Cram with Square Polyominoes

Authors

  • Michael Fraboni Moravian University
  • Emma Miller Moravian University

DOI:

https://doi.org/10.33043/2NzN6BBENQ

Abstract

We will consider expansions of CRAM, a game frequently studied in the area of combinatorial game theory. The game of CRAM is classically played with dominoes, a type of polyomino. We will define CRAM WITH HIGHER POLYOMINOES and use efficient packing results to establish the outcome classes for several board shapes and choices of polyominoes.

Author Biographies

Michael Fraboni, Moravian University

Michael Fraboni is a professor of mathematics at Moravian University. He is interested in involving undergraduates in meaningful research experiences on combinatorial game theory related topics.

Emma Miller, Moravian University

Emma Miller graduated from Moravian University in 2022 with a bachelor’s of science in physics and mathematics. This paper was grew from her senior honors thesis which focused on the expansion
of common combinatorial games. Emma is currently employed fulltime and is currently considering continuing her education in either mathematics or science management.

References

Michael Albert, Richard J. Nowakowski, and David Wolfe, Lessons in play, A K Peters/CRC Press, 2007.

Elwyn R. Berlekamp, John H. Conway, and Richard K. Guy, Winning ways for your mathematical plays, 2nd ed., Vol. 1, A K Peters/CRC Press, 2001.

Emma Miller, Gabrielle Demchak, Victoria Samuels, Jacob Freeh, and Jacob Smith, Fixed cram with higher polyominoes Unpublished Work (2021).

Emma Miller, Mitchel O’Connor, and Nathan Shank, Clumsy packing of polyominoes in finite space, arXiv, 2022.

Joseph O’Rourke, Jacob E. Goodman, and Csaba D. Tóth, Handbook of discrete and computational geometry, 3rd ed., Chapman and Hall/CRC, 2017.

Bill Sands, The gunpost problem, Mathematics Magazine 44 (1971), 193–196.

Stefan Walzer, Clumsy packings in the grid, Bachelor’s Thesis, Karlsruhe Institute of Technology (2012).

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Published

2026-03-03

How to Cite

Fraboni, M., & Miller, E. (2026). Cram with Square Polyominoes. Mathematics Exchange, 17(1), 39–48. https://doi.org/10.33043/2NzN6BBENQ

Issue

Vol. 17 No. 1 (2023): Mathematics Exchange, Fall 2023

Section

Articles

License

Copyright (c) 2026 Michael Fraboni, Emma Miller

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.