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The game Empty and Divide consists of two bins each with a positive number of chips....

The game Empty and Divide consists of two bins each with a positive number of chips. To move, a player chooses a bin, eats all the chips in that bin and then redistributes the chips from the other bin so that the bins again have a positive number of chips. The game ends when neither player can move. In other words, the game ends when both bins have exactly 1 chip.

a) Find a nimber which is equivalent to a position of Empty and Divide with 4 chips in one bin and 5 in the other.

b) Find all winning moves from the sum of the game in Part (a) with a Nim game starting with two chips.

Math   Statistics-And-Probability   
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