Brain Teasers

The U2 teaser

This is an actual test given by a leading software development company to prospective employees:

U2 (a music group) have 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 etc..

Each band member walks at a different speed. A pair must walk together at the rate of the slower man's pace:-

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.

Notes:- There is no trick behind this. It is the simple movement of resources in the appropriate order. There are two known answers to this problem.

Please do not bother to send me email asking for a solution to this problem. I have a policy not to reveal solutions to my teasors. This is to let everyone have fun. Many people asked for a solution and after I turned them down came up with the solution themselves. If you get to the solution I can certainly verify it. But I havnt got any such requests because once you have the answer you know it is right.

The three prisoner problem

If you think your probability fundes are clear, test them on this problem:

A prison warden has randomly picked one prisoner among three to go free. The other two would be executed. The gaurd knows which one will go free but is forbidden to give any prisoner information regarding her status. Let us call the prisoners X, Y and Z. Prisoner X asks the gaurd privately which of Y or Z will be executed, arguing that since she already knows that at least one of them must die, the gaurd won't be revealing any informartion about her own status. The gaurd tells X that Y is to be executed. Prisoner X feels happier now, since she figures that either she or prisoner Z will go free, which means that her probability of going free is now 1/2. Is she right, or are her chances still 1/3? Explain.