A crippled rook can move on a chessboard in the following way: from a square, it can move to an adjacent square sharing a common side, and every two consecutive moves must be at right angles (i.e., the rook makes a \(90^\circ\) turn at every move).
A cycle is a sequence of squares which start and end at the same square, and traces out a valid path that the crippled rook can move according to the rules above. A non-intersecting cycle consists of pairwise distinct squares, with the sole exception of the starting and ending square.
What is the length of the longest possible cyclic, non-intersecting route of a crippled rook on a \(15 \times 15\) chessboard?
This problem is shared by Aman R.. It was created by Michal Rolinek.
Details and assumptions
The length of the route is the number of squares that the rook travels on.