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April 16, 2014

Homework Help: Math (please help Steve)

Posted by Nick on Wednesday, August 7, 2013 at 10:02pm.

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∘ 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 1515 chessboard?

Details and assumptions
The length of the route is the number of squares that the rook travels on.

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