Cookie Monster Devours Naccis
Leigh Marie Braswell, Tanya Khovanova
TL;DR
This paper investigates the minimal number of moves needed for Cookie Monster to empty jars with various cookie distributions, providing bounds and exact values for sequences like Fibonacci and Tribonacci.
Contribution
It introduces the Cookie Monster number concept and explicitly computes it for Fibonacci, Tribonacci, and other nacci sequences, expanding understanding of this problem.
Findings
Bounds established for the Cookie Monster number
Exact values computed for Fibonacci and Tribonacci sequences
Analysis of the problem for nacci sequences
Abstract
In 2002, Cookie Monster appeared in The Inquisitive Problem Solver. The hungry 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 Cookie Monster number is the minimum number of moves Cookie Monster must use to empty all of the jars. This number depends on the initial distribution of cookies in the jars. We discuss bounds of the Cookie Monster number and explicitly find the Cookie Monster number for Fibonacci, Tribonacci and other nacci sequences.
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