Question: Consider a candy maker. The candy maker maintains an inventory of sweets consisting of chocolates, candies, and gummies. The candy maker starts out with an

Consider a candy maker. The candy maker maintains an inventory of sweets consisting of chocolates, candies, and gummies. The candy maker starts out with an empty inventory. At every step, the candy maker can update the inventory by one of the following steps: - Make one chocolate. - Trade two chocolates for two gummies and one candy. - Trade two candies for one gummy and one chocolate.

Prove (by induction) that the candy maker will always have at least as many gummies as candies. Show all the steps. Written responses only. Explain the steps.

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