Taboo: You can press the elevator button if and only if no elevator is moving down.
Is there a finite sequence of moves that allows you to ride in elevator e?
Taboo: You can press the elevator button if and only if no elevator is moving down.
Is there a finite sequence of moves that allows you to ride in elevator e?
Goal: Suppose you want to use elevator e (for some fixed e=1, 2, ..., n).
Move: If you press the button and an elevator other than elevator e arrives, you can tell it to go to any floor you wish.
Goal: Suppose you want to use elevator e (for some fixed e=1, 2, ..., n).
Move: If you press the button and an elevator other than elevator e arrives, you can tell it to go to any floor you wish.
The way the elevator logic works is this: when you press the elevator button, the one closest to you (= one on floor number min(fk, k>0)) is told to go to 0. If there is a tie then, of those on the same lowest floor, the elevator with the smallest index is told to go to 0.
The way the elevator logic works is this: when you press the elevator button, the one closest to you (= one on floor number min(fk, k>0)) is told to go to 0. If there is a tie then, of those on the same lowest floor, the elevator with the smallest index is told to go to 0.
You are on the bottom floor (floor 0, lets call it) of an apartment building with no basement. There are n elevators, which we index 1,2,...,n. Assume the elevators are initially on floors f1, f2, ... , where fk>0 is the floor elevator k is currently on, 1<=k<=n.
You are on the bottom floor (floor 0, lets call it) of an apartment building with no basement. There are n elevators, which we index 1,2,...,n. Assume the elevators are initially on floors f1, f2, ... , where fk>0 is the floor elevator k is currently on, 1<=k<=n.
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