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

I made the assumption to consider the 10m as a unit, thereby there could be no partial backtracking; the prisoner and/or guard have to be at the entrance of a side branch or at the end of it. 

There are 28 units within the puzzle.  If one deviates down a side corridor they emerge with an even number of units to traverse.  It the other does the same that margin will still be even.

At some time they must halve that even difference and so meet.

Now, if the corridor was 90m long, with 8 10m side passages, the prisoner, with a little thought, has a very good chance.

Posted by brianjn on 2007-02-05 22:08:33