On the Cookie Monster Problem

• Published in 2013
• Added on 2016-05-19

The Cookie Monster Problem supposes that 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 Cookie Monster number of a set is the minimum number of moves the 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 jars containing cookies in the Fibonacci, Tribonacci, n-nacci, and Super-n-nacci sequences. We also construct sequences of k jars such that their Cookie Monster numbers are asymptotically rk, where r is any real number between 0 and 1 inclusive.

Links

• http://arxiv.org/abs/1309.5985v1
• http://arxiv.org/pdf/1309.5985v1

Other information

BibTeX entry

@article{OntheCookieMonsterProblem,
	key = {OntheCookieMonsterProblem},
	type = {article},
	title = {On the Cookie Monster Problem},
	author = {Leigh Marie Braswell and Tanya Khovanova},
	abstract = {The Cookie Monster Problem supposes that 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 Cookie Monster number of a set is the minimum number of moves
the 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 jars
containing cookies in the Fibonacci, Tribonacci, n-nacci, and Super-n-nacci
sequences. We also construct sequences of k jars such that their Cookie Monster
numbers are asymptotically rk, where r is any real number between 0 and 1
inclusive.},
	comment = {},
	date_added = {2016-05-19},
	date_published = {2013-12-07},
	urls = {http://arxiv.org/abs/1309.5985v1,http://arxiv.org/pdf/1309.5985v1},
	collections = {Puzzles,Animals,Food,Fibonaccinalia,Fun maths facts},
	url = {http://arxiv.org/abs/1309.5985v1 http://arxiv.org/pdf/1309.5985v1},
	urldate = {2016-05-19},
	archivePrefix = {arXiv},
	eprint = {1309.5985},
	primaryClass = {math.HO},
	year = 2013
}