A token is placed in one square of a m×n board, and is moved according to the following rules:
[*]In each turn, the token can be moved to a square sharing a side with the one currently occupied.[*]The token cannot be placed in a square that has already been occupied. [*]Any two consecutive moves cannot have the same direction.The game ends when the token cannot be moved. Determine the values of m and n for which, by placing the token in some square, all the squares of the board will have been occupied in the end of the game. combinatorics proposedcombinatorics