

Steve Martin Inner circle 1119 Posts 
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 nextfastest  it takes him 2 minutes to cross the bridge. Chris is the nextfastest  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 Inner circle Sweden 1143 Posts 
I found two slightly different solutions.
/Tomas 
Steve Martin Inner circle 1119 Posts 
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 Inner circle New Jersey 1740 Posts 
I agree with Tomas.
(He's an ace at these.) 
stanalger Special user St. Louis, MO 996 Posts 
The two differ only in the second and fourth (returnthetorchtotheothers)
crossings. 
0pus Inner circle New Jersey 1740 Posts 
Now you are giving too much away.

mike paris Regular user 179 Posts 
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 Eternal Order Ossining, NY 27017 Posts 
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.
...to all the coins I've dropped here

TomasB Inner circle Sweden 1143 Posts 
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 Regular user 179 Posts 
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 Inner circle Sweden 1143 Posts 
Mike, once the slowest pair have walked across there can be a fast one already there to bring the torch back.
/Tomas 
mike paris Regular user 179 Posts 
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 Inner circle 1119 Posts 
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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