No...I can't...I'm busy

It finally qualified! OK, here's the solution, with an explanation.

This isn't really a riddle, it's a test of lateral thinking. And it's a lot harder than it looks - very few people are able to work it out from first principles, but once you know the answer it's obvious!

The key to solving it is the time taken by each man. That's obvious, what isn't so obvious is how to fit the times together. Most people start by assuming that the most important thing is minimising the time spent bringing the flashlight back cross the bridge, as this is effectively wasted time. So they start by sending man D (the quickest) across with A, then coming back and taking B and C, in turn. This minimises the "return time" to 2 minutes, allowing the maximum possible for the others to cross. But the total "crossing time" adds up to 17 minutes (10 minutes for A+D, 5 minutes for B+D and 2 minutes for C+D), and the 2 minutes return time makes a total of 19 minutes, which is too long!

To find the solution, you need to look at it from a different angle. And the real key is not the return time, it's the crossing time.

Take a look at those times again. A takes 10 minutes, and B takes 5 minutes. If they go across separately, that's 15 minutes for the two of them. But if you send them across together, it only takes 10 minutes. However, you obviously can't have one of them come back again, as that would waste far too much time. This means that they can't be the first to go across (as if they did, one of them would have to bring the flashlight back), and they can't be the last to cross (as there's no way for them to get the flashlight in order to do so). So they have to be the second (middle) pair to cross.

Now that I've given you the necessary clues, most of you should have worked it out by now. But here's the solution in full, complete with the timings, for those that still don't believe it can be done in 17 minutes:

1. The starting positions are like this:
   ABCD ¸,ø¤º°`°º¤ø,¸
   (that's the bridge, by the way!)
   
   
2. D and C cross the bridge together.
   Time taken: 2 minutes. Total time so far: 2 minutes.
   Positions after this step: AB ¸,ø¤º°`°º¤ø,¸ DC
   
   
3. D returns with the flashlight.
   Time taken: 1 minute. Total time so far: 3 minutes.
   Positions after this step: ABD ¸,ø¤º°`°º¤ø,¸ C
   
   
4. A and B cross the bridge together.
   Time taken: 10 minutes. Total time so far: 13 minutes.
   Positions after this step: D ¸,ø¤º°`°º¤ø,¸ ABC
   
   
5. C returns with the flashlight.
   Time taken: 2 minutes. Total time so far: 15 minutes.
   Positions after this step: DC ¸,ø¤º°`°º¤ø,¸ AB
   
   
6. D and C cross the bridge together.
   Time taken: 2 minutes. Total time so far: 17 minutes.
   Positions after this step: ¸,ø¤º°`°º¤ø,¸ ABCD
   

There you are! It's easy when you know how

I'm not even gonna try. It looks too complicated!

I tried to figure this out while it was in qualification. I couldn't. I suspect there is some kind of clever trick that I'm overlooking. That's the way these things usually work. When you hear the answer you slap your forehead and say: "Why didn't I think of that?"

I can do it in 19 minutes.

yes but it would be easier if you explained it better

1 and 2 go over together and then 1 brings the flashlight back across and 5 and 10 go over together and then 2 goes back and gets 1 and 1 and 2 go back across and it takes 17 minutes.

It is a bit clever see my above comment.

good explanation
That makes much more sense now.

I don't want to figure it all out but I know it can be done. If two are crossing together, you don't add their times together, it takes only as long as the slowest person. Like if A and B cross together, it only takes 10 minutes, not 15.

Cute bridge. lol

You think we have time for this? I have a gazillion errands to run in my on-line time.

yes I can

I love the bridge!

I'm really not intelligent.....I don't even understand the question.

Yes I can.

Very good of you msgman! You had your thinking cap on!

My 12 year old grandson had three similar questions given to him in school. He got two of them correct. I can't concentrate long enough to do the problems, they're for young folks. I apologize.

this is the answer
d and c cross together = 2 minutes
d comes back with the flashlight and gives it to a and b =1 minute
they cross ( 10 minutes) with the flashlight and hand it to c whose on the side and c returns (2 minutes) to get d with the flashlight and they cross (2 minutes)
2+1+10+2+2=17

Ah..........wha