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Challenge 273: Chessboard Freddy

Freddy the fly (see challenges 141, 147, 163, 244) has landed on a standard 8 x 8 chessboard that has been left lying around in the school canteen. Always one for a mathematical problem, Freddy wants to know if he can find a route from the square he has landed on to the nearest corner square. His route must have the following two properties: it must take him through every square on the chessboard and he may only move to another square by crossing the edge that is shared by the two squares involved.

Will Freddy be able to find a route like this? If so, give a way of determining such a route, but if not explain why not.

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