Guide the rook
Posted: Fri Aug 05, 2016 6:47 pm
In a $n \times n$ board, there are some walls between adjacent squares, such that any two squares are still connected by a path not going through any wall. $A$ chooses a finite string of UP, DOWN, RIGHT, LEFT. A rook placed in some square of that board moves according to that string unless a wall or end of board is reached in which case it simply skips that move. Can $A$ choose such a string such that no matter where $B$ places the walls and the rook, the rook still visits every other square on that board following his string?