Chocolate Numbers

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Ji, Caleb ; Khovanova, Tanya ; Park, Robin ; Song, Angela (2015)
  • Subject: Mathematics - Combinatorics | 11B99

In this paper, we consider a game played on a rectangular $m \times n$ 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... View more
  • References (9)

    [1] M. H. Albert, R. J. Nowakowski, and D. Wolfe, Lessons in Play: An Introduction to Combinatorial Game Theory, A K Peters/CRC Press, 2007.

    [2] W. N. Bailey, Generalized Hypergeometric Series, Cambridge, 1935.

    [3] E. R. Berlekamp, J. H. Conway, and R. K. Guy, Winning Ways for Your Mathematical Plays, Volume 1, Taylor and Francis, 2001.

    [4] G. H. Hardy, E. M. Wright, An Introduction to the Theory of Numbers, Oxford University Press, 6th edition, 2008.

    [5] E. L. Ince, Ordinary Di erential Equations, Dover Publications, 1956. [1926]

    [6] J. G. Propp, Games of No Strategy and Low-Grade Combinatorics, http://faculty.uml.edu/jpropp/moves15.pdf

    [7] A. N. Siegel, Combinatorial Game Theory, American Mathematical Society, 2013.

    [8] H. S. Wilf, generatingfunctionology, A K Peters, 2006.

    2010 Mathematics Subject Classi cation: Primary 11B99.

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