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You can catch up to the trespasser.
Go to G. If trespasser is at C, go to D. When the trespasser is at B, go in the sequence A, I, and F. The trespasser will be trapped in room H.
In order to determine the outcome of any given mansion, let me first define "dead-end" rooms. Dead-end rooms are rooms like H where the trespasser can be trapped if you are in the correct room (ie F). It is easy to see that if there are no dead-end rooms, then the trespasser can evade you indefinitely.
If there exists a dead-end room, there is no reason for the trespasser to ever enter it, except to delay the inevitable. F, one of the rooms that makes H into a dead-end, is always an equal or better alternative, because F has the same options for movement and more. The only time that the the trespassing ghost might move to H rather than F is if F can be attacked the next turn, while H can't. But if the trespasser moves to H for this reason, you can move to F and trap him the next turn.
Since there is always an equal or better alternative for either ghost than to move into a dead-end room, the dead end room can be eliminated, leaving a mansion with an equivalent outcome. Therefore, one by one, the dead-end rooms are eliminated, until there are none left to eliminate. If there is more than one room left, the trespasser can evade indefinitely. If there is only one room left, you can catch him.
As an example on how to use this method, your mansion's rooms can be eliminated in the following order (the order is not unique): H, F, B, C, A, D, E, I, J, leaving only G.
Bob Smith also has an interesting method that can be generalized to any mansion here. |
