The Bear Creek School
Redmond, WA 98053
Department of Mathematics
Cambridge, MA 02139
Thomas Jefferson High School for Science and Technology
Alexandria, VA 22312
Phillips Exeter Academy
Exeter, NH 03833
In this paper, we consider a game played on a rectangular
m × n gridded
chocolate bar. Each move, a player breaks the bar along a grid line.
Each move after that consists of taking any piece of chocolate and
breaking it again along existing grid lines, until just
This paper enumerates the number of ways to break an
m × n bar, which we
call chocolate numbers, and introduces four new sequences related to
chocolate numbers. Using various techniques, we prove interesting
divisibility results regarding chocolate number sequences.
Full version: pdf,
(Concerned with sequences
Received September 21 2015; revised versions received November 29 2015; December 26 2015.
Published in Journal of Integer Sequences, December 29 2015.
Journal of Integer Sequences home page