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

Say it takes the guard, and therefore the prisoner, 1 unit of time to go along one segment of corridor or branche (10 meters). As the guard slows down, speeds up or even stops, this will vary according to clock time, but it defines guard time.

There are 9 side branches. Number the intersections where the branches meet the main corridor 1 - 9 from left to right.  The prisoner will arrive at any given odd numbered intersection after an odd number of units of time, regardless of any backtracks or excursions along the side branches. As the guard starts toward intersection 9, he will also arrive at odd intersections after an odd interval of time from the start.

In order for the prisoner to pass the guard unnoticed, the prisoner must be one unit away from the guard at a specific time, so the prisoner can go toward where the guard was at the beginning of the interval while the guard goes down a side branch, and continue on the main corridor while the guard returns. But note that this entails the guard and the prisoner being 1 unit away on the main corridor simultaneously.  But this can't be, as both the prisoner and the guard are to be on the same parity (odd or even) at any given time.

So the prisonor cannot get lucky and escape.

Posted by Charlie on 2007-02-05 14:35:14