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Coins and Plates. You have n plates, each with one coin. There are two operations possible. Each operation costs you one coin. Promotion: You can pay a coin from plate i. Add two coins to plate i+1. Swap: You can pay one coin from plate i. Swap the coins in plates i+1 and i+2. Note that you pay from one plate, and do something to the next plate(s). Let c(n) be the maximum number of coins in plate n. (a) Prove that c(4)20. (b) Using part (a), if you wish, prove that c(5)300. (c) What have you managed to get for c(5) ? I can get over 800