UPDATE (5 September): Based on the answers I've been getting,
it seems I have not done too good a job at explaining the format I'm asking for,
from the solution. Consider, therefore, the image below.
This picture depicts a 3by2 chessboard, and on it (in red) the path of a rook. The rook begins at a2, moves to c2, then left to b2, down to b1, right to c1, left again to a1, and then up to a2 to complete its tour. This will be depicted in the solution as follows:
000201 050304The solution contains here 2 lines, each with 3 pairs of digits. This is because the board is 3by2. Each pair of digits corresponds to a square on the board. The value associated with each pair of digits, ranging from 00 to 05, gives the information of the move number on which the rook alights at that particular square: it begins at the 00 square, moves on to the 01 square, from there to the 02 square, etc.. I hope this clarifies the issue. This month's question comes from Yaron Gvili. More credits will be given on the solution page. Consider a rook traveling in legal rook moves across a standard 8x8 chessboard. We are interested in closed rook tours. That is, we are interested in a sequence of 64 consecutive moves made by the rook that visits every square on the board exactly once, and returns ultimately to the original position. The object this month is to find a path which can be taken by the rook that maximizes the total distance traveled. (For example, a move from "e1" to "e3" requires two units of distance to be traveled.) Uncharacteristically for Using your Head is Permitted, this month no proof of optimality is required. (However, if you send in a proof, you will get an asterisk next to your name.) To be considered a solver, please send in your proposed rook tour in the following format. Send in 8 lines of text, each with 8 consecutive pairs of digits. Each pair denotes a position on the board, and the value of the twodigit number should be a value between 0 and 63, denoting at which move the rook traveled to this board position. For example, if the question was asked for a 2x2 board, one solution would have been 0001 0302indicating that the rook started at "a2", moved to "b2", down to "b1", left to "a1" and then closed the tour by moving back to "a2", where these positions are as indicated on the board below.

List of solvers:Harald Bögeholz (3 September 17:41)Dieter Beckerle (3 September 18:14) Daniel Bitin (4 September 05:42) Dan Dima (6 September 22:52) Lorenz Reichel (*) (7 September 05:38) RaduAlexandru Todor (8 September 12:07) Stefanie Homberger (9 September 20:59) Kan Shen (14 September 07:16) Andreas Stiller (20 September 16:07) Dharmadeep Muppalla (30 September 05:04) Rohan Joshi (1 October 07:44) 
Elegant and original solutions can be submitted to the puzzlemaster at riddlesbrand.scso.com. Names of solvers will be posted on this page. Notify if you don't want your name to be mentioned.
The solution will be published at the end of the month.
Enjoy!