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There is a family who needs to cross an old rotted bridge at night. They all begin on the same side. You have 17 minutes to get all of them across to the other side. A maximum of two people can cross at one time. Also, there is one flashlight with a low battery. In order to be safe, no one can cross the bridge without a flashlight. That is to say, any party who crosses, either 1 or 2 people, must have the flashlight with them. The flashlight must be walked back and forth, it cannot be thrown, etc. Each person walks at a different speed. A pair must walk together at the rate of the slower person.

Kid     :  1 minute to cross
Wife    :  2 minutes to cross
Husband :  5 minutes to cross
Grandpa : 10 minutes to cross

For example if the kid and grandpa walk across first, 10 Minutes have elapsed when they get to the other side of the bridge. If the grandpa returns with the flashlight, a total of 20 minutes have passed, and the flashlight goes dead without the entire family one the other side.

I realized some people might have heard this one. If that is the case, then do not post hints or a solution. This is NOT a trick problem.

If the world should blow itself up,the last audible voice would be an expert saying it can't be done

This post was edited by Hawkeye on Mar 24, 2006.

Hey, I got one (this one not being so much a question of advanced math knowlege ;p).

(:um, spoiler warning:)

Wife and kid go over (2 min. total), kid comes back (3). Grampa and dad go over (13), wife comes back (15). Wife and kid go over (17).

You're here, aren't you? You're talking to me, aren't you?

Congrats! I wasn't allowed to say anything, as I had heard and solved this before. That spoiled all the fun for me :P I am still waiting on a problem on derivatives though ;) Those are the things I like the most, and can solve the most (assuming he doesn't find a problem that involves e^x^2^2x or some weird thing similar to that).

But Hawkeye, you don't necessarily have to find something with derivatives... think about what could happen if I didn't know how to solve it :D Heh that would be a real bad thing after I have bragged about me liking derivatives and stuff ;)

Un bacio è un'apostrofo rosa scritto tra le parole "ti amo".

Wife and kid go over (2 min. total), kid comes back (3). Grampa and dad go over (13), wife comes back (15). Wife and kid go over (17).

I think this is wrong because the flashlight has not been brought back across the bridge for the Wife and kid after the Dad and Grampa go over. The flashlight goes over, it has to come back in order for the others to use it. Somebody help me out here =)

Good job, Bunk. He got it right. :)

Majic, it is easy to see how something could get lost in translation of the solution. So I made this to depict the steps along the way (note * indicates where flashlight is)

<nobody>                  |========| Kid Wife Husband Grandpa*
                              0
Kid Wife*                 |========| Husband Grandpa
                             +2
Wife                      |========| Kid Husband Grandpa*
                             +1
Wife Husband Grandpa*     |========| Kid
                             +10
Husband Grandpa           |========| Kid Wife*
                             +2
Kid Wife Husband Grandpa* |========| <nobody>
                             +2
                             = 17

The derivatives problem is coming up, my dear. :D

If the world should blow itself up,the last audible voice would be an expert saying it can't be done

Ok I see now that Bunk is right. The way he wrote out the solution confused my feeble brain and I lost track of the flashlight because he never stated who had it. =(

I must admit that I honestly attempted to get a solution and after 30 minutes of thought I still couldn't find one. I was never good at math.

Don't be so hard on yourself, Majic.

I don't post easy questions deliberately. This question inparticular is very difficult to reason through. People always tend to think about the return trip, but fail to realize that the importance lies with reducing minutes by combining high minute cross times.

I.e., if Grandpa and the Husband had not been sent together, they would have been sent separate, which would have definitely made a combined 15 minutes as opposed to 10 minutes together.

Also, it isn't really a math problem as it is just a logic problem. :)

If the world should blow itself up,the last audible voice would be an expert saying it can't be done