In a top security prison, BigBang, there is a tradition that any inmate can obtain freedom by passing through a 100m-long corridor without being caught by a blind guard. The corridor has nine 10m-long perpendicular branches on one side at every 10m and is so narrow, that only one person can pass at a time.

The inmate and the guard start walking toward each other from the opposite ends of the corridor at the same time. The guard may decide to check any of the side branches. The only rule is that the inmate has to maintain the same speed as the guard's at every moment.

Is it possible to get lucky and escape from BigBang?

Prisoner _|_|_|_|_|_|_|_|_|_ Guard

(In reply to Trivial Solution by Joe)

If the prisoner must walk the whole segment at one time, then Charlie's solution is right. Also, trivial solutions such as not passing a corridor or not moving at all exist, but other than that, there is a strategy to pass the guard. The prisoner should walk in the hallway towards the guard and stop if/when the guard is in the hallway, the prisoner is next to a side corridor, and the prisoner is two spaces or less from the guard. Then:

a) Go into a side corridor and hope the guard passes by
b) Backtrack until the guard goes into a side corridor himself, then go forward trying to pass him by.
c) Backtrack completely and give up

After a) or b), and the corridors are empty, the prisoner should check to see if he is closer or further to the exit than the guard. Of course if he is closer to the exit than the guard is, he will make it out. If he comes out of the corridor before the guard passes by (which may be preventable if he can see the guard pass) or the guard surprises him by coming out of the corridor early, he simply has to backtrack until he wishes to duck into a corridor (hence choice a) or the guard ducks into a corridor (choice b). If the guard chases and captures the prisoner in a corridor or comes out at a moment close enough to capture the prisoner, then the prisoner is out of luck.

The choice between options depends on how likely guard is to go into a corridor, and the probability of how the guard is likely to go in before turning around

Posted by Gamer on 2007-02-05 18:55:45