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Summary
The Cookie Monster wants to empty a set of jars filled with various numbers of cookies. On each of his moves, he may choose any subset of jars and take the same number of cookies from each of those jars. The minimal number of moves to accomplish this depends on the initial distribution of cookies in the jars. We discuss bounds of these Cookie Monster numbers and explicitly find them for jars containing numbers of cookies in the Fibonacci, Tribonacci, and other nacci sequences.
Additional information
Notes on contributors
Leigh Marie Braswell
Leigh Braswell ([email protected]) is a senior at Phillips Exeter Academy and will be attending MIT next year. She is especially interested in combinatorics and mathematical puzzles. She also enjoys computer programming and ballet.
Tanya Khovanova
Tanya Khovanova ([email protected]) is a lecturer at MIT and a freelance mathematician. She received her Ph.D. in mathematics from Moscow State University in 1988 and has returned to research after some time in industry. Her current interests lie in recreational mathematics including puzzles, magic tricks, combinatorics, number theory, geometry, and probability theory. She writes the popular math blog blog.tanyakhovanova.com and mentors high school students interested in research. When not thinking about mathematics, she enjoys ballroom dancing. Actually, sometimes she thinks about math while dancing—and about dancing while solving problems.