Counting Candy Sequences an Enumeration Problem
RESONANCE-JOURNAL OF SCIENCE EDUCATION（2023）
Abstract
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?
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Key words
Recursive relation,paths on a graph,Delannoy numbers,inner product,mathematical induction
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