Penny Game Rules: The game begins with a group of 10 pennies. Two players take turns making moves. On their move, a player takes either 1 or 2 pennies away from the group. The player who is forced to...

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Extracted text: Penny Game Rules: The game begins with a group of 10 pennies. Two players take turns making moves. On their move, a player takes either 1 or 2 pennies away from the group. The player who is forced to take the last penny loses the game. Suppose we play a version that starts with n in the pile, and where a player can take anywhere from 1 to r pennies on their turn. [Note that n and r are fixed before the game starts.] How can you tell which player has a winning strategy, based on the values of n and r? Thoroughly explain. Include a discussion of examples that you looked at.