The Rope Bridge

Four people need to cross a rickety rope bridge to get back to their camp at night. Unfortunately, they only have one flashlight and it only has enough light left for seventeen minutes. The bridge is too dangerous to cross without a flashlight, and it’s only strong enough to support two people at any given time.

Each of the campers walks at a different speed. One can cross the bridge in 1 minute, another in 2 minutes, the third in 5 minutes, and the slow poke takes 10 minutes to cross. How do the campers make it across in 17 minutes?

 

 

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Solution

To get everyone across in 17 minutes, we need the two slowest people to travel across together; otherwise we're wasting too much time. Once we
get them across, how do we not make one of them walk back with the flashlight? Just have one of the faster people already there waiting to


sprint the flashlight back across.
person A: 1 minute
person B: 2 minutes
person C: 5 minutes
person D:10 minutes

1. A & B cross. total time: 2 minutes.

C |--------------------------| A
D |                                       | B
   |--------------------------| flashlight

2. B comes back. total time: 4 minutes.

C |--------------------------| A
D |                                       |
B |--------------------------|
flashlight

3. C & D cross. total time: 14 minutes.

B |--------------------------| A
   |                                        | C
   |--------------------------| D
                                             flashlight

4. A comes back. total time: 15 minutes.

A |--------------------------| C
B |                                          | D
   |--------------------------|
flashlight

5. A & B cross. total time: 17 minutes.

|--------------------------| A
|                                             | B
|--------------------------| C D
                                               flashlight
 
Another valid solution is to have A bring the flashlight back in step 2.


Solution


Four people need to cross a rickety rope bridge to get back to their camp at night. Unfortunately, they only have one flashlight and it only has enough light left for seventeen minutes. The bridge is too dangerous to cross without a flashlight, and it’s only strong enough to support two people at any given time.

Each of the campers walks at a different speed. One can cross the bridge in 1 minute, another in 2 minutes, the third in 5 minutes, and the slow poke takes 10 minutes to cross. How do the campers make it across in 17 minutes?

Difficulty
  • Moderate
Type
  • Logic
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Comments

this solution is wrong. if B and A cross it will be a total time of 3mins not 2mins. then if B comes back then it will be a total time of 5 mins. then if C and D cross then just them two will be 15mins, add that onto the 5 mins and it will become 20mins. then if A crosses then it will be a total time of 21mins. and then if B and A cross it will be a total time of 24mins NOT 17MINS!!
- kitty (25 May 2009)

No you are wrong, they are walking together, remember they need to have the flashlight. The faster person will walk at the pace of the slower person. this solution is correct
- Tyler (18 Jun 2009)

Kitty you're not the smartest.
- jimbo (10 Oct 2009)

If you piggy back some one you can cut your time down tremendously, have the one minute guy(A) piggy back B, go back for C, then go back for D, total 5 minutes.
- chris (31 Jan 2010)

PS I understand that you were looking to do it 17 mins., but why not 5 mins. as a teaser.
- chris (31 Jan 2010)

i was gonna say have the 10 minute person cross the bridge and hold the flashlight while and then have the one minute go, then the two minute, and then the five minute go, so that while the 10 minute guy was on the bridge the whole time, the other guys were crossing one at a time and there were only 2 people on the bridge at any one time
- i3irdhousex23 (7 Mar 2010)

i was gonna say the same thing as 13irdhousex23

i was fully thinking, i go this one easy, then i wasnt right ahah
- lol um (16 Mar 2010)

hey chris, try carrying a guy that walks ten times slower than you at the same speed you can walk without a load.
- jim (28 Apr 2010)

well chris if 10 minutes go first the lighting source wont cover each person during his way may be just covers a small part but not whole distance still dangerous
- (17 May 2010)

you guys are wrong , just thinking of how to cross it would take much longer.

piggy back is wrong cause it's a rickety bridge, the weight of two people in a certain point will collapse the bridge.

sprinting is wrong too. the statement said that it's dangerous, then why sprint ? that's the whole point of having the flash light--to avoid danger!

the statement is also a WRONG ! if it's dangerous and it's night time , and it's not in the city, no one in their right mind would walk as slow as ten minutes if they wanted to get home alive.
If it's a rickety rope bridge , people will walk faster and be more careful. Just like in the highway, people drive faster their to cross it with less time, but they are also careful.

and sorry to say , its a rope bridge, not a maze. a bridge only goes one way. why not try to have two cross them and move on with the other two. and reserve the light for their way home.

If the camp is beside the bridge, people would have thought of replacing the rope for something much more sturdy. Or even help them get across or put up lights on the bridge.

If the flashlight has only 17 minutes to hold, then how would they walk home if they used it all up for crossing the bridge ? they crossed the bridge but they still can't walk home. Isn't that a funny scenario?

- BLUEheart (3 Jul 2010)

i say awesome :)

- (17 Aug 2011)

I really like it when men and women arrive jointly and share opinions, fantastic website, preserve it up.

- Diablo 3 (11 Sep 2011)

I suggest that they:
1) just huddle together right where they are at and cross slowly in the morning;
2) consider walking around the canyon in the morning;
3) use your cell to call AAA to bring a new set of batteries for the flashlight.

- Surviror123 (5 Dec 2012)

person d holds light and begins with a each walking at their own pace.when a finishes b begins at his pace. when he finishes c begins at her own pace. by the time d finishes c will have finished for 2 minuites
- sean (5 Jan 2014)

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