Friday, April 11, 2014

The U2 riddle

Problem : 

U2 has a concert that starts in 17 minutes and they must all cross a bridge to get there. All four men begin on the same side of the bridge. You must help 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 1 or 2 people, must have the flashlight with them. 

The flashlight must be walked back and forth. It cannot be thrown and other tricks like that are not needed to solve the problem. The solution is simply a matter of allocating resources in a certain order. Each band member walks at a different speed. A pair must walk together at the rate of the slower man's pace: 

Bono: 1 minute to cross
Edge: 2 minutes to cross
Adam: 5 minutes to cross
Larry: 10 minutes to cross
For example
if Bono and Larry walk across first, 10 minutes have elapsed when they get to the other side of the bridge. If Larry then returns with the flashlight, a total of 20 minutes have passed and you have failed the mission. 


Let’s name the as A,B,C & D and let’s assume that they take 1,2,5 and 10 minutes respectively. Here is how they should cross the bridge. 
ABCD |—————————–-------|
CD     |——-AB(2min)————->| ( AB comes and A returns)
ACD   |<——-A-(1min)————--|B
A       || ——-CD(10min)———>| BCD  (CD come and B returns)
A ||    |<——-B-(2min)————--|
AB     |—————————–-------|ABCD  (AB come)
If you count all the trips ie. 2+1+10+2+2, it will be 17 minutes



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