# Crossing the Bridge Puzzle

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Four people need to cross a rickety bridge at night. Unfortunately, they have only one torch and the bridge is too dangerous to cross without one. The bridge is only strong enough to support two people at a time. Not all people take the same time to cross the bridge. Times for each person: 1 min, 2 mins, 7 mins and 10 mins. What is the shortest time needed for all four of them to cross the bridge?

vipin Scholar Asked on 26th July 2015 in
on 26th July 2015.

A and B cross first using up 2 minutes.
A comes back making it 3
C and D cross making it 13 minutes
then B crosses back over making it 15 minutes.
And finally A and B cross together to make it 17 minutes!

SherlockHolmes Expert Answered on 4th September 2015.

First Assume that A takes 1 min., B takes 2 min, C takes 5 min and D takes 10 min.

First A & B cross the bridge and they took 2 min
A returned and he took 1 min.
C & D cross the bridge and they took 10 min.
B returned and he took 2 min.
A & B cross the bridge they took 2 min.

Therefore, The shortest time is 17 min.

John Shepherd Starter Answered on 5th December 2015.

Assumption: A person carrying the torch illuminates the whole bridge.

Representation:

b2 – destination end
b1 – starting end

people – p1 p2 p7 p10 (number denotes time taken for crossing)

Solution: 13 mins.

At t = 0 min,

p1, p2 start journey to cross towards b2 from b1 (p1 has the torch)

At t = 1 min,

p1 reaches b2 and starts back towards b1. (has the torch)
p2 in bridge (1 min)

At t = 2 mins,

p2 reaches b2.
p1 reaches back to b1.
p7, p10 start towards b2. (p7 has the torch)

At t = 9 mins,

p2 in b2
p7 reaches b2
p10 in bridge (7 mins into the journey)

p2 starts towards b1 (has the torch)

At t = 11 mins,

p7 in b2
p10 in bridge(9 mins)
p2 reaches b1
p1 in b1

p2 starts towards b2 (has the torch)

At t = 12 mins,

p7 in b2
p10 reaches b2
p2 in bridge (1 min) (has the torch)
p1 starts towards b2

At t = 13 mins,

all reach b2.

blackholer Starter Answered on 11th January 2017.

Assumption: – If two person walks together they will move according to the person walking slower than the other one because of torch constraint.

A – 1 min
B – 2 min
C – 7 min
D – 10 min

First send C & D : time taken – 10 min

Send A to get the torch and bring it back : time taken – 2 min (to & fro)

Now A & B can go together : time taken- 2

Total time – 10 + 2 + 2  = 14min

tusharsinghsoam Starter Answered on 28th September 2016.

A would not be Able to go to bring the torch in complete DARK without torch

on 29th September 2016.

Yeah…I missed that part
Thanx 🙂

17 mins is the right answer.

on 29th September 2016.

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