Bridge Over Troubled Students
There are four men who want to cross a bridge. They all begin on the same side. You have 17 minutes to get all of them across to the other side. It is night. There is one flashlight. A maximum of two people can cross at one time. Any party who crosses, either one or two people, must have the flashlight with them. The flashlight must be walked back and forth, it cannot be thrown, etc. Each man walks at a different speed. A pair must walk together at the rate of the slower man
Man 1: 1 minute to cross
Man 2: 2 minutes to cross
Man 3: 5 minutes to cross
Man 4: 10 minutes to cross
For example, if Man 1 and Man 4 walk across first, 10 minutes have elapsed when they get to the other side of the bridge. If Man 4 returns with the flashlight, a total of 20 minutes have passed, and you have failed the mission.
Communicated by Jeff Miller.
so glad to hear. once you send a correct soln I’m happy to send the password to the student/teacher corner, which has supplemental material.
I love using these riddles with my students.
Yes. I keep it hidden as it’s valuable to work on the problems first and if there are posted solutions often the temptation is too great…. If you are a teacher, once you solve a problem I’m happy to give you access to the student/teacher corner, which has discussions on how to use these in classes.
Is there an answer key? Thanks
Once you solve a problem email me at [email protected] (or email me for a hint). I’ll then provide, if you wish, the password for the student/teacher corner, which has a lot of aids to use these in classes.
Hi I’m a homeschool teacher. Amy I please have the solution to this problem?
email me at [email protected] for a hint
what is the answer
Please write in English
Sure — drop me an email ([email protected]), but I think this comment was meant for a different riddle.
Thank you for the problem and its solution which I noticed on the comment column. Could you please tell me how to connect to binomial expansion or any algebraic expression.
Thanks
you eventually realize there are a few very popular problems with many
variants!
We have a classic problem for children similar to this, in India. It goes like this- a man has to ferry a tiger, a goat and a bundle of hay across a river. He can ferry only one at a time, or the boat would sink. He can’t leave the goat and the tiger together and take the hay, or the tiger would eat the goat. Also , the hay and the goat can’t be left in a bank alone. How would he ferry all three? Children love this one.
yes
do you also add the time it takes for man x to get back across w/the flashlight?
yes
Do all four have to end on the other side?
[email protected]: your email doesn’t work, your soln is correct.
nope — must go all the way
We are really enjoying these but we are stuck here, is there a way to go part of the way across without the flashlight?
email to you bounced – email me at sjm1 AT williams.edu
plz tell me the ans i can’t figue it out and i want to ask my friends. i can’t ask them without knowing the ans
anonymous: correct (sjm1 at williams.edu)
I’ll send a hint
This is really confusing!!!
the flashlight is very weak and only works if you’re right next to it. //s
The key to this riddle (to me) is the following statement: ‘Any party who crosses, either one or two people, must have the flashlight with them’.
Answer:
First, 4 and 3 cross the bridge. Then, 4 takes the flashlight to go get 1. However, while 4 is crossing to get 1, 1 is walking towards 4 (this is allowed because the stem states that the flashlight must be with one of them, not that they must be right next to each other) and then 1 walks 4 towards the other end (i.e., towards 3). Once, 1 walks 4 to the other side of the bridge, he (man 1) takes the flashlight and walks towards 2, while 2 walks towards 1. When they meet, 2 and 1 walk towards the end of the bridge. This process takes roughly 13 minutes.
Ritish: correct (and correct on other one); not posting as these are the solns
let me send a hint first ..s
what is the answer to bridge over troubled students and how do you work it out
email me at sjm1 AT williams.edu — tried emailing y ou but it bounced. //s
wow this is a very hard solution… wish i do really know the answer lol this is pretty HARD
But this takes 20 minutes — there’s a way to do it in 17. Email me at sjm1 AT williams.edu if you want to chat more. //s
1&4 – 10
1 – 11
2&3 – 16
2 – 18
1&2 – 20
Didn’t think I could do that.
email me at [email protected] for a hint ..s
im confused
yes, but there’s a way to do it in just 17 minutes! email me at [email protected] if you want a hint.
easy, i think
man one 1 min
man two 2 min
man three 5 min
man four 10 min
1 and 2 go, 2 min
1 comes back, 1 min
1 and 3 go, 5 min
1 comes back, 1 min
1 and 4 go, 10 min
in total=19 minutes!!!
nope, but your second attempt was correct (not posting as its the soln)
first number 2 and 5 (5min) number 2 come back (7min)he take number 1 (9min)
number 1 come back (10min) he take number 4 (2omin)
hahhahaha
you can do it with binomial coefficients, but this isn’t the right approach (though the answer happens to be close…).
To: Anonymous: Submitted on 2012/01/12 at 2:02 am: Correct, well done! Not posting as it’s the soln.
1 and 2 go…1 comes back…5 and 10 go…2 comes back…1 and 2 go again. 17!
J-crew: correct, well done. not posting as it’s the soln. (You can also email solns to be at [email protected]). //s
unknown (72.45.58.222 Submitted on 2011/12/18 at 2:16 pm): well done, not posting as this is the soln
You have the wrong values — the third person takes 5 minutes to go over, the fourth takes 10. This gives a total time of 19 minutes I believe.
Man 1 and 2 go across = 2minutes
Man 1 goes back across = 3minutes
Man 1 and 3 go across = 5minutes
Man 1 goes back across = 6minutes
Man 1 and 4 go across = 16minutes
Everyone is across in 16 minutes
there’s actually two solutions, but they’re essentially the same
it took me a while before i got it
email me at [email protected] if you want a hint. ..s
Oh wait… I just found out how to do it in 18 minutes… but I still can’t figure out how to do it in 17 minutes!
I found out how to do it in 19 minutes… this one is difficult.
I’ll email you a hint
It takes 20 minutes! Ok….how do youdo this one?
to Anonymous
123.238.226.142
Submitted on 2011/10/30 at 5:03 am
CORRECT, WELL DONE! Not posting as it’s the soln.
Email me for a hint/soln
still can not find the answer
To Kofi (posted on 2011/09/23 at 12:03 pm): correct!
Man 1 and Man 2 go 2mins
Man 1 returns 1min
Man 3 and Man 4 go 10min
Man 2 returns 2mins
Man 1 and Man 2 go 2mins
Gives total of 17mins
Hint: 5 and 10 need to walk together….
as of i know, it takes 19 mins to cross… how is it possible within 17 mins
Glad you enjoyed it. //s
that’s so awesome article , thank you 🙂
Correct answer! You could also switch who comes back first. I normally don’t post answers as then others see the answers, and when answers are online people tend to go to them first without the joy of trying the riddle. You can always send me answers at sjm1 AT williams.edu.
For which riddle? Sorry for the delay in answering — the system hadn’t told me there was an attempted post! My email is sjm1 AT williams.edu
Usually not as then people will be able to see the answer, and that removes a lot of the fun.