Guide the rook

For discussing Olympiad Level Combinatorics problems
Nayeemul Islam Swad
Posts:22
Joined:Sat Dec 14, 2013 3:28 pm
Guide the rook

Unread post by Nayeemul Islam Swad » 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?
Why so SERIOUS?!??!

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asif e elahi
Posts:185
Joined:Mon Aug 05, 2013 12:36 pm
Location:Sylhet,Bangladesh

Re: Guide the rook

Unread post by asif e elahi » Fri Aug 05, 2016 8:26 pm

Hint:
Try to construct such a string.

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