and this must be carried on the bridge at all times. It cannot be thrown across the river.

They must cross no more than two at a time, travelling at the speed of the slower person.

What must they do for all of them to arrive on the other side of the river in no more than 17 minutes?
Any man who reads too much and uses his own brain too little falls into lazy habits of thinking.
Albert Einstein
TomasB
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I found two slightly different solutions.

/Tomas
Steve Martin
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Yes - that's right. There are two.
Any man who reads too much and uses his own brain too little falls into lazy habits of thinking.
Albert Einstein
0pus
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I agree with Tomas.

(He's an ace at these.)
stanalger
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The two differ only in the second and fourth (return-the-torch-to-the-others)
crossings.
0pus
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Now you are giving too much away. Smile
mike paris
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Allowing for the return trips , I still arrive at 19 minutes
Dave + Adam 10 mins
+1 return
Chris + adam 5 mins
+i return
Bill + Adam 2
total 19.
unless there is a rope for him to swing back on, who is going to volunteer the answer.
Jonathan Townsend
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Is there something more efficient than setting up a table or tree search for doing this class of problem?

On the "real world" type side of this puzzle...
Let me get this right... One has a motercycle with sidecar, one has a nice italian sportscar and at least one has has a tandem bicycle. And the bike easily fits on the back of the car... and none of them have a cellphone that works. Presuming none of them are birds or bats of course. Smile
...to all the coins I've dropped here
TomasB
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Mike, you are wasting too much time by not letting the slowest pair walk together. So the reasoning would be that if you can't move a slow one across very fast, you might as well get another slow person over at the same time to be done with him also and not waste time on him later.

And I think that answers Jonathan's question also. Once you get the idea just mentioned there's really only two ways to do it and both ways will end up taking the same amount of time. So no exhaustive search is neccesary since you can reason your way to the solution.

/Tomas
mike paris
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Thomas,if the 2 slowest go across together dave 10 and chris 5, it will still take chris 5 minutes more to return across the bridge with the torch, that's 15 minutes already used,there are still 3 more people to cross and return? so it still don,t make sense .(to me)
TomasB
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Mike, once the slowest pair have walked across there can be a fast one already there to bring the torch back.

/Tomas
mike paris
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Ok ,got it, thanks,see what I mean about some easy ones are hard.(they are ALL easy when you know) he he.
Steve Martin
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When I first heard this puzzle it took me AGES to find the solution. After many attempts I first concluded it was impossible. It's easy when you know how, of course!
Any man who reads too much and uses his own brain too little falls into lazy habits of thinking.
Albert Einstein
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