Crossing the Bridge Puzzle
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?
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!
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.
Assumption: A person carrying the torch illuminates the whole bridge.
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.
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
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