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February 9, 2009

Bridge crossing problem

A group of four people has to cross a bridge. It is dark,
and they have to light the path with a flashlight.
No more than two people can cross the bridge simultaneously,
and the group has only one flashlight. It takes different
time for the people in the group to cross the bridge.
When two people together goes through the bridge,
the time taken by them to cross the bridge is the time taken
by the person with highest crossing time:

A crosses the bridge in 1 minute,
B crosses the bridge in 2 minutes,
C the bridge in 5 minutes,
D crosses the bridge in 10 minutes.

What is the minimum time in which they can cross the bridge.........???

Give with explanation.......!!!!!!!!


Sajal said...

can u plz solve this
i dont think that it has any logic

Secret Squïrrel said...

Ok. The people have to travel across in pairs (because the bridge is rickety or whatever) but as they only have one light source, one person must bring it back with them, leaving the other on the far side of the bridge (obviously it's too far/risky to throw it back). The limiting factor is that each pair must travel at the speed of the slowest member, so if A and C cross, it will take them 5 mins even tho' A can move faster. However, if A returns with the torch, it will only take them 1 min to come back.

I've done this one before so I'm going to let you have another think about it if you like.

Ashish said...

19 minutes

Secret Squïrrel said...

You can do better!

Secret Squïrrel said...

Ok, here's the answer; 17 minutes.

The trick is to not have C and D cross separately as that is already 15 minutes.

A & B cross  + 2 =   2 min
A returns     + 1 =   3
C & D cross +10 = 13
B returns     + 2 = 15
A & B cross  + 2 = 17 minutes

Anonymous said...


A&B cross +2= 2 min
A returns +1= 3 min
A&C cross +5= 6 min
A returns +1= 7 min
A&D cross +10= 17 minutes total

same answer different explanation

Secret Squïrrel said...

Nope - 3+5=8 not 6! That's the 19 minute method. C and D must cross together.

Babu vincent said...

A 1 minute,B 2 minutes,C 5 minutes,
D 10 minutes.

trip1 - A+B =2
'B' return with flash light=2

trip2 - C+D =10
'A' return with flash light=1

trip3 - A+B =2

17 minutes

dorin said...

it takes 10 minutes
D goes first with the flashlight and lights the way for the others: A, B and C (1+2+5=8)