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Question: 1 a rook chess piece is placed on the upper...

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(1) A rook chess piece is placed on the upper right hand corner of an mxn grid (see for instance the example of a 5 x 9 grid below). In the lower left hand corner of the grid there is a death trap death trap> Players alternate in turns by moving the chess piece either some (greater than 0) number of spaces to the left or some number of spaces down always closer to the death trap. The person who moves the rook piece onto the space with the death trap loses. For which values of m and n does the first player have a winning strategy in the game? For which values of m and n does the second player have a winning strategy in the game? . Generalize the game to three dimensional chess board with m × n × k pieces and determine when the first player has a winning strategy.
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