# Crippled Rook

**Discrete Mathematics**Level pending

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.