Rooks Puzzle

A peaceful rook moves on a chessboard like a rook, except that when he comes to another piece, he stops just in front of it (instead of capturing it). Moreover, such rooks always move as far as they can along any row and column (until blocked; if they do not run into a blocker, they fall off the end of the board).

Starting from the configuration of 7 rooks on a 7x7 board shown, find a sequence of moves that moves the rook in the upper left (shown as a red "A") to the empty square in the center.

The trick is to keep the "A" in play (not boxed in) while moving the other rooks around.  If it weren't for the need to move "A" into the center -- that is, if I could move any old rook into the center -- then it could be done in 13 moves.  But since it's A that has to move, it takes 15 moves.  I'm not sure this is the only solution, or even if it can be done in fewer than 15 moves.  Here it is:

Related pages in this website

The webmaster and author of the Math Help site is Graeme McRae.
     [home]  [email]  [search]  [Links to Math Sites]  [Whiteboard]