Mathematics
Mathematics, 07.08.2019 03:10, Gillo34

Consider the game of up-and-down rooks played on a standard chess- board. player i has a set of white rooks initially located in the bottom row, while player ii has a set of black rooks in the top row. in each turn, a player moves one of its rooks up or down a column, without skipping over the other rook or occupying its position. the first player who cannot move loses. this game is not progressively bounded, yet an optimal strategy exists. find such a strategy by relating this game to a nim position with 8 piles.

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Consider the game of up-and-down rooks played on a standard chess- board. player i has a set of whit...

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