A Candy Lover Learns to Optimize

Abstract

A container has two types of candies: Type A and Type B. Concerned about her child's well-being, a wise mom pronounces, “Each day, you can choose two candies from the container random. If they are of different types, you can eat them both. If they are of the same type, eat only one and return the other to the container.” We analyze the expected number of days needed to eat all candies in the container and the proportion of days the child eats two candies. Several other variations are either worked out or left for readers to solve.