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The Mathematics of Various Entertaining SubjectsResearch in Recreational Math$
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Jennifer Beineke and Jason Rosenhouse

Print publication date: 2015

Print ISBN-13: 9780691164038

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691164038.001.0001

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The Cookie Monster Problem

The Cookie Monster Problem

Chapter:
(p.231) 16 The Cookie Monster Problem
Source:
The Mathematics of Various Entertaining Subjects
Author(s):

Leigh Marie Braswell

Tanya Khovanova

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691164038.003.0016

This chapter examines the problem of the “Cookie Monster number.” In 2002, Cookie Monster® appeared in the book The Inquisitive Problem Solver by Vaderlind, Guy, and Larson, where the hungry monster wants to empty a set of jars filled with various numbers of cookies. The Cookie Monster number is the minimum number of moves Cookie Monster must use to empty all the jars. The chapter analyzes this problem by first introducing known general algorithms and known bounds for the Cookie Monster number. It then explicitly finds the Cookie Monster number for jars containing cookies in the Fibonacci, Tribonacci, n-nacci, and Super-n-nacci sequences. The chapter also constructs sequences of k jars such that their Cookie Monster numbers are asymptotically rk, where r is any real number, 0 ≤ r ≤ 1.

Keywords:   Cookie Monster, Cookie Monster number, Fibonacci sequence, Tribonacci sequence, n-nacci sequence, Super-n-nacci sequence, algorithms, cookies

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