2. You're facing your friend, Brenda, in a "candy-off" game involving a pile of 100 caramels and one peppermint patty. You LOVE peppermint patties. The game has the following rules: You and Brenda will take turns grabbing at least one and no more than five caramels from the candy pile in each turn. The person who removes the last caramel will also get the peppermint patty. Did I already say, "you love peppermint patties?" (a) Suppose Brenda lets you decide who goes first. There is a strategy to make sure you win the peppermint patty. What is it? (b) Does your strategy change if the pile of caramels starts with 102? How? (c) In part (a) what is the largest number of caramels that Brenda can take, assuming you play your strategy guaranteeing the peppermint patty?

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