Browsing by Subject "recursive relation"

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    A Candy Lover Learns to Optimize
    (University of Regina, 2023-03) Do, Anh Phuong; Rashid, Mamunur; Sarkar, Jyotirmoy; Mathematical Sciences, School of Science
    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.
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    Counting Candy Sequences
    (Springer Nature, 2023-05) Sarkar, Jyotirmoy; Mathematical Sciences, School of Science
    A bottle contains 7 Type A and 7 Type B candies. Each morning, you select two candies at random: If they are of opposite types, eat them both; otherwise, eat one and return the other to the bottle. Continue until all candies are eaten. If ever the bottle contains only one candy, select and eat it. How many distinct candy sequences are possible?