Crossing a bridge

[Tim West]

Four DJs are off to play at a party, but they have to cross a bridge. It's night time (of course), and they have only got one torch between them.
Unfortunately, the bridge is weak, so only two of them can cross at once. Also, they must carry the torch when they cross, so they can see where they're going.
Now, they can all walk at different speeds:

Hixxy can walk really fast, he can cross the bridge in 1 minute.

Sharkey can walk almost as fast, he takes 2 minutes.

Brisk is a lot slower, he takes 5 minutes.

Breeze is the slowest of the lot, he takes 10 minutes.

Importantly, when two walk together, they must walk at the speed of the slower person. They all have to cross the bridge.
Now, the question...how fast can they do it? Can Sharkey make his gig, which starts in 17 minutes???
Cheers,
--Tim
PS Extra Double Plus Bonus Points to anyone who listens to these guys *g*. PLUR.
[ May 05, 2004: Message edited by: Tim West ]

[Rajiv]

19 mins...
guy who takes 1 min will always be traversing back and forth,first he will take guy with 2 min ,return back then 5 min,and then 10 min....

[Arjun Shastry]

I know the answer,it was a favourate question for companies during test.

[Tim West]

Ram - Yeah, that's how I heard about it too (from a friend). Thanks for not ruining the fun by telling everyone !
Rajiv - They can do better than that!
Cheers,

--Tim

[Tim West]

Ahh too smart...took me ages to work it out
Well done though!

--Tim

[HS Thomas]

I just realised why I could do it, though.
Posted a similar question myself in this very forum.
So I'll delete my response and let someone else have a go.
Nothing like practise making perfect.

[shankar vembu]

hmm. i arrived at 19 mins which seems to be pretty straightforward. but 17 mins
can it happen that the fastest guy while returning need not have to walk the whole distance, the torch is ON and maybe when he is 1/2 way or 3/4 way, the guy from the opposite direction can start walking following the light thus saving time. is this allowed ? still thinking ......
regards.

[David O'Meara]

Nope, each person has to walk the whole way.
Hint: Instead of modeling the solution around the fastest guy, what if you model it around the slowest?

[jonty rhodes]

i tutor 8th graders in toronto, ontario..Can you beleive it, it was one of their math puzzle assignments..So, yeah i know the answer but won't spoil it for other..Its NOT 19 though..

[fred rosenberger]

It can be done in 17 minutes. the trick is to minimize the time for the 5 and 10 minute guys. But i don't want to give it away too easily.

[Stefan Wagner]

Well - in the last moment you could program a solution of brute force trying every possibility.

[Marc Peabody]

=== bridge
1 2 5 10 djs by speed
> and < direction of movement
5 10 === >1 2 *the fast djs go first (= 2min)
5 10 1< === 2 *one takes the torch back (+ 1m = 3min)
1 === >5 10 2 *the slow djs go (+ 10m = 13min)
1 2< === 5 10 *then two brings it back (+ 2m = 15min)
=== >1 2 5 10 *one and two are left (+ 2m = 17min)

[Tim West]

Well done :-)
...And no-one listens to these guys??? Y'all don't know what you're missing out on!!
Hmm, I'm gonna find another problem to post :-D

--Tim