Rules for folding polyminoes from one level to two levels

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Polyominoes have been the focus of many recreational and research investigations. In this article, the authors investigate whether a paper cutout of a polyomino can be folded to produce a second polyomino in the same shape as the original, but now with two layers of paper. For the folding, only “corner folds” and “half edge cuts” are allowed, unless the polyomino forms a closed loop, in which case one is allowed to completely cut two squares in the polyomino apart. With this set of allowable moves, the authors present algorithms for folding different types of polyominoes and prove that certain polyominoes can successfully be folded to two layers. The authors also establish that other polyominoes cannot be folded to two layers if only these moves are allowed.


  • [1] Brzustowski, J. "Can you win at Tetris?", Master's thesis, The University of British Columbia, Canada, March 1992.

  • [2] Burgiel, H. "How to Lose at Tetris", The Mathematical Gazette, 81(491), 194-200, July 1997.

  • [3] Frederickson, G. N. Dissections: Plane & Fancy. Cambridge University Press, 1997.

  • [4] Frederickson, G. N. "Folding Polyominoes from One Level to Two", The College Math Journal, 42(4), 265-274, September 2011.

  • [5] Golomb, S. W. Polyominoes: Puzzles, Patterns, Problems, and Packings, Princeton University Press, 1994.

  • [6] Martin, G. E. Polyominoes: A guide to puzzles and problems in tiling, The Mathematical Association of America, 1987.

Journal Information

Mathematical Citation Quotient (MCQ) 2016: 0.05

Target Group

researchers in the fields of games and puzzles, problems, mathmagic, mathematics and arts, math and fun with algorithms


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